Publications/alpha-tlca.ps
author Christian Urban <christian dot urban at kcl dot ac dot uk>
Fri, 03 Jun 2016 11:08:09 +0100
changeset 445 8cee34f58582
parent 14 680070975206
permissions -rw-r--r--
updated
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%%Title: alpha-tlca.dvi
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%%Pages: 15
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% 
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% (1) the Windows ANSI characters are almost all in their Windows ANSI
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% fonts, and it makes no difference on other systems. The only Windows
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% irritation not having them in TeX positions.
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% 
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% (2) Remaining characters are assigned arbitrarily to the lower part
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%
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%
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%     PostScript      MacRoman        TeXBase1
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%     --------------  --------------  --------------
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%     /notequal       173             0x16
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%
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% 0x10
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% 0x20
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% 0x30
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% 0x40
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% 0x50
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% 0x60
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% 0x70
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% 0x80
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% 0xD0
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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  1093
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1101
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Christian Urban <urbanc@in.tum.de>
parents:
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  1102
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1103
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1105
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1401
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1402
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1403
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1404
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1405
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1406
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1407
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1408
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1409
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1410
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1411
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1412
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1413
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1414
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1415
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1416
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1417
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1418
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1419
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1420
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Christian Urban <urbanc@in.tum.de>
parents:
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  1421
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1422
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1423
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1424
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1425
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1426
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1427
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1428
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1429
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1430
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1431
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1432
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1433
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1434
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1435
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1436
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1437
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1438
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1439
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1440
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1441
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1442
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1443
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1444
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1445
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1446
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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%%CreationDate: 1992 Feb 19 19:56:16
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1460
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1465
/FullName (CMTI10) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1466
/FamilyName (Computer Modern) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1467
/Weight (Medium) readonly def
Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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/FontMatrix [0.001 0 0 0.001 0 0] readonly def
Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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dup 88 /X put
Christian Urban <urbanc@in.tum.de>
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dup 97 /a put
Christian Urban <urbanc@in.tum.de>
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dup 98 /b put
Christian Urban <urbanc@in.tum.de>
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dup 99 /c put
Christian Urban <urbanc@in.tum.de>
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dup 115 /s put
Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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  1489
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1490
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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  1492
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1493
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Christian Urban <urbanc@in.tum.de>
parents:
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  1494
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1495
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1496
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Christian Urban <urbanc@in.tum.de>
parents:
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  1497
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Christian Urban <urbanc@in.tum.de>
parents:
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  1498
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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  1501
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Christian Urban <urbanc@in.tum.de>
parents:
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  1502
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1503
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Christian Urban <urbanc@in.tum.de>
parents:
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  1504
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Christian Urban <urbanc@in.tum.de>
parents:
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  1505
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Christian Urban <urbanc@in.tum.de>
parents:
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  1506
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Christian Urban <urbanc@in.tum.de>
parents:
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  1507
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Christian Urban <urbanc@in.tum.de>
parents:
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  1508
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1509
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Christian Urban <urbanc@in.tum.de>
parents:
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  1510
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Christian Urban <urbanc@in.tum.de>
parents:
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  1511
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Christian Urban <urbanc@in.tum.de>
parents:
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  1512
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Christian Urban <urbanc@in.tum.de>
parents:
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  1513
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Christian Urban <urbanc@in.tum.de>
parents:
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  1514
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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  1517
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Christian Urban <urbanc@in.tum.de>
parents:
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  1518
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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  1521
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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  1528
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Christian Urban <urbanc@in.tum.de>
parents:
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  1529
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Christian Urban <urbanc@in.tum.de>
parents:
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  1530
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Christian Urban <urbanc@in.tum.de>
parents:
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  1531
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1532
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1533
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1534
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1535
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1536
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Christian Urban <urbanc@in.tum.de>
parents:
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  1847
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1848
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1849
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1850
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1851
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1852
38DD5C4467F9DD8C5D1A2000B3A6BF2F25629BAEC199AE8BD4BA6ED9BBF7DABF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1853
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1854
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1855
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1856
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1857
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1858
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1859
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1860
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1861
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1862
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1863
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1864
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1865
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1866
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1867
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1868
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1869
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1870
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1871
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1872
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1873
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1874
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1875
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1876
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1877
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1878
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1879
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1880
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1881
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1882
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1883
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1884
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1885
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1886
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1887
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1888
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Christian Urban <urbanc@in.tum.de>
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  1890
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Christian Urban <urbanc@in.tum.de>
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  1891
%!PS-AdobeFont-1.1: CMTT9 1.0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1892
%%CreationDate: 1991 Aug 20 16:46:24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1893
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1894
11 dict begin
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1895
/FontInfo 7 dict dup begin
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1896
/version (1.0) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1897
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1898
/FullName (CMTT9) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1899
/FamilyName (Computer Modern) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1900
/Weight (Medium) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1901
/ItalicAngle 0 def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1902
/isFixedPitch true def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1903
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Christian Urban <urbanc@in.tum.de>
parents:
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  1904
/FontName /CMTT9 def
Christian Urban <urbanc@in.tum.de>
parents:
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  1905
/PaintType 0 def
Christian Urban <urbanc@in.tum.de>
parents:
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  1906
/FontType 1 def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1907
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
Christian Urban <urbanc@in.tum.de>
parents:
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/Encoding 256 array
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1909
0 1 255 {1 index exch /.notdef put} for
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1910
dup 97 /a put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1911
dup 102 /f put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1912
dup 108 /l put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1913
dup 109 /m put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1914
dup 114 /r put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1915
dup 118 /v put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1916
readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1917
/FontBBox{-6 -233 542 698}readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1918
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1919
currentdict end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1920
currentfile eexec
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1921
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1922
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1923
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1924
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1925
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1926
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1927
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1928
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1929
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1930
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1931
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1932
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1933
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1934
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1935
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1936
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1937
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1938
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1939
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1940
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1941
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1942
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1943
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1944
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1945
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1946
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1947
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1948
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1949
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1950
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1951
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1952
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1953
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1954
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1955
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1956
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1957
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1958
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1959
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1960
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1961
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1962
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1963
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1964
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1965
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1966
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1967
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1968
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1969
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1970
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1971
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1972
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1973
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1974
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1975
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1976
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1977
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1978
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1979
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1980
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1981
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1982
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1983
0000000000000000000000000000000000000000000000000000000000000000
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1984
cleartomark
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1985
%%EndFont 
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1986
%%BeginFont: CMMI7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1987
%!PS-AdobeFont-1.1: CMMI7 1.100
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1988
%%CreationDate: 1996 Jul 23 07:53:53
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1989
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1990
11 dict begin
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1991
/FontInfo 7 dict dup begin
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1992
/version (1.100) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1993
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1994
/FullName (CMMI7) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1995
/FamilyName (Computer Modern) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1996
/Weight (Medium) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  1997
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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11 dict begin
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2136
/FontInfo 7 dict dup begin
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2137
/version (1.0) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2138
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2139
/FullName (CMSY9) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2140
/FamilyName (Computer Modern) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2141
/Weight (Medium) readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2142
/ItalicAngle -14.035 def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2143
/isFixedPitch false def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2144
end readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2145
/FontName /CMSY9 def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2146
/PaintType 0 def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2147
/FontType 1 def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2148
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2149
/Encoding 256 array
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2150
0 1 255 {1 index exch /.notdef put} for
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2151
dup 0 /minus put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2152
dup 14 /openbullet put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2153
dup 25 /approxequal put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2154
dup 27 /propersuperset put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2155
dup 33 /arrowright put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2156
dup 41 /arrowdblright put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2157
dup 50 /element put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2158
dup 54 /negationslash put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2159
dup 56 /universal put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2160
dup 62 /latticetop put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2161
dup 66 /B put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2162
dup 94 /logicaland put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2163
dup 95 /logicalor put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2164
dup 96 /turnstileleft put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2165
dup 102 /braceleft put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2166
dup 103 /braceright put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2167
dup 104 /angbracketleft put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2168
dup 105 /angbracketright put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2169
dup 106 /bar put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2170
dup 110 /backslash put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2171
dup 114 /nabla put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2172
readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2173
/FontBBox{-30 -958 1146 777}readonly def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2174
/UniqueID 5000819 def
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2175
currentdict end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2176
currentfile eexec
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2177
D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2178
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2179
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2180
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2181
221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2182
27D1663E0B62F461F6E40A5D6676D0037D33F24E2FAC2B0009AD3C8350CDF8CC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2183
65BCA87979C36D14CB552E9A985E48BE4E88ECA16DF418749AF04FDD2B0E1380
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2184
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2185
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2186
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2187
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2188
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2189
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2190
3291497B92172E1E0D19D43658E30217D218F235EE9781B2A7E9CE49610C6F64
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2191
4B9B235BEB128EF55B1AA406EFA2928B9826807C9E960A10EF9A0861A94F9F89
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2192
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2193
F04D222D2F6CBEA4424681F68DB5D831012AB70CF5598CA19426E9C84BB2ACF9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2194
A4C7F0A96D818520A297834CFE591111D2FDE3C3715EB49737BD331C778835B4
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2195
BA0B5A8E52E85448A5ACD7EBA5D6EEEF35384110BD08E20CE26594B335CAD2D6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2196
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2197
56A533505B51668467B1BEB6502B63E2C8C7F44ABC47166D1FAB7D76D420AB4F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2198
FCEC1D5255CE0C1396C07E901EB654902586E58740E5DFD7B80BBBE5E08B8958
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2199
6FB6F683AC6D2FC4C150B6F136C98E0B04E435E64E8C3D39C3D1CE24AD4E5866
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2200
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2201
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2202
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2203
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2204
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2205
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2206
D844F0D5A5F637EAFC6FF31C7AD8FAB5B23918CF23B7C34EF396D8E79061562A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2207
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2208
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2209
9475E2C276FA9AEF4957A81AB9B00A95EADC7710FC6113E741E14F9D803FBEC8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2210
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2211
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2212
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2213
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2214
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2215
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2216
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2217
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2218
ACACE57E9C05A763FF26489081AB7558413A932C44DB0B2AD54A5F453D7423C8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2219
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2220
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2221
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2222
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2223
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2224
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2225
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2226
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2227
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2228
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2229
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2230
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2231
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2232
C8A7173E3EF603185EC7DA7C31ABCA2C00CF076D7B6B54DB04B45D54D9AE2B3A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2233
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2234
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2235
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2236
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2237
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2238
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2239
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2240
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2241
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2242
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2243
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2244
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2245
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2246
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2247
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2248
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2249
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2250
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2251
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2252
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2253
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2254
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2255
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2256
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2257
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2258
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2259
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2260
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2261
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2262
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2263
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2264
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2265
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2266
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2267
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2268
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2269
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2270
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2271
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2272
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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dup 14 /openbullet put
Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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dup 54 /negationslash put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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dup 56 /universal put
Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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dup 66 /B put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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dup 94 /logicaland put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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dup 95 /logicalor put
Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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dup 103 /braceright put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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dup 104 /angbracketleft put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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dup 105 /angbracketright put
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
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Christian Urban <urbanc@in.tum.de>
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currentfile eexec
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2693
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2695
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2696
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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Christian Urban <urbanc@in.tum.de>
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diff changeset
  2855
B69B92E78F3461D64A84A6E9783666A1164FC11790151455850C12FD189D4D41
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2856
A644A57F5B5679D4460435E7F344EDB316365F42392C80DC760A3B5004FCE36D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2857
A656E7F48419940502C96D96A09B1154D741810AC6F806DF79CDB893506F9720
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2858
094C90F22EE517EC935E62B93CEC947CDAC47D6A8C35F0123DEE6526620645C4
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2859
7747A96CCD422F3F525C9CE57CB2B108F9AD5A34E2900A6583F40BF1C96FF9E0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2860
EC9DDF388404789075E4715049E4A5BD2BA4B0CA1F77C18BFD6727EB20C2EEC6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2861
66D80AA4657179CC37E261B26B9205B1387354E4AFDDAB97689C3E853B32C220
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2862
3B3E85AFB4E5DCEF5D04A1CF84559DDCB6487AF977E2A63AA171A465BD177653
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2863
F2CD7E1B87D4130F497B84729ABDA7B540B061E4D5295E20C90916333FB76F6C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2864
FC736937F59ED0E8F719C714D10E1EC8EE4E91065FFC36C86E90264B10FF668C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2865
D4B4E1E597088FF3978C5EE6959A438FFA4756F01C93AD5F7147A7E2A44F3313
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2866
115EC2CB10412519993C61058CE55DD25C2F5584599F22CAF9D7A3097FE8783C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2867
46D656BEE681E0B2373311A889522DF28758ACD71CE42AB97719CCC9AF68A51D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2868
1E12448B475817CC0EC8328CCCE0C3613656D2C8545E2B5AA964365EC3546E61
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2869
7AB25565E1DA28F7F538DC0E7B879E8822143A26C6180BB6170D31F28D2DD5EC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2870
7F928DFF17D6C63E09EC2E7027631267F21DE976446F1443EB5AA3143D8789E2
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2871
2E54178A9C38295D7BAD1DC516B5AF531CE4889CCF4328E7F46E345C20AC9611
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2872
145DAF9E7313F396E697D31374DAD75CA74E55B43B1ED1644DF18E3CAA51646A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2873
A9BF25CB6D207E8EB938B4B18F537285A526A71C282EBDCC3C41A5B7F5074A19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2874
FB7B06B59DF7E4AAAEA6A3E065DEF9647368312A47E27ACCEB2679E5F1F8672F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2875
F7CE2A0C5A1BCDB6E8F757A0074CC3AC1FB2BB7A4984F57ED5C3DC1741E2C9F0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2876
B3D126D40B656B1D3DD303C2D5189983D4C6A183FA4C447377983A86CDCD4E0E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2877
EE4A362FC729B6CBB0D89F9749FA10733CB3CC3311AC4CE3E95610D3F9D5A504
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2878
34D2763B3BFC27455325A6A3C1118FCF38AA03F7B40B2F1B34DC143A55AD5A96
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2879
58CF15F16013D7FED38156077B111B99C4EFE9E790FE21941F702D6AFB3779EC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2880
FE4E4E020ABDADAE0C35CA49655FF8A70910DFA4C3F005B748B8A98E5DDCF153
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2881
A2BF5CD49A50FAC56DFECEE86E7D93BCF9B1BF5D9BAA1510002F0EDD92EEE43C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2882
8D57BD0F7E6851C2C158EA9AB172F45BAF3CA7CC5941B6AD257B21F281032BED
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2883
5D9F0F8B3700CEA904425188553ACF3BE19D4C3B5047E2F0EB418373EFFBF297
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2884
A564A0A5BFD018531589A12075041735EAEAE84D071D077EC8CDC7F6FB427F4B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2885
1496CACC2C424DC5A536DA08F32F0A9DF00A22AE83803A108A91DC9AAB9F1DD1
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2886
DA75D256DD32509EE5E3DE00625E7C046C5D8C39E1A80C57ABD153A3786D5414
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2887
4558D6676B82AFCF4BF8DAD5645F2AD108D36B947265059F1CB394B8E6C39B89
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2888
1FEF214D9D617A5997209784723FB97A37A97BD45F95A90E26B171060D2FEC7A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2889
BD1BA5E7CDD3A9B2A2DDEEBBF5A3A9247AA02AD21DE135205D180418728BF71F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2890
A8D0DD0E255C00A9148D8D68452735F00631B0F76FC34ECB455B71F858CE687B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2891
D9EAC6365087B070E96BF04CA106F7AB8E616FDBDC0F8B73AD0DFC6E33252514
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2892
82BBABC03A3E30B156C6FFFEB246228198AE019C557C21EE3C150B7BB4BA490F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2893
5802CCDED89D2CA360AA8DB3F6E86D136F9FFBE40B1BD8FC1F2C346296FB999B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2894
5C7BD6CBB70B5E7FEEEF6EE9FC446B68A71E816F13271BFB65F869EF60EE4EE9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2895
E75D859E75E06E2B2F0E3A71F07DF37B10710461DD86DB96AD6BF05083C10635
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2896
88467A56763E24969419FFF78C6EB525C4CAFB7FA90D3E8832BAC21E6C4DC312
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2897
6F62400FE677451AA7B1D238F13241B599C8A3CA0452B353F7D550F0E2A9F307
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2898
44E1B1FC5AAA7157492081D0439F112B4D10EC22878337DB9E5BC76D35BD2F57
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2899
D55B32D4626ADBB67FB71DC56A7CD442E6BFEF109271128BF0AA28611200B48C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2900
DBF9EE5C6B16860866E8C59C2B56F032AD9548ACBA16B7DA1AC98E885F127797
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2901
6A6C4446789EE81B1370E20D27ACDA811FDD40B5195F38B554FAD093FC5400F9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2902
4F16E3D2114A243A84136DC4098B1DD18313CE1700ED518E9FC2334ABE9D5343
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2903
F33FF79298172FC936BAE8EC03E170841319D67B9EC18851F583AC0ABAA7BB56
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2904
171F83171219AD70C898AADFB2E1D318BAA77A4B3DCC0280B808524139B69455
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2905
1C011B533B7CAF60BBB9821E1357DB2410B850B140234A41F33311BA021E6274
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2906
9DB66D91FFCFD82AF90ACF1B8F0E924616B3CE2DB5CA2A2DA75ABB5501C2100D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2907
5F7857D380892964E6DBABA809305976E5B9A59E8FC44ACC7C38D2C24EF9BF7A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2908
E1792F7B3EF84E5F5BABCB5E5C706D87D36A27C3268877C79FB2B8492674A285
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2909
7D3427D6AF250A9D2485A244D77AD4B1D2C8AB0599AD23A70861E7FD40626809
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2910
4FA38F78D3CF59E5D56AC0F1865CEE68F94BA7F691E9AADDA0874DCFCB3D3BD8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2911
37F4FB402548BE57AAB153EA5BF03144B91714BBECACF4497C0DF392809BE5F3
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2912
14468D49A61722ADA92DCADD70DDC252552A9B47B74202E568DFE9B2EC407A84
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2913
7D366ACEEBB450B470DDAFEC1DAC402725CE05A1F5EB50219C12F999999D3E7A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2914
36945B2FBED3C14575E339D0D28F6F54AE8056E079A80428E594782BCE1836A1
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2915
9C6CAF3607AF4A3337F44AACD1139D6C762755B4BBDE891B856A9F0DF4539E74
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2916
91AB34543FA709D19F1D2B569414CA0CC3DC71FD4B11EAA5B26ED4FB75D713DE
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2917
529BB1A883B9B4360AE6F348C026B443C408CD417D4244B5E5F33A8BA3B68442
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2918
A94645ADC53A4B7DB6FBC948A2F5D9A63BC096E9FFA89A15D906E0CA223362DB
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2919
E33C0C1ED8A430F925BA29A2679B19EE6E135360A176150DB6CC139614271991
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2920
C382054B68C32482BDFFF1B8DFA933232329F8F4C8B2BFF99E95D9DC549DBF3D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2921
65B491A3C1612B9B31AD420E49693EFF320B6173696188E6BF272A16674E278B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2922
DF79BA94AE7032083012AC4DA04DBA90EBB1A1D9E361E450A8DCC5A5DCF0F25E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2923
C973AA99C8580CFB4489F6F555C4486A79E1EF05A1F6C129383B41C45EFB1DFC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2924
EDD651B60D7FC48304A04F369E4115243DE12FDB0A283D99ECC91696B2E41446
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2925
2A68BEB41764C0CB4FEA6541FCE6D2D36F6C8C63F13B37E7B711C49FE7C01342
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2926
E8E14BFD3BCCC3EC27289AD64A0811FBDE463466BF456EAC3CCDAB2EE44E8F24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2927
49AE09D64D42136BF4BD397420E597B382B01A8B58B0EC06F764348D7C7EAC1C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2928
0C479B841580BE84E4385937A0E8C53040F28846AFBE28822FEF5614AF822B2B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2929
A631A6FBB7B89246C69C206558119224B924B06A8ED72C57B1BB31733AEFC2D6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2930
510763C9CD5A2373544EE0A88DC2F971C8282C8E88F8D3E2B75396BD84DD9CA9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2931
FDE7BDC865E5B88FDC8D62645B14C4A05790BA847B1399DBD0F491CAF341FB8C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2932
B438C50729BF4E9DA2EAC78FF01A5A1DEF1F0C5EF0B59A418B664C8D146590E3
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2933
698410077EB0FE0584B2BCCBD576C37EBA36B253913A37D474121044B0E71680
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2934
A83510663BB4EA3CB90F0159DE624CC02FBC8ED2A54B48C45288515E9C66843D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2935
61AE187185503C58CEE4EE5E38C86B671730A59B6CDC7EBF8DFE3753EBC61207
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2936
2EFE9A6336AAD9CE63D8B5DE1A8BAA7A7D0CECAEFC627399692FB3836E5462E7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2937
1C820FA275D12C0CA18FF8DD21D895A64987FED13CFB195D3DE1B7DEC50E5141
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2938
19BECB584211FE02A6E6829B58505B565EF9AF7CB3A7DA877C7E8DB185346C45
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2939
37CF63D0481E8E9283A0B689FC4778034B7987B6298CC4F3EEC55B898DA4C4ED
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2940
BD4C3BBD494121722CD6D25C889C653497E307776C0D63869B5D9C155C672CE6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2941
CB335BEA1D0229F6AB8F380127D1AEA97F68BE2D730E5E3FBDAB711608867253
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2942
8A349FCAAFABD10A0EAF09926EF9D18BD26C16C38DB36FAC88B2B1EF62FE29E1
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2943
6F425463EDE2BC8308C4810440C1BCFEE5E7D4FACBCCE12BDCD5A9268A9A3910
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2944
9AB7631B5A554D58B53FB83FD7504F5481AE117EE627F7E865FBAC49C2952937
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2945
615C06CB85EF8D44D08C6B4E7538E2F50FDCD0DB2F8DDBEB107E41476FD51862
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2946
5BEBD0BFA9980ECF9BE083594DCC4CD4ED9DF5CE68A083DF497E8CC314D36FD0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2947
6312C56F48C4901A4A28B4506266A12701F1C5988CABDD7F416B94942FED2231
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2948
6CE5E74AB96CCB04942BE7A5B603F56B59765D2E737489002A64280A64DC9CE0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2949
2DA04A9879F9833A135FEFF42DD66733C84F9DA4EA055876B29EFDE6B3812CDE
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2950
1B18A68BB2F412B80C79D6D60770C3EE8B4734F7B7E2E04AF0CBA33A9369B5BD
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2951
623E881103D64068A4F0E407105EE81783BB1BF1810C97AC3956E5AA46152418
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2952
32B4842D32A6428FEFF74A98648359FFCF2742483E413444439FC0FA8B4DC7E3
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2953
18D179ACC4601F20036A81A837ED4BB6F06AB3C36F54EF5F6BC5B009F1B32868
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2954
99845E293E56425AC4ED2A98A443DEACE6F85694FDA1340FD57BC52FDD37B78A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2955
6A683DEA39BA4E6E4B2B0995CA5B6621FA168BF617DD55409D23128D9C6C52C6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2956
E59E8816E19A4E29994D6CB67B53FDFF4BD1451425AE3082BA38AB4A749D0B42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2957
553F937C287E9A471CA038E296A305A6C0D096BC8045A643E176F101DE9E87C5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2958
22F8A38C27D8C30BF01FB8B9404FA4370A9F39CDC23AFE16AD32A244CAAB62F9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2959
3C0379219AC5AB4235284CB9032C0D16455787CE0E2FF338BBBB5A36C6390637
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2960
8467C52AA4E798056F581C03CAF744DD7923549DD949FDAE7585CFF1F0401E35
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2961
32360CE3699EA9D059C486E345A600E7E5934DD9E48AA4504DF55BDF25358729
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2962
E070FE4C8DBF54C0D3BE68D1F7EFAA23998F2FE46D05BCB2CC14C027B4C0161D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2963
52F1CE0C412AF3046BCE1F6F1AEF2500A377D27BD2A58B91FA54BEE2EB8CF269
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2964
55F0171656BCF32F9CCD98930A931B51148D8F8EF0D7FDAE1BF22452403D5F07
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2965
F37067FB3A1477CA96AFE0A9CE18896CF0C63A6ECFB7D4617D213953DDA8107C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2966
EFF46D1189015BD734BD09F7C76C1E62A3C37943A9B9DEAB246850EB8000B1B1
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2967
E0C1098D2FE738E4EAA51036950A393F3C9CE9DAE110D4F5E3C9BE20E2454E32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2968
8287DD4481EC25499D6F6228DEBBDEEC1539D92EF15C89C02CBF730FCD808FC9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2969
E2B89CE340B3730A57C250C5C64465B092CCB0ED42A41D5DEBF7DE5EB9DFB055
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2970
A20D4C1A57D368560B0F65F372A1C18E3DDD56C0DC5567DF753C71A67059CED3
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2971
507584D82FBAB41F5945127B1BA5FF524ED73CEA1AABE47634970369D22FFE3D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2972
FB24653E3AFE2569056273F701E96B985E9175A7A4B8B9EEA4E1BCF8B491317B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2973
FCA592005B9F8D311BE97E0CFB41BAD0A205680E35956053410F22BA87DC91F7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  2974
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diff changeset
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22AEEB877FF489581DA6FA8DA64944555101EB16F7AB0B717E148B7B98D8DBFD
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3128
730C52937E226545CF8DC3E07C5BA30739BAFCD0F2B44275A6D503F582C0FB4F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3129
449963D0AD2FAFDE33BA3D77BCA9D1DF878DDAFCA2E22CC4BACD542B282164C7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3130
97C2BDE318AF9D501CA21F6E662E7AAB75A5F24D2C182E598D175D44E88AB19A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3131
E7CD59584F95B389183EE21B525BF52A3F23C0FE5383A5565A19361D716F508C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3132
AAB78411CA5A4D27552CC1C435760D5A89D535B71C593E755C616661363308DA
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3133
A683F54ED0C23FB2C225A008392B0B719F66F11A946A090B7C00B662A3C69599
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3134
B4ECB0CC70C85C4BBBF207E0026F6C7A19F2ACFB7A60804FC98A4BFFD7BFFF2B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3135
9529E6D9D4238002BBC255BC62959D6F3381FE06E0621B879D5FE5B541D45A1E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3136
759A6E7DC32B1D1632368D09A97039DF255B6492B1B2B7E2C1434E8306ECA7D3
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3137
5A79B6D614B4979F10988BC76ED53A5F45315CD7DA216221F842FD0F3E050DD2
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3138
BAC23C984D506D8F7D614BCB6B244F5F41321549BB0BD041FBF3053307168680
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3139
3435E9C94570B51B9FD153B1698729A664B0B9090DA041DADF5808BA0F15BED9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3140
A66A55FFFCBA7E6F27B7DAD1917527C0AA55037B04FA356901AFAC122CA74916
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3141
6F56D4451078235C3261C82D401C2BEA8870C331B783F5591C9A8BCD5782BEEC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3142
AA9FF0990A3295E8E70AE2FFC9B545A4FB8D51DE1833C34863DE925F5DE4998F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3143
743DA7E50C25C8E5AAEE5D0A8763E4EEC1378E35869C246C1DDEDEF13F31F5D5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3144
8116FF18F12158599D12D31297AC251049B957FDF3FE565E58A590730F403D87
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3145
9E27F6835A0997127AA15674CD5E387BF678C6D19548114582063E483D5D9470
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3146
606965A32F413BD0C6B03BC67997DC24A5EE9A8FE848AD293C6202C3134D5186
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3147
404FED8AA16353EE00E7FF19B3106FDEECFD720B5461107EB2AB374C7500FF97
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3148
190631305CCB3F853D2B16AAB4FD2D9F925AFCD24E47CD7109D4B0484D062B0D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3149
1648BEE9D445AD10B532A2B187BBA7BFB8A1F9D8580F5E7A2257F125355A87ED
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3150
48A0453CF76E9E1C984225895282880B6D606A576745767B6E42B2AFECA63078
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3151
8F851E42B3D754790A0AC892D3748255A10110AE8F4017B1C6C22BF187EEFA61
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3152
F1166DEA9D0AA42F15C913996490004EA9E9031811BB6A13847E6D07A51F6F3A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3153
2C0660CDB9D77001868DD87C87C31D8B811EEF1C5A3D84E4E68FB317708AAFF7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3154
3AA211B063BF12D77A1AD7DC7397D5E67C6DFE8D6D6804E95DD4A537B2BD017C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3155
AC93404F8D434AE0BDA084C7E707146F27F5E8E2E61C8FE8335C5A29CC30E809
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3156
8A382135E1E96533751C8C7C95C0F8A7A4256071AE3082BD048BC00BCAD159DA
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3157
11E61ADA7B49B827D1B6149AE571A495974150BAC042D45D40864C22B0D1F439
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3158
1252E5BE6DBC18907EA805FD898CA2B979CF8FAC2873127294FB9353FA51E7E4
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3159
003ACA0C9AF8036AE953413095994FA5A067F90E17893515877E79D9E2367B05
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3160
E593144CAC5FA961850E6EC62410280C4F3945697185E1429575CD8B90603F04
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3161
84C82E1DFCBA0611FAE51D42603446FB010D3E02CF0737D21D59C897A35184F1
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3162
BAD1F3868CD0A67D8751DF5C88E573974CD31F560A978021F0DB094EFFE9007D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3163
1C21120E492E9085A02B05830440F910F4E19E0F1EC90C43E8B35E9D62462E9E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3164
5B73521C77397804926EB3C2AFDBBFE0633C7A076F57CFBF755CDFA8B4B661AF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3165
49FB30B2A0CC52FEF27E48E10CE0095CA4C9495BEB20365A89D65CF7D1A45C22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3166
0BCEDBDCE7A9DDC508EEEEB846BF77D43A418D25954EB64D8E44E4E9F920CE16
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3167
C14BBB47ACF6D0228D6F8F19543815316CBA060058C728E2E2AD440E8A4E4CDC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3168
617022B6571A16C612B1013D0F80F0CE218EA1041E5E18D17C3D4E75D9964254
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3169
7EED90C06D9958D218D2247C5D86101248746670EEB782182EFDE040EEA325BC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3170
18251F508A69382CCBB4D34E1B061B1750F817FE07BCA6EFE3E1A4FA8B0D2679
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3171
4DA1A866AB7DE61E24636096A8F825F649CFA8D9A8C5B9ED559B726F263E684E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3172
5334B7737A5DFDD0B754864F622D007AE087F9F35E34727968876C299ABB91ED
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3173
A8B1608DFEBEA17548A1545A3BA43091A7A8CD067C73A342D1FC2F249BDB713E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3174
94ABA90DC578AE69C6F76D214CE7D497280632C4F362991801B3BF7E139495C1
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3175
8A89781D710B9BF7C362ED2F8EB471F7D7EF8936798FB56BF88D80C541188FA7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3176
6E5A408304C43BB6DACA14B5B7C59D2691046A3306736B6D81320FE95C5801BB
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3177
F300D8AE31D71D397F40921175E95AF2BF81671C93C48DA4EC7FA93BA1E9B738
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3178
FE074570BE3B790419C2BD8B4C344C0898360574E6DEADC0D6DFD52C73E4DFCE
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3179
E5400CE7AD9CC401055C609B7364C5A080EA89BFE5F6CD9EA7E9021DDFA10216
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3180
6F54976CC996CC2B54CAD3E2768361EA64D04A3B5CA97634687B01AC6617E456
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3181
DC3D3376FAA538BDB4A175788D49E1F02E3B4D3EF91578BA86B1DA40CE09BE3B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3182
3CA42E82AA1F86124FE03B0359E4AB5B31304C37FBA1B0A18E9AAF0FC8791664
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3183
35A96A04C50DDD8D6C9F75BA0C6BBF9248CA191344AFC13477D4F7C015F22D85
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3184
D93AE55E5F33AF5D8E736320A1D6A4C11E96AC834E74EA09EA082DBAE5D71328
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3185
B6A2E2C2EAC9C8A977D1D9E59D4F6E64472DB52200F14CAF7F3BB5BD63EB323D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3186
571F7B5201C1B7120C6FFC35B94D7F654F57BE19094FE35EFC541D9760F94B2D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3187
A0F054E0FA003209C86400C128FB36BB8EE8315DCC358C6D8F1409A4A104E130
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3188
E2F951DECCB1B5A32AF5C9731CE51ECB1C082408CC6AFD970DAE5AA05935A879
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3189
4FAB4446FD7301076A440133B2040E90591B43BB6DEF8F0A4C3A367A9DC9ED38
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3190
35C3F2D9463314958873984707212709F008707BC87A53C2F8798CF60935966B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3191
9357C54D0248463D6C7334D8B180D69D16DFF67666653005BCA9AFAA4D34C2B5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3192
156DA6DADD28A0814BD0F8D63941C3553C0F980D1C02234E8CA2FABFF1B3D758
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3193
02B0D89AC01F3735F7B0F475FA39D1D4A5857B2186C8386EB88D166D81EB1523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3194
6C7903C7AF7FF47DF12B3DB985A7080F86CC6A8CC260099484C90BF12B8191E2
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3195
2D2B02FC020854CE8D345A31917EF4AB2A0503EE8B92D029366CA1B9E112FBD5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3196
1231584E42D45F13A6E33D965E55E5CBEFF5B62DF25C602D55D3D35BBFE1527A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3197
D322B1FA4725BDB8485E55A794ADABF9EC60C1A4A8E8B8C45D974AFD80E8F550
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3198
FBC1F2FD18A2C08C01C01327F4F026D23E043E7F0A7CDF7C54BC4E444754802F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3199
585CFDB1F6CBA0EA276D503B4696DCD66D97E4E539C060E33ACD4D33D9C91073
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3200
D4972BBC94B4F0C4201E73C0DB054890BE918D78F59E720495951006EBFC29AA
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3201
A2741D59F73AB749F4E51FB8DE19581520B5274DDAC567AD818C25AEABF1C588
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3202
F6A4DD7C58C226CE57A1E7E586EDD62400FE7F9A4C96DE81D1D80549B709B38B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3203
CF483D260F2E92A86E5C59865EBC98CF4EED4ABF0D1D52DEDB78766D86293263
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3204
42E61C1D93981C02F99E76B99E60086760B6FF7C5E570B727A2D4C6FD54F838E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3205
B7D69D39416972E515042B3AF92746E43E9B1359EA91CE4AD70B918624572BBD
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3206
3BFABDAD624491BF3EB34FC6CDBC486F82422D4E03F374F6FB4B7179DBA6B19C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3207
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3208
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3209
CF1DE8B569F25384D6BD6C66F4E5A3F42799E26793BB04FC6579F60588A2B500
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3210
216D643AB38D80F77934835C6FFC5151059D6E2A3B043E133BA834DBDA5A8629
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3211
44044AD212BCA9DA5701379F8B7642FE16D6FC3CA72B7122E859DDCF44B38A2F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3212
C1D39BCEB8118FA99D7FC26EA1F929DD366927C31002FAFC711CEEC3195C66CD
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3213
6603B58141C4E2364ABEE640F9762195209EFB5FF71E1F3C4E5A8E1F89EE860C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3214
2260905CD4DF5F226ADAC4B1C815E5E7E4FEF760379717A10735D5E6B68EFBB9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3215
549BFD933F51DD81C1FA058965F543C61D0BDC0C36CA55761B4AE920715D40DC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3216
81B13BC88D6DF20B8C5FDE68DFAA0976776AB3080BFEED6126BE996C91C85A0B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3217
D7223579AD33CB7192A07CBF1BB55CACFB6659AA0C873AD1EF9C0BB72D7C5D81
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3218
FA852BDEE116575A97B64707F2932F69B03FA4D2A0933552EAA3887B2D92885D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3219
FF61B4B0EA39A12AC0020F4A5D8BB29E8E15391662D9ADD9D4296F569526432C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3220
48B325A54A94AB451C2B63A54E2BADDFC4C58D315E247475F69506079FC2640D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3221
F7A6C3FEF2FEC73F4435E2292F379CD9F0D67027BEEC9E374D65277DBAF0CC2F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3222
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3223
A88A99AB6EC6DAE25C8CF39118711AFB22953BFA7ADB8B2A4DA142B3CBA17560
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3224
745720C5A87C58E50BF3F6E34BBFF9AFF86FE7DBF90ABED527E3431E4A06A844
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3225
5F0ED393195BF7164B67AE3878D9FA8E587343FF9E9E17870EA36EE6FEE0AC14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3226
D1A16E1761C09E493E733F1B0020480CE36CCB19EFBE7058C7A2659C25C7EA90
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3227
AE4BFF33B9EC0C8E2E5CAA2BAB84F93116ECD71AD769BD22CBB9D8A37754FC2D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3228
11444C25ED8BBFA118EE8D737D4CC325E5329EEABCB54A5E56BE90D2F2D4B87C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3229
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3230
FEFCFEDE595231EA7CE9EEEAE05518EE057A2B6FCBF28867D1B67C0EFA3CC721
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3231
0C0E8093678968E0F79F0B4218644A57730868FC0FF74445C533DA34B6495527
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3232
4EB4735324870E5DB019BD05D653EFD2B04CC6BE5DBF24668FA94A3A21F2043B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3233
032776B64265031D50744278AEAFABD87C0D32A130B83681F8EC2FB9D2990F11
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3234
AC463DD481D9694DB63D80F4D32B9ABD7ED276EA847032D4CFA4DD7F25356F3E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3235
9C808260A1F2C70BEC80098BF593417A1B16616D066CB28291D4DAC8268C207A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3236
AFD8624E88D7E5E1E548A83965DF3F4702221BB50C9EFB064799B5DA43209535
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3237
B72B108065465395F2B2BF4C5C520485DEFFD22934337CE6AB3889ECCE86D237
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3238
C823057BC225D325E8C72403C7327917FED7178F940E34B9CD671C4178F351C8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3239
4C50CA0511AF48E50C521F3B5CDF62E966169A7B180539B21D99241DE7F4B509
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3240
BF202B703A8D10BF69C18F7AEF14122530E44B274F8251165ACAC128DA5B3774
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3241
A84DD18D62EA8A2B27B0DE497A3B77D7FA96FB82F51B4BFAFA9DA7C7AC61009D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3242
FE9BCBAD571878DDA10E52FA3DCF305754E848EEB6340B818EE3DF9D8287B935
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3243
681703CE5AF2F09DFF789C45B38791B831E94F56538B27C75BD90AC11F3DBC4D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3244
2687E0366286576AD59A6647B0BABE2B00CCFB2FEAD8B927080E65AE23347969
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3245
1CA219AD84A0C7B1F947BA7E91E11E4E0D2580185FF89B62059B41EA739FE087
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3246
648629961A26A9CB2049778CEF8D7BCEC71D8C1D237A0FFCE3F3AAB2C458E60D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3247
95C1910A34E37078CB0DE7A043BC2EB74C6C7272B56E11606A172E22CCA890E5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3248
45019135B5E38C4B29341A99FF01FA0EDD4180F6EB3B2F0A9E0AC94A8314A58D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3249
2E97078EDAC8BCD338FF879DC96DE54701A380999421CCA2A6674B5618B0F4F5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3250
823ED3CBDB309156F1AD1B94BB939347F7374684813170AD9384FD56116FFB18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3251
475D3504C57A3C27A869A49D46C7A5EA69FD2D1D5E37203C8644B9E48059E6CD
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3252
6E87A461D61D3B481493774085709168565EEB1CFC03D841F758EFCD64F527C4
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3253
E997FED21EEC1F0E104CC7DDE106F9405D231F15412A6920820E5B578D700411
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3254
9F6D612600C7A8EB92016140375C532D5B499B1ED38581F0F8FB34222B20DC51
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3255
3A6EBC0161C9A7D3458F5018B1589577F0EA20C16F32962400BCF1C2070E60F3
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3256
194E6898698CFA44B6F2948309B3DAFF12BF680F66E84CE7EA52D276154FF691
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3257
D1F05E63DC7940A9E9FA1C7261B6C7B8B20A9B0C8413CD958BF8B4E6F787CA06
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3258
0E1D01AAC6742F3B573DE53E807DCC9FFC1DC1F60C4C6DDAEF553AEF24D1FF24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3259
AE26803320E170EDAB1EFB40E63E70103396EBC45F7D5B1393346822C56E4101
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3260
9351D4B60787D14A9BA52F7BC63974DF4281151D6293088D997B7796C07E5318
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3261
773D22F7355854022E300F91CA2C94242AB7319DF2C13610AF9AC5735AB2CB83
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3262
6943E053CA62B778BE50DC744D1B13649E9FBB3EB362B11C6F52981E4BD92563
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3263
1EEDA4C6C118FDD5B551507DBB88EBFA6DCF6C05DA64BB98FD67292C1097AB2B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3264
A62A8A4EBB71B182D75602A2232CCD407903E0A4EE7295010A16F459971917DC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3265
F77BDF79B1E11996F73FFB2D556194049CB3707416E7450B42658073A9F34B34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3266
2938E581D4AABB2027D04625DF32E661B2DBDFAD2D0950F3EAA0AC34044430A7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3267
3DAF151FDBC8528099BF34039A16DD1066BC557D01AC1CF633009BD52052E164
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3268
C4E630E667D11F9399AE31BE203C70F73AED42D4390F9FA6EBCD86E270C39186
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3269
A9CBBCEBD79E9A12A81E7DA3A7A7E7FF586E8714D46B4C7DA5D4BE3E29DD55AC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3270
4E9960DF3E49E9182B87300A88373421834AD5F2FBB0868969068E1B913B129D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3271
1D8E38D609B6488576AA7320B77833B815BDB62A73CFCDF454CC91A6DBB6430F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3272
0B97596DDF80CFD4AAB6CBFFD534132F967588C83E2E4518BEC7E3BB18306C22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3273
0D1AA10C2E4431EC3D41105A98077C5854929ECB50B0C66554D27532001C9CDA
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3274
DD97DC913B3370B1BF2ACE69CE2CF4CF70202F5617298724CB2176F52C42807D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3275
948866CC0C62BBD16B6A98DAB8BF99887B763F38CBE85C6C6233B401446C847A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3276
A5F94C613935B4C7D069B4B55D7ECF63E5FB11FDBAF5D586A5C0667B9BB62AE6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3277
DAE88AFB0BFAF640BC75BA3C593D1700672AB2F84243B5CAEB4F4E28309B9DA9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3278
E2DE7830A9B85DCC95408CDB8723A9C2AFE68CDA816BD2CD398DB35D07228BA1
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3279
55DF0DE49F59EBF8377520A25CEDDB8F680EB1F063F90CEC31BCD114A7041CCE
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3280
F1B46BDBA4310211BAF57F2EC0595A240387E6DC92C2855D23C8CB37EFDAA8EF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3281
F8F65275DE8083792AC7194B44395F25FE2354CA560779F2D7BD83A5ACA00A94
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3282
CA6522768122BDA1120D7AC349E58430FF652171E07BEF2A8AC9E401A593B491
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3283
4C9188CBA59873815F10524D435B6A4232DF1FD246AE7E51FE36242F341526E2
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3284
C46E0E7E1DA0859C3ED74F926F366B22E5DE139ABC481E8080CC69B902C8EA39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3285
8D65AB3D20EFED25C7795041384523F433D52E6751625590DBBB5777EFF0DC7F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3286
A85843C3760BD8392FE7935317A2B3CDEBFBE4078C5936177ACCD8919FE91862
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3287
798F63849C10C92EEA4D61E1014D5B7D662C29C67CF8E584127893AD79F2A0D8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3288
B8559605B918B8CCAC88E6A3BE0A14BEFB7E3C40F20B7B521D63CB37CB4BF880
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3289
5C71F6D2DBF462027F846961B3C84DAEC53E1E23DD552B8EB0747F2DA744698E
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3290
31AB983B28EAC73082F1B6322DE9E62235FDF9A209426149C1EDAF19D8FD6457
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3291
8B3816348325C41DDAABFD7BCE9899E4D364ECD92ED27C2CD4FEB6A642262DD0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3292
94E3277D9694CB49E56FA035D267793BF233D36AB81BF25189DDB262B0E7C4AD
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3293
9BD0E565D13E2EC494C3516F679B05CC28C706D945D5C5717610DFBB0B3690CA
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3294
3FB0BDB8243B16248D1692CADCCBD8AF8878C07602D1CC147F8F3D3CC4AFF624
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3295
0D95561547580607583E79F5A871534DB5F80FFA8BB82C85B1AB78427F2C7C06
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3296
2FDE668A7B16E40E903BC738DBB85C9544C6A97B8F4590E6BE2B8F948CB6DF43
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3297
646EBA6D365F0F66BD6795B47AE81BB663AD77F8A5D6EC10B6F5A1A52A16220D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3298
7CD4C134A38BD30AC72261319247F43F6C313015F82E812753FC5A3428CCCEFC
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3299
4B652D6DDC918100D5D4FDFE96E2782B2AB4D41FCA217AF0D150DC52A2F01668
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3300
74A11F3C794C4939F0CC3F7CB7C98F1308AD8A283E5F170DDD39ACFFD20E9A57
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3301
5795071BFB9B86519D187DAA9E4E85C22B3BF9C26C1974480048439989F594F5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3302
AF352FDB359DC9CD2685C4DADDF98EA1E8D2772A0136923D7C5639B7BF882392
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3303
D1D52E850E27B4AB7C58ACC342A2F769C416E7C8602FA4DDDC1FBD4BEE780F65
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3304
16A97BDF3CD37262D028BB282ADC38343902C7B61AA4C4F3E354E60FD2286FC4
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3305
511E9128B6F3D0B8AF4EE6C83E30B593E503048A57646F9D2D69C2E5DBAA954D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3306
93F05428EB60DE1009051D3CC3EB9E76587A9BC40D1867E07AB4BEE2F863340A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3307
347DD281B8CF5B89E2B0D5EEC68DEAA2F15698F72930F4C7C368B829ABEADEF7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3308
3D0409C2DAEF81AD9E655C44D819A9610EC319B6A96BDD4B60BF513B09EBD6A8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3309
BA169B17D8D7EEDAA34C7B802AC16FE6E06B2B5B9B2F4C67991430DDAFBFA194
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3310
02564D6789273C0E2F51E8CC96A76BC22E2446BAC13B2CA622B39E5DD2760245
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3311
7F456D9AE8A3B0D69B869EB8C9A776D5EEA21A28FB8515CCF9A3B5DBD1617B98
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3312
5FD957D74643CBFB0B760C08AF0BE4824BEF0DCF40BDA0AB291FC22FC99E4CA8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3313
DB687197E19438AB3947D4598F7D318ADF2719EF420195DC790709C2CD062739
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3314
A87951F783D6CB57E6B7674C5C2187F228B7F4112293F4F9CE4D46D3ED42F36C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3315
F67803BC261EF21CCF9422EC52F9069B5AEB67C095F4BDAC499F409493980C8A
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3316
C4A9E57F0C15F50AB5EED7DF4CBB8AA06600C9168EB55D3A851342FCC872F093
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3317
D78D5E71547E41815059E00B2CC200B80E11264F3F3E28521054CA0B6EE75606
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3318
F57B079CF93924646A90B25EABFF040A3B57B5365E53B9CFD9DB576AA56AB6F8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3319
D83655014D92B534FA67B1BDCFE73632125DC6609FCD264374037F0804140285
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3320
98211391D36C0950533CF5743290660AFC774523359E424B4E19855C1EA8C725
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3321
C5B904159CF7992B8EBB925D449172F0BC428915CF02938443DFC44725F4DFA8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3322
E89490F9ED9814E15CFED993ACAEF05828AF27BDCB50DF0DAED2B9C103FA70A4
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3323
CF16A33A070C881ED51AAA75B1ED963A47E92F21D74754E4E1822A5D3C94C301
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3324
ABFCAC75925BAE9F9D87FBC1976F93A70ABAB5FD9CD05BE0859E1714F42BD808
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3325
E9178FD9991BEDAAF26DBB6FE6964719CFF8478BCF3662708EAAB1DA7BB328DF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3326
35CBAE809A122F770E35FC1927B3C0253F2512B84A7036B630852FE7CD6F2642
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3327
987CD6A9542F349CF17B80AA00A30CBE50F36DC3CF8FEBD10E95E3663E3FF7EB
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3328
95A07B49F68A162E1F7AC7EC2C84AC8B448507F5ED4C8DD3C56A57C451052354
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3329
629FB2289E595D0990C743117E2DD5A70AC012FA55555EDB8E48EEFBE57DB167
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3330
A46FAAB6728816782ACCE31B32A42FCEB0DB87C4A066A1FE91372AC4D8313B64
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3331
83EE234D2D9BCC11EFA7D12B1E40339368CDA78395E79D348591854CBCD0ED84
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3332
D9B183B8BEA18565A01DDCA022168AF068E84C82230FA03A0B838DE72C9775F0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3333
A9D9EC606316BFEFD644B3F41C14738FC2E8E302ED9A9DC92A4A7B66E1C73CAE
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3334
E6A476087AEC9845A7BF30B4942D96FCF045F621F001F4389A173A8839189888
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3335
187DEE74A231083E2307FB2E3157D01B306B804C679DE3A85D368F9381CD3DBF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3336
B538F5C832B4F2F7BD336DC4715A20E3C7B6BC7ADFCA894899EA1CA874101C39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3337
390473C9A346600DABFA3807288A1CA14874D890A9C5FC1735FB57C4C63B8D49
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3338
61559125A80345A0E010EAEDA03C8E94264D6FB6646AC4DA5016EA6C49EAC611
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3339
5C72DF523A06B4C4EBC436ED0E122B63EF2C4B238BF990A20F564BACBD83D93D
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3340
0CFE8A61AE50EFB0025C012EBCB8F04F4A59272B740D51275A8EEFD13500AFFF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3341
7E6AE93FF0D591FE651445788ECA36637ADFDBDF02C53FDCBDD2B04452C12884
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3342
A6595EB8FE744CCD4E5E526C7D9B992048FC68025DE0F234638B165B76E8802B
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3343
006F8768D7C2AAF569DC7BE2815E17E2CD760C3E3FE96A84B5518F8726A04B58
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3344
394F804A3C7688FC9CA0906906F0BF0019C089829117932F22606545EE322657
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3345
0BB13777286A83872EA812620AA7B123E5089AAFA3F33CE91F45471C6B0DC260
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3346
B9DA7D51CB51681716044B71F12557730E6D3D4050D9B5935AB649159D8373D2
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3347
2352EFCE6866CDF4C4419CB6E9F85FD8DCEEF842EC3D9BEB8CBCC2A15425A9CF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3348
23DA5998C37841AC24B301F841DFFE075B5CC29A5A0CF48D5C561D3B080D33BF
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3349
04E55F29D721CB2120416A3EA94402D27ECEAE5ED945A4E3E18E725A15E7DB68
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3350
7641A9C9A4F45C17E0F4D93D780527585C6D0844F23CDF26DA6BC9F19A180641
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3351
CFAEC182258A762D7160AFD42A09B34680BDC9BF46C3473803EA1540E92D88A0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3352
C222299503DAF08FBA533B52818443D5DC1F56B2E55C00C6657420340A1EAFEE
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3353
85E17FE904D002EE7E683101047CB28911F15107D6AF9FB2D0CCBF419AC32485
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3354
CFD0B0ACE6C5D67BF7B29B51BFE68F1EA5617A900C391AF656F88AF1EF70B1A0
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3355
3739ACE44847004472C9232C105C68BBBD7D8CC2C37163AD3067A61E3209F90C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3356
F4AB4CDBA35BC2CD0C581009294D81AF5A9C657A3E87986859FF267500F27321
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3357
3802869B14DB725626E9E84A35099CCB160F6E136732EBF7DBD4F0FF5F3D195C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3358
4ABE912DA15329698B6CDB4593261C4829886E15A1C2C1FDD9B4FDE37282B710
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3359
E401F2B7208AD30AC9309AA37FE14FDD6DED4F278E6453626A8C45945EF8D7C6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3360
DECFA8C5936ABDF010FCB8DE8D644186216E26E8AE78EE980CAD1C020C7F627C
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3361
DD40125DC170B29FF842C895442DF94C86AAE0666535FB01B2E35F9164224965
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3362
2615B196DE7268F61595237E727D037C9033C58590F344176F9873D4BE30FC0F
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3363
EC825BAA05455CF89DD98BAA4277B2A4F5E02D38DD3DA3A03373C7E4C9BAE152
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3364
E97CF44029AE9ED74EDBDA9FEC885E333280E35C6397864403A982488691EF62
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3365
AAA72AE96E62E2D1BD722A1156BDC9F6C1379C18DE2EE6810C031CDA994247D5
Christian Urban <urbanc@in.tum.de>
parents:
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rf /FM 134[33 2[33 37 21 29 29 37 37 37 37 54 21 33 1[21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3663
37 37 21 33 37 33 37 37 12[42 37 2[46 1[50 62 42 2[25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3664
54 2[46 1[50 1[46 7[37 1[37 5[37 2[19 1[19 2[25 25 37[37
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3665
2[{TeXBase1Encoding ReEncodeFont}41 74.7198 /Times-Italic
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3666
rf /FN 133[36 38 44 1[37 1[28 36 35 1[39 2[68 23 6[36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3667
40 33 33 41 8[63 1[45 1[45 47 4[61 74 5[60 49 1[63 55
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3668
58 58 1[38 1[38 1[21 21 11[38 18[44 1[44 3[45 9[49 10[47{}37
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3669
74.7198 /CMMI9 rf /FO 136[54 1[42 25 29 33 2[37 42 62
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3670
21 42 1[21 1[37 1[33 42 33 42 37 12[50 13[46 4[54 6[25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3671
4[37 37 37 37 37 2[19 46[{TeXBase1Encoding ReEncodeFont}27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3672
74.7198 /Times-Bold rf /FP 131[45 1[45 45 45 1[45 45
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3673
45 45 45 1[45 45 45 45 45 45 45 45 45 1[45 45 45 45 45
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3674
45 3[45 1[45 1[45 45 3[45 45 45 3[45 45 45 4[45 1[45
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3675
4[45 1[45 45 2[45 7[45 45 2[45 45 45 2[45 45 45 3[45
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3676
35[{TeXBase1Encoding ReEncodeFont}49 74.7198 /Courier
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3677
rf /FQ 105[37 27[33 37 37 54 37 37 21 29 25 37 37 37
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3678
37 58 21 37 1[21 37 37 25 33 37 33 37 33 3[25 1[25 1[54
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3679
1[71 54 54 46 42 50 1[42 1[54 66 46 54 29 25 54 54 1[46
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3680
54 50 50 54 6[21 37 37 37 37 37 37 37 37 37 37 1[19 25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3681
19 2[25 25 25 36[42 2[{TeXBase1Encoding ReEncodeFont}67
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3682
74.7198 /Times-Roman rf /FR 162[18 1[18 26[47 2[47 2[18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3683
5[30 30 30 30 7[24 24 40[{}11 49.8132 /CMR6 rf /FS 162[19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3684
1[19 29[51 2[19 7[33 33 7[26 26 40[{}8 58.1154 /CMR7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3685
rf /FT 104[83 2[37 37 25[42 42 60 42 42 23 32 28 42 42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3686
42 42 65 23 42 23 23 42 42 28 37 42 37 42 37 3[28 1[28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3687
3[78 1[60 51 46 55 1[46 60 60 74 51 1[32 28 60 60 46
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3688
51 60 55 55 60 5[23 23 42 42 42 42 42 42 42 42 42 2[21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3689
28 21 2[28 28 28 35[46 46 2[{TeXBase1Encoding ReEncodeFont}69
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3690
83.022 /Times-Roman rf /FU 137[60 66 2[53 66 66 60 66
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3691
1[33 2[33 66 60 1[53 66 53 1[60 16[73 10[80 3[86 19[40
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3692
45[{TeXBase1Encoding ReEncodeFont}19 119.552 /Times-Bold
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3693
rf end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3694
%%EndProlog
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3695
%%BeginSetup
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3696
%%Feature: *Resolution 600dpi
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3697
TeXDict begin
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3698
%%PaperSize: A4
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3699
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Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3700
%%EndSetup
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3701
%%Page: 1 1
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3702
TeXDict begin 1 0 bop 958 448 a FU(A)-12 b(v)o(oiding)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3703
b(Equi)o(v)o(ariance)g(in)f(Alpha-Pr)n(olog)1342 737
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3704
y FT(Christian)20 b(Urban)1876 707 y FS(1)1932 737 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3705
FT(and)g(James)h(Chene)o(y)2551 707 y FS(2)565 879 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3706
FR(1)637 911 y FQ(Ludwig-Maximilians-Uni)n(v)o(ersity)f(Munich)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3707
FP(urban@mathematik.uni-muenchen.de)p FQ(\))1124 971
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3708
y FR(2)1196 1002 y FQ(Edinb)o(ur)o(gh)f(Uni)n(v)o(ersity)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3709
FP(jcheney@inf.ed.ac.uk)p FQ(\))759 1302 y FO(Abstract.)41
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3710
b FN(\013)p FQ(Prolog)30 b(is)f(a)g(logic)h(programming)h(language)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3711
(which)e(is)g(well-suited)h(for)759 1393 y(rapid)25 b(prototyping)h(of)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3712
f(type)g(systems)g(and)g(operational)h(semantics)f(of)f(typed)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3713
FN(\025)p FQ(-calculi)759 1485 y(and)21 b(man)o(y)g(other)g(languages)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3714
(in)m(v)o(olving)g(bound)h(names.)f(In)f FN(\013)p FQ(Prolog,)g(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3715
(nominal)h(uni-)759 1576 y(\002cation)f(algorithm)g(of)f(Urban,)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3716
(Pitts)e(and)j(Gabbay)f(is)g(used)g(instead)g(of)g(\002rst-order)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3717
(uni\002-)759 1667 y(cation.)f(Ho)n(we)n(v)o(er)m(,)f(although)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3718
FN(\013)p FQ(Prolog)e(can)h(be)g(vie)n(wed)g(as)f(Horn-clause)h(logic)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3719
(program-)759 1759 y(ming)e(in)f(Pitts')f FM(nominal)i(lo)o(gic)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3720
FQ(,)g(proof)g(search)g(using)g(nominal)g(uni\002cation)g(is)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3721
(incomplete)759 1850 y(in)26 b(nominal)h(logic.)e(Because)i(of)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3722
(nominal)g(logic')l(s)g FM(equivariance)i(principle)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3723
FQ(,)e(complete)759 1941 y(proof)j(search)g(w)o(ould)g(require)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3724
(solving)g(NP-hard)g FM(equivariant)g(uni\002cation)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3725
FQ(problems.)759 2033 y(Ne)n(v)o(ertheless,)18 b(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3726
FN(\013)p FQ(Prolog)g(programs)h(we)e(studied)i(run)f(correctly)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3727
(without)f(equi)n(v)n(ariant)759 2124 y(uni\002cation.)j(In)g(this)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3728
(paper)m(,)g(we)g(gi)n(v)o(e)h(se)n(v)o(eral)f(e)o(xamples)h(of)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3729
FN(\013)p FQ(Prolog)g(programs)h(that)f(do)759 2215 y(not)i(require)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3730
(equi)n(v)n(ariant)h(uni\002cation,)f(de)n(v)o(elop)i(a)e(test)f(for)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3731
(identifying)h(such)g(programs,)759 2307 y(and)e(pro)o(v)o(e)f(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3732
(correctness)h(of)f(this)g(test)f(via)h(a)g(proof-theoretic)h(ar)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3733
(gument.)523 2570 y FL(1)99 b(Intr)n(oduction)523 2755
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3734
y FT(Logic)19 b(programming)e(is)k(particularly)e(suited)h(for)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3735
(implementing)f(inference)h(rules)h(de\002ning)f(re-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3736
2855 y(lations)f(o)o(v)o(er)e(terms.)i(Man)o(y)f(interesting)f(e)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3737
(xamples)h(of)h(such)f(inference)f(rules,)i(ho)n(we)n(v)o(er)m(,)d(in)m
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3738
(v)n(olv)o(e)523 2954 y(terms)28 b(with)g(binders)f(and)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3739
FK(\013)p FT(-equi)n(v)n(alence,)e(for)h(which)h(Prolog,)f(for)g(e)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3740
(xample,)f(pro)o(vides)h(little)523 3054 y(assistance.)h(In)f([3])f(we)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3741
i(presented)e FK(\013)p FT(Prolog)o(,)h(which)g(is)h(designed)e(to)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3742
(simplify)g(programming)523 3153 y(with)g(binders.)f(F)o(or)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3743
(instance,)g(the)h(operation)e(of)i(capture-a)n(v)n(oiding)c
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3744
(substitution)j(for)g FK(\025)p FT(-terms)523 3253 y(can)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3745
b(be)g(implemented)e(in)j FK(\013)p FT(Prolog)e(as)i(follo)n(ws:)529
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3746
3395 y FP(id\(X,X\).)529 3510 y(subst\(var\(X\),X,T,T\).)529
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3747
3601 y(subst\(var\(X\),Y,T,var\(X\)\))253 b(:-)23 b(not\(id\(X,Y\)\).)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3748
529 3693 y(subst\(app\(M,N\),X,T,app\(M',N'\)\))-17 b(:-)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3749
b(subst\(M,X,T,M'\),)10 b(subst\(N,X,T,N'\).)529 3784
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3750
y(subst\(lam\(a.M\),X,T,lam\(a.M'\)\))28 b(:-)23 b(a)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3751
b(#)f(T,)g(a)g(#)h(X,)f(subst\(M,X,T,M'\).)523 3928 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3752
FT(where)21 b(the)h(terms)g FJ(var\(X\))p FT(,)f FJ(app\(M,N\))g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3753
FT(and)g FJ(lam\(a.M\))g FT(encode)g(v)n(ariables,)g(applications)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3754
4028 y(and)26 b FK(\025)p FT(-abstractions.)f(The)g(predicate)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3755
FJ(subst\(E,X,T,E'\))f FT(de\002ned)h(by)h(the)g(clauses)g(holds)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3756
4127 y(only)f(if)h FJ(E')g FT(contains)f(the)h(result)f(of)h(the)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3757
(usual)h(capture-a)n(v)n(oiding)d(substitution)h FJ(E[X:=T])h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3758
FT(in)523 4227 y(the)20 b FK(\025)p FT(-calculus.)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3759
4327 y(T)-7 b(w)o(o)29 b(features)g(of)h FK(\013)p FT(Prolog)f(are)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3760
(immediately)f(visible)i(to)g(the)f(user)-5 b(.)30 b(First,)g(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3761
(term)f(lan-)523 4426 y(guage)c(includes)h(the)h(term-constructor)c
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3762
FI(\000)p FK(:)p FI(\000)j FT(for)g(forming)e(abstractions,)i(which)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3763
(are)g(used)g(to)523 4526 y(encode)20 b(binding.)f(Second,)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3764
FK(\013)p FT(Prolog)h(has)g(a)h(freshness-predicate,)c(written)j(as)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3765
FI(\000)p FJ(#)p FI(\000)p FT(,)e(b)n(uilt)i(into)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3766
4625 y(the)29 b(language;)e(this)j(predicate)e(ensures)g(that)h(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3767
(name)g(does)f(not)h(occur)f(freely)g(in)h(a)h(term)e(\(by)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3768
4725 y(a)h(name)f(we)h(mean)f(lo)n(wer)n(-case)g(symbols,)g(for)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3769
(instance)g FJ(a)h FT(in)f(the)h(e)o(xpression)e FJ(lam\(a.M\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3770
FT(\).)523 4825 y(In)e(this)h FJ(subst)p FT(-program,)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3771
b(the)k(freshness-predicate)e(is)j(used)f(to)h(mak)o(e)e(sure)h(that)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3772
(no)f(v)n(ariable)523 4924 y(capture)19 b(occurs)h(inside)g(the)g(term)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3773
g(being)f(substituted.)p eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3774
%%Page: 2 2
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3775
TeXDict begin 2 1 bop 648 448 a FT(T)-7 b(o)23 b(illustrate)g(ho)n(w)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3776
(the)g FJ(subst)p FT(-program)d(calculates)j(the)g(result)h(of)e(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3777
(capture-a)n(v)n(oiding)523 548 y(substitution)19 b FH(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3778
FK(\025b:a)24 b(b)p FH(\)[)p FK(a)f FH(:=)f FK(b)p FH(])p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3779
FT(,)f(we)f(consider)f(the)h(query:)1023 732 y FP
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3780
(subst\(lam\(b.app\(var\(a\),var\(b\)\),a,var)o(\(b\),R\))396
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3781
b FT(\(1\))523 916 y(T)-7 b(o)20 b(solv)o(e)g(this)h(query)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3782
b(,)18 b FK(\013)p FT(Prolog)i(uni\002es)g(it)h(with)f(the)g(head)g(of)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3783
g(the)g(fourth)f FJ(subst)p FT(-clause)530 1100 y FP(subst\(lam\(a)1025
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3784
1108 y FR(1)1057 1100 y FP(.M)1147 1108 y FR(1)1182 1100
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3785
y FP(\))-12 b(,X)1305 1108 y FR(1)1338 1100 y FP(,)g(T)1416
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3786
1108 y FR(1)1450 1100 y FP(,)g(lam\(a)1708 1108 y FR(1)1741
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3787
1100 y FP(.M')1850 1108 y FR(1)1885 1100 y FP(\)\))g(:-)18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3788
b(a)2116 1108 y FR(1)2151 1100 y FP(#)12 b(T)2253 1108
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3789
y FR(1)2287 1100 y FP(,a)2377 1108 y FR(1)2412 1100 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3790
FP(#)g(X)2514 1108 y FR(1)2548 1100 y FP(,subst\(M)2908
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3791
1108 y FR(1)2942 1100 y FP(,X)3032 1108 y FR(1)3066 1100
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3792
y FP(,)-12 b(T)3144 1108 y FR(1)3178 1100 y FP(,M')3287
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3793
1108 y FR(1)3321 1100 y FP(\))g(.)523 1284 y FT(where,)15
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3794
b(as)j(in)e(Prolog,)f(the)h(v)n(ariables)g FJ(M)p FT(,)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3795
FJ(X)p FT(,)h FJ(T)f FT(and)g FJ(M')h FT(ha)n(v)o(e)e(been)h(replaced)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3796
(with)h(fresh)g(v)n(ariables)523 1384 y(\(indicated)i(by)h(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3797
(subscript\),)f(and)h(also)h(the)f(name)g FJ(a)g FT(has)h(been)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3798
(freshened)e(\(we)i(shall)h(return)e(to)523 1484 y(the)f(dif)n(ference)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3799
f(between)g(v)n(ariables)h(and)g(names)g(later\).)g(The)g(uni\002er)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3800
(that)g FK(\013)p FT(Prolog)g(calculates)h(is)523 1583
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3801
y FJ(app\(var\(a\),var\(a)1323 1595 y FS(1)1357 1583
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3802
y FJ(\)\))h FT(for)e FJ(M)1641 1595 y FS(1)1678 1583
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3803
y FT(,)h FJ(a)h FT(for)e FJ(X)1951 1595 y FS(1)1988 1583
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3804
y FT(,)i FJ(var\(b\))e FT(for)h FJ(T)2511 1595 y FS(1)2567
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3805
1583 y FT(and)f FJ(lam\(a)2955 1595 y FS(1)2991 1583
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3806
y FJ(.M')3113 1595 y FS(1)3151 1583 y FJ(\))h FT(for)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3807
FJ(R)p FT(.)523 1683 y(Ne)o(xt,)22 b FK(\013)p FT(Prolog)f(checks)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3808
(that)g(the)g(freshness-predicates)e FJ(a)2290 1695 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3809
FS(1)2327 1683 y FJ(#)i(var\(b\))f FT(and)h FJ(a)2913
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3810
1695 y FS(1)2950 1683 y FJ(#)g(a)g FT(hold,)f(and)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3811
1783 y(continues)14 b(unifying)f(the)i(ne)n(w)g(query)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3812
FJ(subst)-14 b(\(app\(var\(a\),)g(var\(a)2700 1795 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3813
FS(1)2720 1783 y FJ(\)\))g(,a,)g(var)g(\(b\),M')3350
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3814
1795 y FS(1)3388 1783 y FJ(\))523 1882 y FT(with)25 b(the)g(third)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3815
FJ(subst)p FT(-clause.)f(Then)g(it)i(uses)f(the)h(\002rst)f(and)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3816
(second)f FJ(subst)p FT(-clause)g(and)h(af-)523 1982
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3817
y(ter)17 b(the)o(y)f(succeed,)g FK(\013)p FT(Prolog)g(returns)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3818
FJ(lam\(a)1878 1994 y FS(1)1914 1982 y FJ(.app\(var\(b\),var\(a)2764
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3819
1994 y FS(1)2798 1982 y FJ(\)\)\))h FT(as)g(the)g(answer)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3820
2082 y(for)j FJ(R)p FT(.)648 2173 y(Another)g(e)o(xample,)h(which)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3821
(illustrates)i(ho)n(w)e(easily)i(inference)d(rules)i(can)g(be)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3822
(implemented)523 2265 y(in)e FK(\013)p FT(Prolog)o(,)h(is)g(the)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3823
(follo)n(wing)f(program)548 2441 y FP(mem\(X,[X|T]\).)548
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3824
2532 y(mem\(X,[Y|T]\))43 b(:-)h(mem\(X,T\).)548 2647
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3825
y(type\(Gamma,var\(X\),T\))87 b(:-)23 b(mem\(\(X,T\),Gamma\).)548
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3826
2739 y(type\(Gamma,app\(M,N\),T\))m(:-)g(type\(Gamma,M,arr\(S,T\)\),)16
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3827
b(type\(Gamma,N,S\))-12 b(.)548 2830 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3828
(type\(Gamma,lam\(x.M\),arr\(S,T\)\))-6 b(:-)6 b(x)h(#)12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3829
b(Gamma,)g(type\([\(x,S\)|Gamma],M,T\))-12 b(.)523 3009
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3830
y FT(implementing)18 b(the)i(usual)g(inference)f(rules)h(for)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3831
(inferring)e(the)i(types)g(of)g FK(\025)p FT(-terms.)535
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3832
3249 y FN(x)h FG(:)g FN(T)32 b FF(2)22 b FN(\000)p 535
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3833
3273 315 4 v 545 3340 a(\000)28 b(.)17 b(x)k FG(:)h FN(T)891
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3834
3289 y(v)s(ar)1103 3253 y(\000)27 b(.)18 b(M)e FG(:)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3835
b FN(S)k FF(!)21 b FN(T)85 b(\000)28 b(.)17 b(N)g FG(:)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3836
b FN(S)p 1103 3273 867 4 v 1341 3340 a(\000)28 b(.)18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3837
b(M)8 b(N)17 b FG(:)k FN(T)2010 3281 y(app)2223 3233
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3838
y(x)f FG(:)i FN(S;)13 b(\000)28 b(.)17 b(M)g FG(:)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3839
b FN(T)85 b FG(\()p FN(x)21 b FF(62)g FN(F)11 b(V)17
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3840
b FG(\()p FN(\000)11 b FG(\)\))p 2223 3272 1019 4 v 2432
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3841
3340 a FN(\000)28 b(.)17 b(\025x:M)g FG(:)k FN(S)26 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3842
FF(!)21 b FN(T)3282 3298 y(l)q(am)523 3550 y FT(Note)j(that,)f(in)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3843
(contrast)f(to)h(for)e(e)o(xample)h FK(\025)p FT(Prolog,)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3844
(abstractions)h(in)h FK(\013)p FT(Prolog)f(bind)g(a)h(concrete)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3845
3650 y(name)i(which)h(is)g FE(not)h FT(restricted)f(to)g(the)f(scope)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3846
(of)f(the)h(abstractions.)f(Therefore)e(it)k(is)g(possible)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3847
3749 y(in)23 b FK(\013)p FT(Prolog)g(to)g(use)h(a)g(name)e(of)h(a)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3848
(binder)e(in)h(the)g(body)f(of)h(the)g(clause,)g(for)g(instance)g(to)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3849
(append)523 3849 y FJ(\(x,S\))f FT(to)g(the)g(conte)o(xt)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3850
FJ(Gamma)i FT(in)g(the)g(third)f FJ(type)p FT(-clause.)f(The)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3851
(implicit)g(side-condition)d(in)523 3949 y(the)i(rule)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3852
FK(l)r(am)g FT(requiring)f(that)h FK(\000)33 b FT(has)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3853
b(no)f(type-assignment)e(for)i FK(x)h FT(is)g(implemented)e(in)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3854
FK(\013)p FT(Prolog)523 4048 y(by)f(the)g(freshness-predicate)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3855
FJ(x#Gamma)p FT(.)648 4140 y(W)-7 b(e)23 b(ha)n(v)o(e)e(implemented)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3856
(a)i(lar)o(ge)f(number)f(of)i(such)g FK(\025)p FT(-calculus)f(e)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3857
(xamples,)g(including)f(type)523 4232 y(systems)26 b(and)e(operational)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3858
f(semantics)i(for)g(System)g(F)-7 b(,)26 b FK(\025\026)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3859
FT(and)f(linear)f FK(\025)p FT(-calculi.)h(Our)g(e)o(xperi-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3860
4323 y(ence)d(from)f(these)h(e)o(xamples)g(suggests)g(that)g(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3861
(combination)e(of)i(concrete)f(names)h(in)g(abstrac-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3862
4414 y(tions)32 b(and)f(the)g(freshness-predicate)e(is)k(v)o(ery)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3863
(useful)h(for)g(programming)e(with)i(binders.)g(One)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3864
4505 y(question,)21 b(ho)n(we)n(v)o(er)m(,)f(might)i(arise:)h(what)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3865
(are)f(the)h(adv)n(antages)e(of)h FK(\013)p FT(Prolog)g(relati)n(v)o(e)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3866
g(to,)g(for)g(e)o(x-)523 4597 y(ample,)29 b FK(\025)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3867
FT(Prolog)f([7],)h(which)g(has)g(both)g FK(\013)p FT(-equi)n(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3868
(alence)e(and)i(capture-a)n(v)n(oiding)d(substitution)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3869
4688 y(b)n(uilt-in)20 b(and)f(the)h(typing)f(rules)i(can)f(be)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3870
(correctly)f(implemented)f(by)i(the)g(tw)o(o)g(clauses:)577
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3871
4847 y FP(\(type)44 b(\(app)h(M)f(N\))h(T\))f(:-)h(type)f(M)h(\(arr)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3872
(S)g(T\),)h(type)f(N)h(S.)577 4938 y(\(type)f(\(lam)h(M\))f(\(arr)g(S)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3873
(T\)\))f(:-)h(\(pi)f(x)p FF(n)p FP(\(type)g(x)h(S)g(=>)f(type)g(\(M)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3874
(x\))f(T\)\).)p eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3875
%%Page: 3 3
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3876
TeXDict begin 3 2 bop 523 448 a FT(\(Notice)19 b(that)g(in)h(this)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3877
(program)d(the)i(typing-conte)o(xt)d(is)21 b(implicitly)e(gi)n(v)o(en)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3878
(by)h(the)g(\223surrounding\224)523 540 y(program-conte)o(xt.)c(This)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3879
b(program-conte)o(xt)c(can)j(be)h(modi\002ed)e(using)i(the)f(uni)n(v)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3880
(ersal)g(quanti\002ca-)523 631 y(tion)25 b(\(i.e.)f FJ(pi)50
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3881
b(x)p FI(n)p FJ(...)p FT(\))24 b(and)g(implications)g(in)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3882
(goal-formulae.)d(Therefore)h(there)h(is)i(no)e(clause)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3883
722 y(for)h(the)g(v)n(ariable)f(case.\))h(W)-7 b(e)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3884
b(\002nd)f(the)g(most)g(important)f(reason)g(in)i(f)o(a)n(v)n(our)e(of)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3885
h FK(\013)p FT(Prolog)f(is)i(that)523 814 y(by)g(ha)n(ving)f(concrete)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3886
(names)i(\(namely)f FJ(x)h FT(in)g(the)g FJ(type)p FT(-e)o(xample\))d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3887
(and)j(freshness-predicates)523 905 y(one)e(can)g(almost)h(directly)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3888
(translate)i(the)f(three)g(typing)f(rules)i(into)f(three)g(clauses)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3889
(and)e(obtain)h(a)523 996 y(correct)19 b(implementation.)e(This)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3890
(should)f(be)h(seen)g(in)g(the)g(conte)o(xt)e(that,)i(despite)g(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3891
(ele)o(gance)e(of)523 1088 y FK(\025)p FT(Prolog,)g(some)h(recent)f(te)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3892
o(xtbooks)f(use)i(\(standard\))e(Prolog)h(for)h(implementing)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3893
(inference)i(rules)523 1179 y(o)o(v)o(er)25 b FK(\025)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3894
FT(-terms.)h(F)o(or)g(e)o(xample)e(one)i(of)g(them)f(presents)h(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3895
(follo)n(wing)f(implementation)f(of)h(the)523 1270 y(typing)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3896
b(rules:)548 1436 y FP(mem\(X,[X|T]\).)548 1527 y(mem\(X,[Y|T]\))43
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3897
b(:-)h(mem\(X,T\).)548 1642 y(type\(Gamma,var\(X\),T\))87
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3898
b(:-)23 b(mem\(\(X,T\),Gamma\).)548 1733 y(type\(Gamma,app\(M,N\),T\))m
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3899
(:-)g(type\(Gamma,M,arr\(S,T\)\),)16 b(type\(Gamma,N,S\))-12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3900
b(.)548 1825 y(type\(Gamma,lam\(X,M\),arr\(S,T\)\))-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3901
b(:-)6 b(type\([\(X)o(,S\)|Ga)o(mma],)o(M,T\))-13 b(.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3902
1996 y FT(which)21 b(calculates)g(the)h FE(wr)l(ong)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3903
FT(type)g(for)g FK(\025)p FT(-terms)g(such)g(as)h FK(\025x:\025x:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3904
FH(\()p FK(x)28 b(x)p FH(\))p FT(.)23 b(Although)c(this)j(prob-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3905
2096 y(lem)h(can)g(be)f(\002x)o(ed)h(by)f(judicious)g(use)h(of)g(cut)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3906
(or)f(side-ef)n(fects,)g(\002rst-order)f(terms)i(of)g(Prolog)f(are)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3907
2195 y(unwieldy)j(for)g(implementing)f(relations)h(o)o(v)o(er)f(syntax)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3908
i(with)g(binders)f(correctly)-5 b(.)23 b(On)j(the)g(other)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3909
2295 y(hand,)20 b FK(\025)p FT(Prolog)h(does)g(not)h(allo)n(w)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3910
(concrete)f(names)h(as)i(binders)d(and)h(therefore)f(operations)g(such)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3911
523 2394 y(as)g(adding)e(the)i(type)f(for)g FJ(x)g FT(to)h(the)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3912
(typing-conte)o(xt)d(need)j(to)h(be)f(encoded)f(using)h(uni)n(v)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3913
(ersal)f(quan-)523 2494 y(ti\002cation,)i(implications)f(in)h(goals)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3914
(and)g(beta-reduction.)648 2596 y(The)30 b FK(\013)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3915
FT(Prolog)h(language)e(is)j(based)f(on)f(nominal)g(terms)h(and)g(uses)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3916
(the)h(nominal)d(uni\002ca-)523 2696 y(tion)f(algorithm)e(of)i(Urban,)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3917
(Pitts,)i(and)e(Gabbay)g([9],)g(which)h(calculates)g(\(most)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3918
(general\))e(uni-)523 2795 y(\002ers)j(modulo)d FK(\013)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3919
FT(-equi)n(v)n(alence.)h(F)o(or)g(e)o(xample,)g(the)h(query)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3920
FJ(?-)14 b(id\(a.a,b.X\))27 b FT(is)i(solv)o(ed)e(in)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3921
2895 y FK(\013)p FT(Prolog)e(by)g(the)h(capturing)e(substitution)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3922
FH([)p FJ(X)33 b FH(:=)g FJ(b)p FH(])26 b FT(since)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3923
FJ(a.a)f FT(and)g FJ(b.b)h FT(are)f FK(\013)p FT(-equi)n(v)n(alent.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3924
2995 y(Ho)n(we)n(v)o(er)m(,)e(nominal)g(uni\002cation)h(is)i(not)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3925
(enough)f(to)i(mak)o(e)g(the)g(programs)e(gi)n(v)o(en)g(earlier)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3926
(func-)523 3094 y(tion)e(as)g(intended.)e(F)o(or)h(this)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3927
FK(\013)p FT(Prolog)e(generates)g(fresh)g(names)g(during)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3928
(proof-search.)f(As)j(seen)523 3194 y(abo)o(v)o(e,)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3929
b(before)f(a)j(query)e(is)j(uni\002ed)d(with)i(the)f(fourth)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3930
FJ(subst)p FT(-clause,)g FK(\013)p FT(Prolog)h(generates)f(a)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3931
3293 y(fresh)17 b(name)h(for)f FJ(a)p FT(.)h(This)g(ensures)g(that)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3932
(substitutions)h(can)f(al)o(w)o(ays)i(be)f(\223pushed\224)e(under)g(a)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3933
(binder)523 3393 y(without)h(risk)g(of)g(capture.)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3934
3487 y(While)25 b(in)g([3])f(we)h(ha)n(v)o(e)f(described)f(our)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3935
(implementation)f(of)h FK(\013)p FT(Prolog)o(,)h(its)h(beha)n(viour)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3936
(can)523 3578 y(be)18 b(justi\002ed)g(in)g(terms)f(of)h(nominal)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3937
(logic)i([8,)13 b(2].)k(F)o(or)g(instance,)g(the)h(generation)e(of)i(a)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3938
g(fresh)f(name)523 3669 y(can)23 b(be)g(e)o(xpressed)e(in)i(terms)g(of)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3939
g(the)1686 3669 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3940
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3941
 1686 3669 a FD(N)1686 3669 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3942
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3943
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3944
 1686 3669
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3945
a FT(-quanti\002er)f(of)g(nominal)g(logic,)g(and)g(an)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3946
FK(\013)p FT(Prolog)f(clause)523 3761 y FJ(A)50 b(:-)f(B1,..,Bn)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3947
b FT(can)15 b(vie)n(wed)g(as)h(the)f(formula)2125 3761
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3948
y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3949
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3950
 2125 3761 a FD(N)2125 3761 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3951
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3952
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3953
 2125 3761 a FK(a)2169
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3954
3773 y FS(1)2207 3761 y FK(::a)2297 3773 y FC(n)2342
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3955
3761 y FK(:)p FI(8)p FK(X)2480 3773 y FS(1)2517 3761
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3956
y FK(::X)2632 3773 y FC(n)2677 3761 y FK(:B)2763 3773
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3957
y FS(1)2800 3761 y FI(^)q(\001\001^)p FK(B)3020 3773
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3958
y FC(n)3065 3761 y FI(\033)p FK(A)p FT(,)h(where)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3959
3852 y(the)24 b FK(X)718 3864 y FC(i)769 3852 y FT(and)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3960
FK(a)957 3864 y FC(i)1009 3852 y FT(are)g(the)g(v)n(ariables,)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3961
(respecti)n(v)o(ely)f(names,)h(in)g(the)h(clause.)f(The)g(problem)f(is)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3962
i(that)523 3943 y(the)k(generation)f(of)h(fresh)f(names)h(is)i(more)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3963
(subtle)h(in)h FK(\013)p FT(Prolog)f(than)f(the)i(usual)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3964
(\223freshening\224)523 4035 y(of)c(v)n(ariables)f(when)g(backchaining)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3965
f(a)i(Prolog-clause.)e(The)i(reason)f(is)i(that)f(distinct)g(names)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3966
(are)523 4126 y(al)o(w)o(ays)29 b(considered)d(to)j(denote)e(dif)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3967
(ferent)g(v)n(alues.)g(Consider)h(the)g(clause)h FI(8)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3968
FJ(X.p\(X\))f FT(and)f(the)523 4217 y(query)19 b FJ(p\(b\))h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3969
FT(written)g(as)h(a)f(sequent)g(as)h(follo)n(ws)1650
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3970
4386 y FF(8)p FP(X.p\(X\))44 b FF(`)g FP(p\(b\))1040
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3971
b FQ(\(2\))523 4555 y FT(When)27 b(constructing)f(a)h(proof)f(for)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3972
(\(2\),)f(Prolog)g(generates)h(a)h(fresh)e(name)h(for)g(the)g(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3973
(ariable)f FJ(X)p FT(,)523 4646 y(say)h FJ(X')p FT(,)g(and)g(then)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3974
(uni\002es)i FJ(p\(X'\))e FT(and)h FJ(p\(b\))g FT(gi)n(ving)e(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3975
(solution)g FJ([X':=b])p FT(.)f(A)h(similar)523 4737
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3976
y FK(\013)p FT(Prolog)o(-clause)21 b(that)g(has)h(a)g(name)f(in)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3977
(place)g(of)g(the)h(v)n(ariable)e(beha)n(v)o(es)g(dif)n(ferently:)g(if)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3978
h(we)h(ha)n(v)o(e)523 4829 y(the)e(sequent)1699 4924
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3979
y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3980
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3981
 1699 4924 a FB(N)1699 4924 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3982
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3983
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3984
 1699 4924 a FP(a.p\(a\))43
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3985
b FF(`)i FP(p\(b\))1034 b FQ(\(3\))p eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3986
%%Page: 4 4
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3987
TeXDict begin 4 3 bop 523 448 a FT(with)22 b(the)h(clause)1108
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3988
448 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3989
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3990
 1108 448 a FD(N)1108 448 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3991
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3992
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3993
 1108 448 a FJ(a.p\(a\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3994
FT(,)e(then)h(\223freshening\224)e FJ(a)j FT(to)f FJ(a')g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3995
FT(leads)h(to)f(the)g(uni\002cation)f(problem)523 540
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3996
y FJ(p\(a'\))p FI(\031)o FH(?)p FJ(p\(b\))p FT(.)15 b(Since)h(nominal)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3997
(uni\002cation)h(treats)h(names)f(as)h(distinct)g(constants,)f(this)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3998
(prob-)523 631 y(lem)24 b(is)h(unsolv)n(able.)c(\(T)m(reating)i(names)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  3999
(as)h(distinct)g(constants)g(is)g(important,)e(because)h(treating)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4000
722 y(them)c(as)i(substitutable)d(entities)i(w)o(ould)f(break)g(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4001
(most-general)d(uni\002er)i(property)e(of)j(nominal)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4002
814 y(uni\002cation,)c(see)i([9].\))e(On)i(the)f(other)g(hand,)f(\(3\))
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4003
h FE(is)h FT(pro)o(v)n(able)d(in)j(nominal)e(logic.)h(This)h(is)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4004
(because)523 905 y(after)26 b(freshening)d FJ(a)k FT(to)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4005
FJ(a')g FT(one)f(can)h(in)g(nominal)e(logic)i(apply)e(the)i(equi)n(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4006
(ariance)e(principle\227)523 996 y(e)o(xpressed)19 b(as)i(an)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4007
(inference)f(rule)1519 966 y FA(3)1718 1085 y FN(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4008
Fz(\001)o FN(B)t(;)13 b(\000)32 b FF(\))21 b FN(C)p 1718
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4009
1120 405 4 v 1753 1187 a(B)t(;)13 b(\000)32 b FF(\))21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4010
b FN(C)2164 1136 y(\031)523 1337 y FT(where)26 b FK(\031)k
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4011
FT(is)d(a)g(permutation)d(of)i(names,)f FK(B)t FT(,)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4012
FK(C)33 b FT(stand)26 b(for)g(formulae)e(and)i FK(\000)38
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4013
b FT(for)26 b(a)g(multiset)h(of)523 1437 y(formulae.)18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4014
b(This)i(means)f(if)h(the)g FE(full)g FT(Horn-fragment)c(of)j(nominal)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4015
(logic)g(were)g(used)h(as)g(the)g(basis)523 1537 y(of)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4016
FK(\013)p FT(Prolog)o(,)h(then)f(we)h(need)f(equi)n(v)n(ariant)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4017
(uni\002cation)i(for)f(complete)h(proof)f(search.)h(Equi)n(v)n(ariant)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4018
523 1636 y(uni\002cation)30 b(solv)o(es)h(a)h(problem)d(not)i(just)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4019
(by)f(\002nding)f(a)h(substitution)g(b)n(ut)g(also)g(by)g(\002nding)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4020
(a)523 1736 y(permutation;)18 b(for)i(e)o(xample)e(in)j(\(3\))e(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4021
(identity)e(substitution)g(and)h(the)g(permutation)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4022
FJ(\(a')49 b(b\))p FT(.)648 1841 y(The)31 b(second)h(author)f(has)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4023
(sho)n(wn)g(in)g([1])g(that)g(equi)n(v)n(ariant)e(uni\002cation)h(and)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4024
(equi)n(v)n(ariant)523 1941 y(matching)17 b(problems)f(are)i(NP-hard.)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4025
(F)o(or)i(proof-search)d(in)j FK(\013)p FT(Prolog)f(this)i(means)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4026
(that)i(one)e(needs)523 2040 y(to)g(guess)g(which)f(permutation)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4027
FK(\031)21 b FT(leads)c(to)f(a)h(proof.)e(Ho)n(we)n(v)o(er)m(,)g(in)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4028
(e)o(xperimenting)c(with)k FK(\013)p FT(Prolog)523 2140
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4029
y(we)29 b(found)e(that)h(such)g(guessing)g(is)h(ne)n(v)o(er)f(needed)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4030
(in)h(the)h(programs)d(we)j(considered.)e(In)h(this)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4031
2240 y(paper)e(we)i(identify)e(a)h(class)h(of)f(nominal)f(Horn-clause)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4032
(programs)h(for)g(which)h(the)g FK(\031)s FT(-rule)g(can)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4033
2339 y(be)k(eliminated)f(from)f(deductions)h(\(this)h(is)g(the)g(place)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4034
g(where)f(equi)n(v)n(ariant)f(uni\002cation)g(prob-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4035
2439 y(lems)20 b(arise\),)e(and)h(thus)g(nominal)f(uni\002cation)f(is)k
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4036
(complete)d(for)g(proof-search.)e(In)j(order)f(to)h(sho)n(w)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4037
2539 y(this)30 b(result,)f(we)g(introduce)e(a)j FE(well-formedness)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4038
FT(condition)e(which)i(guarantees)f(that)h(nominal)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4039
2638 y(uni\002cation-based)18 b(proof)h(search)g(is)j(complete.)d(This)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4040
h(condition)f(roughly)f(says)j(that)f(a)h(clause)g(is)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4041
2738 y(\223insensiti)n(v)o(e\224)e(to)i(the)f(particular)f(choice)g(of)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4042
h(names)g(occurring)e(in)i(it.)648 2843 y(Some)c(programs)g(do)g(not)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4043
(satisfy)g(this)h(condition.)d(F)o(or)i(e)o(xample,)e(in)i(the)g(follo)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4044
n(wing)f(program)523 2943 y(calculating)j(a)i(list)g(of)f(bound)e(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4045
(ariables)i(of)g(a)g FK(\025)p FT(-term,)g(the)g(last)h(clause)f(is)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4046
FE(not)f FT(well-formed.)659 3100 y FP(bv\(var\(X\),[]\).)659
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4047
3191 y(bv\(app\(E1,E2\),L\))110 b(:-)23 b(bv\(E1,L1\),)43
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4048
b(bv\(E2,L2\),)h(append\(L1,L2,L\).)659 3283 y(bv\(lam\(x.E\),[x|L]\))
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4049
20 b(:-)j(bv\(E,L\).)523 3442 y FT(In)30 b(the)g(last)g(clause,)g(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4050
(result)g(accumulated)e(in)i(the)g(second)f(ar)o(gument)e(depends)i(on)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4051
g(which)523 3542 y(name)j(is)i(chosen)e(for)h(the)g(binder)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4052
FJ(x)p FT(.)j(In)e(contrast,)g(the)h(names)g(chosen)f(in)h(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4053
FJ(subst)g FT(and)523 3641 y FJ(type)21 b FT(e)o(xample)e(do)i(not)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4054
(matter)h(\(up)f(to)h FK(\013)p FT(-equi)n(v)n(alence\))d(and)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4055
(therefore)f(will)j(satisfy)f(our)f(well-)523 3741 y(formedness)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4056
(condition.)648 3846 y(The)25 b(e)o(xistence)g(of)g(a)h(tri)n(vial)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4057
(syntactic)h(criterion)e(for)h(deciding)f(when)h(a)h(clause)g(is)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4058
(\223insen-)523 3946 y(siti)n(v)o(e\224)c(to)g(the)h(choice)e(of)h(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4059
(name)g(seems)g(unlik)o(ely)-5 b(.)21 b(Consider)m(,)g(for)g(e)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4060
(xample,)g(allo)n(wing)g(names)523 4046 y(to)27 b(only)f(occur)g(bound)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4061
g(or)g(in)i(binding)d(position\227then)g(the)i FJ(type)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4062
FT(-program)d(w)o(ould)i(be)h(ruled)523 4145 y(out)c(since)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4063
FJ(x)g FT(occurs)f(free)h(in)g(the)g(body)f(of)g(the)h(clause.)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4064
(Restricting)g(free)g(names)f(to)h(occur)f(only)523 4245
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4065
y(in)i(the)f(body)f(of)h(a)h(clause)f(w)o(ould)g(permit)f(the)i(clause)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4066
f FJ(r\(X\):-id\(X,a\))f FT(which)g FE(is)j FT(sensiti)n(v)o(e)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4067
4344 y(to)h(the)g(choice)f(of)h FJ(a)h FT(since)f FJ(id)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4068
FT(\223propagates\224)d(the)j(choice)g(for)f(the)h(name)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4069
FJ(a)i FT(back)e(to)h(the)g(head)523 4444 y(of)20 b(the)h(clause)g(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4070
FJ(id)f FT(is)i(de\002ned)d(in)i(the)g FJ(subst)p FT(-e)o(xample\).)c
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4071
(Our)j(well-formedness)f(condition)g(is)523 4544 y(therefore)h(more)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4072
(subtle;)h(it)g(is)h(a)f(test)g(whether)f(a)h(certain)g(matching)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4073
(problem)g(deri)n(v)o(ed)g(from)g(the)523 4643 y(clause)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4074
b(is)h(solv)n(able.)d(Despite)i(being)f(technically)g(relati)n(v)o(ely)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4075
f(comple)o(x,)g(well-formedness)g(can)523 4743 y(be)c(automatically)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4076
(v)o(eri\002ed.)p 523 4837 473 4 v 558 4893 a Fy(3)606
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4077
4924 y FQ(The)g(corresponding)i(right-rule)e(has)g(been)h(sho)n(wn)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4078
(to)f(be)g(admissible)g(in)g(nominal)h(logic)f(in)g([5].)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4079
eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4080
%%Page: 5 5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4081
TeXDict begin 5 4 bop 648 448 a FT(The)31 b(paper)f(is)i(or)o(ganised)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4082
(as)j(follo)n(ws:)f(Section)g(2)h(describes)f(nominal)f(terms,)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4083
(formulae)523 548 y(and)f(the)h(inference)e(rules)i(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4084
FK(\013)p FT(Prolog)o(')-5 b(s)31 b(proof-search)d(procedure.)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4085
(Section)j(3)g(introduces)e(a)523 648 y(well-formedness)j(condition)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4086
(for)i(clauses)h(and)f(sho)n(ws)h(that)g(the)f FK(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4087
FT(-rule)g(can)h(be)f(eliminated)523 747 y(from)f(proofs)f(in)m(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4088
(olving)f(only)i(well-formed)e(clauses.)j(Section)f(4)h(describes)f(ho)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4089
n(w)g(the)g(well-)523 847 y(formedness)19 b(condition)h(can)g(be)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4090
(automatically)f(v)o(eri\002ed.)f(Section)i(5)g(concludes)f(and)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4091
(describes)523 946 y(future)f(w)o(ork.)523 1212 y FL(2)99
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4092
b(T)-9 b(erms,)26 b(F)n(ormulae)e(and)i(Pr)n(oof-Sear)n(ch)g(Rules)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4093
1404 y FT(The)e(terms)h(used)g(in)g FK(\013)p FT(Prolog)f(are)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4094
FE(nominal)e(terms)j FT(\(see)f([9])f(for)g(more)g(details\))h(as)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4095
(de\002ned)f(by)523 1495 y(the)c(grammar:)1414 1586 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4096
FN(t)h FG(::=)h FN(a)f FF(j)h FN(\031)s Fz(\001)o FN(X)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4097
b FF(j)21 b(hi)g(j)h(h)p FN(t;)13 b(t)p FF(i)21 b(j)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4098
FN(a:t)g FF(j)h Fx(f)p FG(\()p FN(t)p FG(\))523 1719
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4099
y FT(where)i FK(a)i FT(is)g(a)f(name,)f FK(X)32 b FT(a)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4100
b(v)n(ariable,)f Fw(f)h FT(a)g(function)f(symbol)g(and)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4101
FK(\031)29 b FT(a)c(permutation)e(e)o(xpressed)523 1819
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4102
y(as)g(a)f(list)h(of)e(sw)o(appings)g FH(\()p FK(a)1337
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4103
1831 y FS(1)1389 1819 y FK(b)1425 1831 y FS(1)1462 1819
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4104
y FH(\))14 b FI(\001)g(\001)g(\001)f FH(\()p FK(a)1694
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4105
1831 y FC(n)1754 1819 y FK(b)1790 1831 y FC(n)1834 1819
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4106
y FH(\))p FT(.)23 b(W)-7 b(e)23 b(ha)n(v)o(e)e(the)h(operations)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4107
FI(\000)p FH(@)p FI(\000)h FT(and)g FH(\()p FI(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4108
FH(\))3196 1789 y Fv(\000)p FS(1)3308 1819 y FT(for)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4109
1919 y(composing)g(\(list)i(concatenation\))e(tw)o(o)i(permutations)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4110
(and)h(in)m(v)o(erting)f(\(list)i(re)n(v)o(ersal\))f(a)h(permu-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4111
2018 y(tation,)30 b(respecti)n(v)o(ely)-5 b(.)28 b(Constants)i(are)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4112
(encoded)d(as)j(function)e(symbols)h(with)g(unit)h(ar)o(guments)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4113
2118 y Fw(f)p FH(\()p FI(hi)p FH(\))p FT(,)22 b(and)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4114
FK(n)p FT(-tuples)f(are)i(encoded)e(by)h(iterated)g(pairs)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4115
FI(h)p FK(t)2214 2130 y FS(1)2252 2118 y FK(;)14 b FI(\001)g(\001)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4116
(\001)f(h)p FK(t)2461 2130 y FC(n)p Fv(\000)p FS(1)2592
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4117
2118 y FK(;)h(t)2659 2130 y FC(n)2704 2118 y FI(ii)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4118
FT(.)21 b(F)o(ollo)n(wing)e([9],)h(we)523 2217 y(refer)f(to)h(terms)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4119
(of)e(the)h(form)f FK(\031)s Fu(\001)p FK(X)27 b FT(as)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4120
b FE(suspensions)p FT(,)e(because)g(the)h(permutation)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4121
FK(\031)24 b FT(is)d(suspended)523 2317 y(in)f(front)g(of)f(a)i(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4122
(ariable)e(w)o(aiting)h(to)g(be)h(applied)e(to)h(a)h(term)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4123
(substituted)f(for)h FK(X)7 b FT(.)648 2408 y(F)o(ormulae)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4124
b(are)i(di)n(vided)f(into)h(goal)g(formulae)e FK(G)k
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4125
FT(and)d(de\002nite)h(\(or)g(program\))d(clauses)k FK(D)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4126
2500 y FT(de\002ned)19 b(as)738 2662 y FN(G)j FG(::=)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4127
FN(p)p FG(\()p FN(t)p FG(\))g FF(j)g FN(G)p FF(^)q FN(G)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4128
FF(j)h FN(G)p FF(_)p FN(G)g FF(j)f(>)173 b FN(B)25 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4129
FG(::=)d FN(G)f FF(\033)g FN(p)p FG(\()p FN(t)p FG(\))172
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4130
b FN(D)24 b FG(::=)2769 2662 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4131
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4132
 2769 2662 a FB(N)2769
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4133
2662 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4134
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4135
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4136
 2769 2662 a Ft(as)7 b FN(:)p FF(8)p Ft(Xs)f FN(:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4137
FF(r)p FN(=B)523 2832 y FT(where)31 b FK(p)p FH(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4138
FK(t)p FH(\))i FT(stands)f(for)f(an)h(atomic)f(predicate)g(with)h(the)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4139
(ar)o(gument)f FK(t)i FT(\(we)g(shall)g(also)g(write)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4140
2932 y FK(A)27 b FT(for)e(such)h(formulae)e(whene)n(v)o(er)g(the)j(ar)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4141
(gument)c(is)k(unimportant\);)d FI(>)p FK(;)14 b FI(^)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4142
FK(;)g FI(_)q FK(;)g FI(\033)26 b FT(are)g(standard)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4143
3031 y(connecti)n(v)o(es;)16 b(and)i FI(r)g FT(is)h(a)f(set)h(of)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4144
(freshness)f(constraints)g(of)h(the)g(form)f FK(a)2644
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4145
3043 y FS(1)2704 3031 y FH(#)23 b FK(X)2865 3043 y FS(1)2902
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4146
3031 y FK(;)14 b(:)g(:)g(:)g(;)g(a)3131 3043 y FC(n)3199
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4147
3031 y FH(#)23 b FK(X)3360 3043 y FC(n)523 3131 y FT(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4148
FK(X)620 3143 y FC(i)676 3131 y FT(and)29 b FK(a)870
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4149
3143 y FC(i)927 3131 y FT(being)e(v)n(ariables)h(and)h(names,)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4150
(respecti)n(v)o(ely\).)e(The)j(intended)e(meaning)g(of)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4151
FI(r)g FT(in)523 3231 y FK(D)r FT(-formulae)22 b(is)j(that)g(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4152
(clause)f(is)h(applicable)e(only)h(if)g(its)h(freshness)f(constraints)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4153
(are)g(satis\002ed.)523 3330 y(F)o(or)c(freshness)f(constraints)h(and)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4154
(quanti\002er)n(-free)e(formulae)g(we)i(shall)h(use)f(the)h(notation)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4155
FK(Q)3230 3342 y Fs(as)5 b FC(;)p Fs(Xs)523 3430 y FT(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4156
FK(Q)22 b FH(::=)h FI(rj)p FK(G)p FI(j)p FK(B)t FT(\))c(to)f(indicate)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4157
(that)h(the)f(terms)h(of)g FK(Q)g FT(are)f(b)n(uilt)h(up)g(from)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4158
(names)i Fr(as)25 b FT(and)17 b(v)n(ariables)523 3530
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4159
y Fr(Xs)31 b FT(\(we)23 b(ha)n(v)o(e)g(the)h(usual)f(con)m(v)o(ention)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4160
(that)j Fr(as)31 b FT(stands)24 b(for)f(lists)i(of)e(names)g(and)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4161
Fr(Xs)31 b FT(for)23 b(lists)i(of)523 3629 y(v)n(ariables;)e(similarly)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4162
1247 3629 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4163
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4164
 1247 3629 a FD(N)1247 3629 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4165
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4166
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4167
 1247 3629 a
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4168
Fr(as)31 b FT(stands)24 b(for)1766 3629 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4169
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4170
 1766 3629 a
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4171
FD(N)1766 3629 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4172
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4173
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4174
 1766 3629 a FK(a)1810 3641 y FS(1)1861
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4175
3629 y FK(:)14 b(:)g(:)2032 3629 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4176
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4177
 2032 3629 a FD(N)2032
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4178
3629 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4179
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4180
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4181
 2032 3629 a FK(a)2076 3641 y FC(n)2145 3629 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4182
FT(and)23 b FI(8)p Fr(Xs)31 b FT(for)22 b FI(8)p FK(X)2697
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4183
3641 y FS(1)2748 3629 y FK(:)14 b(:)g(:)g FI(8)p FK(X)2974
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4184
3641 y FC(n)3019 3629 y FT(\).)24 b(W)-7 b(e)24 b(call)g(a)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4185
3729 y FK(D)r FT(-formula)16 b FE(closed)j FT(when)e(it)i(has)e(no)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4186
(free)h(v)n(ariables)e(and)h(free)h(names,)f(that)g(is)i(the)e(formula)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4187
f(must)523 3828 y(be)24 b(of)g(the)h(form)1093 3828 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4188
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4189
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4190
1093 3828 a FD(N)1093 3828 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4191
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4192
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4193
 1093 3828 a Fr(as)7 b FK(:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4194
FI(8)p Fr(Xs)g FK(:)p FI(r)1440 3840 y Fs(as)e FC(;)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4195
Fs(Xs)1615 3828 y FK(=B)1720 3840 y Fs(as)t FC(;)p Fs(Xs)1894
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4196
3828 y FT(.)25 b(Fig.)f(1)h(sho)n(ws)f(tw)o(o)h(e)o(xamples)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4197
(illustrating)h(ho)n(w)523 3928 y FK(D)r FT(-formulae)18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4198
b(relate)i(to)h(the)f FK(\013)p FT(Prolog)o(-clauses)g(gi)n(v)o(en)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4199
(at)h(the)h(be)o(ginning.)648 4028 y(There)j(is)j(a)e(delicate)h(point)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4200
e(with)i(respect)f(to)h(binding:)d(while)j(in)f(nominal)f(terms)i(the)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4201
(con-)523 4127 y(structor)f FK(a:)p FH(\()p FI(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4202
FH(\))h FT(is)g FE(not)g FT(a)g(binder)e(in)i(the)f(traditional)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4203
(sense)g(\(it)h(only)f FE(acts)g FT(as)h(a)g(binder\),)e(in)h(for)n(-)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4204
523 4227 y(mulae)19 b(the)g(quanti\002ers)1297 4227 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4205
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4206
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4207
1297 4227 a FD(N)1297 4227 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4208
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4209
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4210
 1297 4227 a FK(a:)p FH(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4211
FI(\000)p FH(\))g FT(and)g FI(8)p FK(X)r(:)p FH(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4212
FI(\000)p FH(\))g FT(do)g(bind)f FK(a)h FT(and)g FK(X)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4213
b FT(,)19 b(respecti)n(v)o(ely)-5 b(.)16 b(Therefore)h(we)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4214
4327 y(ha)n(v)o(e)24 b(the)g(usual)g(con)m(v)o(ention)d(that)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4215
(formulae)f(are)h(identi\002ed)g(if)g(the)o(y)g(only)f(dif)n(fer)g(in)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4216
(the)f(names)523 4426 y(of)g(binders)f(\(i.e.)h FI(8)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4217
FK(X)r(:)p FH(\()p FI(\000)p FH(\))g FT(and)1538 4426
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4218
y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4219
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4220
 1538 4426 a FD(N)1538 4426 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4221
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4222
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4223
 1538 4426 a FK(a:)p FH(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4224
FI(\000)p FH(\))p FT(\),)g(and)g(operations)e(on)i(formulae)e(need)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4225
(to)g(respect)g(this)523 4526 y(con)m(v)o(ention.)17
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4226
b(As)k(a)g(result)f(the)h(de\002nition)e(of)h(the)g(permutation)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4227
(operation)h(introduced)f(for)i(nom-)523 4625 y(inal)k(terms)g(in)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4228
([9])g(needs)f(to)h(be)g(e)o(xtended.)e(W)-7 b(e)25 b(de\002ne)f(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4229
(generalised)f(permutation)e(operation)523 4725 y FK(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4230
Fu(\001)600 4737 y Fv(B)649 4725 y FH(\()p FI(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4231
FH(\))27 b FT(that)f(depends)e(on)h(a)i(set)f(of)g(v)n(ariables)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4232
FI(B)s FT(.)g(The)g(permutation)f FK(\031)29 b FT(only)c(acts)i(upon)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4233
(v)n(ari-)523 4825 y(ables)i FE(not)i FT(in)e FI(B)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4234
FT(.)f(Whene)n(v)o(er)g(a)h(permutation)e(is)j(\223pushed\224)e(under)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4235
(a)j FI(8)p FK(X)r(:)p FH(\()p FI(\000)p FH(\))p FT(-quanti\002er)m(,)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4236
(then)523 4924 y FK(X)k FT(is)21 b(added)f(to)h(the)g(set)g(of)g(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4237
(ariables)f(the)g(permutation)f(does)i(not)f(af)n(fect.)g(The)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4238
(de\002nition)g(of)g(the)p eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4239
%%Page: 6 6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4240
TeXDict begin 6 5 bop 523 369 2882 4 v 523 807 4 439
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4241
v 600 457 a FP(subst\(var\(X\),X,T,T\).)600 549 y FF(8)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4242
FN(X)r(;)12 b(T)6 b(:)22 b Fq(?)13 b FN(=)g FF(>)21 b(\033)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4243
FN(s)p FG(\()p Fx(var)p FG(\()p FN(X)6 b FG(\))p FN(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4244
b(X)r(;)f(T)6 b(;)13 b(T)e FG(\))600 664 y FP
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4245
(subst\(lam\(a.M\),X,T,lam\(a.M'\)\))39 b(:-)45 b(a)12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4246
b(#)h(T,)f(a)g(#)g(X,)g(subst\(M,X,T,M'\).)653 755 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4247
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4248
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4249
653 755 a FB(N)653 755 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4250
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4251
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4252
 653 755 a FN(a:)p FF(8)p FN(M)t(;)h(X)r(;)g(T)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4253
6 b(;)14 b(M)1137 723 y Fp(0)1159 755 y FN(:)22 b FF(f)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4254
FN(a)f FG(#)9 b FN(T)d(;)13 b(a)21 b FG(#)9 b FN(X)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4255
FF(g)13 b FN(=)h(s)p FG(\()p FN(M)t(;)e(X)r(;)h(T)6 b(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4256
b(M)2211 723 y Fp(0)2233 755 y FG(\))f FF(\033)g FN(s)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4257
FG(\()p Fx(lam)p FG(\()p FN(a:M)8 b FG(\))p FN(;)13 b(X)r(;)g(T)6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4258
b(;)14 b Fx(lam)p FG(\()p FN(a:M)3246 723 y Fp(0)3269
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4259
755 y FG(\)\))p 3402 807 4 439 v 523 810 2882 4 v 523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4260
953 a FO(Fig)o(.)e(1.)j FQ(T)-6 b(w)o(o)15 b(e)o(xamples)g(sho)n(wing)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4261
(ho)n(w)e FN(\013)p FQ(Prolog)q(-clauses)g(relate)g(to)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4262
FN(D)r FQ(-formulae)g(\()p FN(s)g FQ(is)f(a)h(predicate)h(symbol)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4263
1045 y(standing)k(for)f FP(subst)p FQ(\).)e(W)-6 b(e)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4264
b(ha)o(v)o(e)g(the)g(usual)g(con)m(v)o(ention)i(that)d(clauses)i(stand)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4265
f(for)g(closed)h FN(D)r FQ(-formulae.)p 523 1122 V 523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4266
2297 4 1175 v 567 1211 a FO(T)-7 b(erms:)1069 1234 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4267
FG([])q Fz(\001)1136 1242 y Fp(B)1182 1234 y FN(a)1246
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4268
1191 y FA(def)1253 1234 y FG(=)30 b FN(a)697 1433 y FG(\(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4269
FN(a)798 1441 y FR(1)845 1433 y FN(a)886 1441 y FR(2)920
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4270
1433 y FG(\))21 b(::)h FN(\031)s FG(\))p Fz(\001)1136
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4271
1441 y Fp(B)1182 1433 y FN(a)1246 1390 y FA(def)1253
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4272
1433 y FG(=)1343 1257 y Fo(8)1343 1325 y(>)1343 1347
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4273
y(<)1343 1481 y(>)1343 1504 y(:)1411 1327 y FN(a)1452
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4274
1335 y FR(1)1644 1327 y FQ(if)c FN(\031)s Fz(\001)1779
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4275
1335 y Fp(B)1825 1327 y FN(a)j FG(=)g FN(a)2009 1335
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4276
y FR(2)1411 1436 y FN(a)1452 1444 y FR(2)1644 1436 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4277
FQ(if)d FN(\031)s Fz(\001)1779 1444 y Fp(B)1825 1436
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4278
y FN(a)j FG(=)g FN(a)2009 1444 y FR(1)1411 1546 y FN(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4279
Fz(\001)1483 1554 y Fp(B)1528 1546 y FN(a)75 b FQ(otherwise)1036
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4280
1733 y FN(\031)s Fz(\001)1107 1741 y Fp(B)1153 1733 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4281
FN(X)1246 1690 y FA(def)1253 1733 y FG(=)1343 1605 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4282
Fo(\()1405 1681 y FN(X)152 b FQ(if)19 b FN(X)27 b FF(2)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4283
b(B)1405 1791 y FN(\031)s Fz(\001)o FN(X)81 b FQ(otherwise)2285
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4284
1234 y FN(\031)s Fz(\001)2356 1242 y Fp(B)2401 1234 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4285
FG(\()p FN(\031)2478 1203 y Fp(0)2500 1234 y Fz(\001)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4286
FN(X)6 b FG(\))2647 1191 y FA(def)2654 1234 y FG(=)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4287
b FN(\031)s FG(@)p FN(\031)2899 1203 y Fp(0)2920 1234
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4288
y Fz(\001)p FN(X)2388 1352 y(\031)s Fz(\001)2459 1360
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4289
y Fp(B)2505 1352 y FG(\()p FF(hi)p FG(\))2647 1310 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4290
FA(def)2654 1352 y FG(=)g FF(hi)2229 1470 y FN(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4291
Fz(\001)2300 1478 y Fp(B)2346 1470 y FG(\()p FF(h)p FN(t)2434
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4292
1478 y FR(1)2468 1470 y FN(;)13 b(t)2530 1478 y FR(2)2564
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4293
1470 y FF(i)p FG(\))2647 1428 y FA(def)2654 1470 y FG(=)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4294
b FF(h)p FN(\031)s Fz(\001)2846 1478 y Fp(B)2891 1470
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4295
y FN(t)2919 1478 y FR(1)2954 1470 y FN(;)13 b(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4296
Fz(\001)3059 1478 y Fp(B)3105 1470 y FN(t)3133 1478 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4297
FR(2)3167 1470 y FF(i)2321 1589 y FN(\031)s Fz(\001)2392
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4298
1597 y Fp(B)2438 1589 y FG(\()p Fx(f)p FG(\()p FN(t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4299
FG(\)\))2647 1546 y FA(def)2654 1589 y FG(=)31 b Fx(f)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4300
FG(\()p FN(\031)s Fz(\001)2885 1597 y Fp(B)2931 1589
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4301
y FN(t)p FG(\))2358 1707 y FN(\031)s Fz(\001)2429 1715
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4302
y Fp(B)2475 1707 y FG(\()p FN(a:t)p FG(\))2647 1664 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4303
FA(def)2654 1707 y FG(=)g(\()p FN(\031)s Fz(\001)2846
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4304
1715 y Fp(B)2891 1707 y FN(a)p FG(\))p FN(:)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4305
FN(\031)s Fz(\001)3084 1715 y Fp(B)3130 1707 y FN(t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4306
FG(\))567 1890 y FO(F)n(ormulae:)996 1914 y FN(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4307
Fz(\001)1067 1922 y Fp(B)1113 1914 y FG(\()p FF(>)p FG(\))1255
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4308
1871 y FA(def)1263 1914 y FG(=)f FF(>)930 2032 y FN(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4309
Fz(\001)1001 2040 y Fp(B)1046 2032 y FG(\()p FN(p)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4310
FN(t)p FG(\)\))1255 1989 y FA(def)1263 2032 y FG(=)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4311
FN(p)p FG(\()p FN(\031)s Fz(\001)1492 2040 y Fp(B)1538
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4312
2032 y FN(t)p FG(\))794 2150 y FN(\031)s Fz(\001)865
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4313
2158 y Fp(B)910 2150 y FG(\()p FN(G)1000 2158 y FR(1)1052
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4314
2150 y FN(?)18 b(G)1168 2158 y FR(2)1202 2150 y FG(\))1255
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4315
2107 y FA(def)1263 2150 y FG(=)30 b(\()p FN(\031)s Fz(\001)1454
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4316
2158 y Fp(B)1500 2150 y FN(G)1560 2158 y FR(1)1594 2150
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4317
y FG(\))17 b FN(?)h FG(\()p FN(\031)s Fz(\001)1798 2158
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4318
y Fp(B)1844 2150 y FN(G)1904 2158 y FR(2)1938 2150 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4319
FG(\))1353 2241 y FQ(for)40 b FN(?)22 b FG(::=)f FF(^)q(j_)2200
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4320
1914 y FN(\031)s Fz(\001)2271 1922 y Fp(B)2317 1914 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4321
FG(\()p FN(G)p FF(\033)p FN(A)p FG(\))2577 1871 y FA(def)2585
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4322
1914 y FG(=)30 b(\()p FN(\031)s Fz(\001)2776 1922 y Fp(B)2822
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4323
1914 y FN(G)p FG(\))12 b FF(\033)h FG(\()p FN(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4324
Fz(\001)3098 1922 y Fp(B)3144 1914 y FN(A)p FG(\))2213
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4325
2032 y FN(\031)s Fz(\001)2285 2040 y Fp(B)2330 2032 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4326
FG(\()p FF(r)p FN(=B)t FG(\))2577 1989 y FA(def)2585
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4327
2032 y FG(=)30 b FF(r)p FN(=)p FG(\()p FN(\031)s Fz(\001)2878
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4328
2040 y Fp(B)2924 2032 y FN(B)t FG(\))2196 2150 y FN(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4329
Fz(\001)2267 2158 y Fp(B)2313 2150 y FG(\()2397 2150
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4330
y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4331
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4332
 2397 2150 a FB(N)2397 2150 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4333
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4334
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4335
 2397 2150 a FN(a:D)r FG(\))2577
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4336
2107 y FA(def)2585 2150 y FG(=)2729 2150 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4337
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4338
 2729 2150
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4339
a FB(N)2729 2150 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4340
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4341
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4342
 2729 2150 a FN(a:\031)s Fz(\001)2862
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4343
2158 y Fp(B)2908 2150 y FN(D)2183 2268 y(\031)s Fz(\001)2254
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4344
2276 y Fp(B)2300 2268 y FG(\()p FF(8)p FN(X)r(:D)r FG(\))2577
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4345
2225 y FA(def)2585 2268 y FG(=)g FF(8)p FN(X)r(:\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4346
Fz(\001)2875 2280 y Fp(f)p Fn(X)t Fp(g[B)3080 2268 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4347
FN(D)p 3402 2297 4 1175 v 523 2300 2882 4 v 523 2447
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4348
a FO(Fig)o(.)12 b(2.)20 b FQ(De\002nition)g(of)g(the)g(permutation)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4349
(operation)g FN(\031)s Fz(\001)2004 2455 y Fp(B)2049
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4350
2447 y FG(\()p FF(\000)p FG(\))f FQ(for)g(terms)g(and)g(formulae.)h(In)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4351
f(the)g(clause)h(for)523 2539 y(the)16 b(ne)n(w-quanti\002er)m(,)h(it)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4352
(is)h(assumed)i(that)e FN(a)f FQ(is)h(renamed,)h(so)g(that)f(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4353
(permutation)h FN(\031)i FQ(can)d(safely)h(be)f(pushed)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4354
2630 y(under)k(the)f(binder)g(without)g(capture.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4355
2917 y FT(permutation)d(operation)g(is)k(gi)n(v)o(en)c(in)j(Fig.)f(2.)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4356
(W)-7 b(e)19 b(use)g(the)f(shorthand)e(notation)h FK(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4357
Fu(\001)p FH(\()p FI(\000)p FH(\))i FT(in)f(case)h FI(B)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4358
3016 y FT(is)f(the)f(empty)f(set.)h(This)g(is)h(a)f(generalisation)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4359
(of)i(the)f(permutation)f(action)h(gi)n(v)o(en)g(in)h([9];)f(ho)n(we)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4360
(v)o(er)m(,)523 3116 y(when)25 b(a)g(permutation)e(acts)j(on)e(a)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4361
(formula)d(with)j(quanti\002ers,)e(it)h(acts)h(only)e(on)h(the)g(free)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4362
(names)523 3215 y(and)20 b(free)f(v)n(ariables.)648 3307
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4363
y(Similar)j(problems)e(arise)i(in)h(the)f(de\002nition)e(of)i(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4364
(substitution)f(operation\227with)f(respect)523 3398
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4365
y(to)g(the)f(abstractions)g FK(a:)p FH(\()p FI(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4366
FH(\))h FT(substitution)f(is)h(possibly-capturing,)c(whereas)j(with)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4367
(respect)f(to)g(the)583 3489 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4368
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4369
 583 3489 a FD(N)583 3489
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4370
y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4371
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4372
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4373
 583 3489 a FT(-)29 b(and)e FI(8)p FT(-quanti\002er)g(it)i(must)g(be)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4374
(capture-a)n(v)n(oiding.)d(F)o(or)j(terms)g(we)h(can)f(use)g(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4375
(de\002nition)523 3581 y(gi)n(v)o(en)e(in)i([9]:)e(a)i(substitution)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4376
FK(\033)k FT(is)d(a)g(function)e(from)g(v)n(ariables)h(to)g(terms)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4377
(with)f(the)h(property)523 3672 y(that)e FK(\033)s FH(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4378
FK(X)7 b FH(\))34 b(=)g FK(X)g FT(for)25 b(all)i(b)n(ut)g(\002nitely)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4379
(man)o(y)f(v)n(ariables)h FK(X)7 b FT(.)26 b(If)g(the)g(domain)f(of)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4380
FK(\033)j FT(consists)d(of)523 3763 y(distinct)e(v)n(ariables)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4381
FK(X)1185 3775 y FS(1)1222 3763 y FK(;)14 b(:)g(:)g(:)g(;)g(X)1476
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4382
3775 y FC(n)1546 3763 y FT(and)24 b FK(\033)s FH(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4383
FK(X)1842 3775 y FC(i)1871 3763 y FH(\))32 b(=)f FK(t)2061
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4384
3775 y FC(i)2114 3763 y FT(for)25 b FK(i)31 b FH(=)g(1)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4385
b FK(:)g(:)g(:)f(n)p FT(,)25 b(we)h(sometimes)e(write)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4386
FK(\033)523 3855 y FT(as)20 b FH([)p FK(X)704 3867 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4387
FS(1)764 3855 y FH(:=)j FK(t)905 3867 y FS(1)942 3855
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4388
y FK(;)14 b(:)g(:)g(:)g(;)g(X)1196 3867 y FC(n)1264 3855
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4389
y FH(:=)23 b FK(t)1405 3867 y FC(n)1450 3855 y FH(])p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4390
FT(.)d(Moreo)o(v)o(er)m(,)c(we)k(shall)g(write)f FK(\033)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4391
FH(\()p FK(t)p FH(\))i FT(for)e(the)h(result)f(of)g(applying)f(a)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4392
3946 y(substitution)h FK(\033)24 b FT(to)c(a)g(term)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4393
FK(t)p FT(;)i(this)f(is)h(the)f(term)f(obtained)g(from)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4394
FK(t)j FT(by)e(replacing)f(each)i(v)n(ariable)f FK(X)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4395
4037 y FT(by)24 b(the)g(term)f FK(\033)s FH(\()p FK(X)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4396
b FH(\))25 b FT(and)e(each)h(suspension)f FK(\031)s Fu(\001)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4397
FK(X)30 b FT(in)25 b FK(t)f FT(by)g(the)g(term)f FK(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4398
Fu(\001)p FK(\033)s FH(\()p FK(X)7 b FH(\))25 b FT(got)e(by)h(letting)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4399
FK(\031)523 4129 y FT(act)d(on)e(the)i(term)f FK(\033)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4400
FH(\()p FK(X)7 b FH(\))p FT(.)20 b(This)h(de\002nition)e(is)i(e)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4401
(xtended)d(to)i(formulae)f(as)i(follo)n(ws:)1160 4327
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4402
y FN(\033)s FG(\()p FF(>)p FG(\))1349 4284 y FA(def)1356
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4403
4327 y FG(=)30 b FF(>)1093 4445 y FN(\033)s FG(\()p FN(p)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4404
FG(\()p FN(t)p FG(\)\))1349 4402 y FA(def)1356 4445 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4405
FG(=)g FN(p)p FG(\()p FN(\033)s FG(\()p FN(t)p FG(\)\))957
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4406
4563 y FN(\033)s FG(\()p FN(G)1094 4571 y FR(1)1146 4563
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4407
y FN(?)17 b(G)1261 4571 y FR(2)1296 4563 y FG(\))1349
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4408
4520 y FA(def)1356 4563 y FG(=)30 b FN(\033)s FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4409
FN(G)1583 4571 y FR(1)1618 4563 y FG(\))17 b FN(?)g(\033)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4410
FG(\()p FN(G)1857 4571 y FR(2)1891 4563 y FG(\))1520
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4411
4654 y FQ(for)i FN(?)i FG(::=)h FF(^j_)2150 4313 y FN(\033)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4412
FG(\()p FN(G)p FF(\033)p FN(A)p FG(\))2457 4271 y FA(def)2465
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4413
4313 y FG(=)30 b FN(\033)s FG(\()p FN(G)p FG(\))12 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4414
FF(\033)h FN(\033)s FG(\()p FN(A)p FG(\))2164 4431 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4415
FN(\033)s FG(\()p FF(r)p FN(=B)t FG(\))2457 4389 y FA(def)2465
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4416
4431 y FG(=)30 b FN(\033)s FG(\()p FF(r)p FG(\))p FN(=\033)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4417
FG(\()p FN(B)t FG(\))2146 4549 y FN(\033)s FG(\()2277
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4418
4549 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4419
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4420
 2277 4549 a FB(N)2277 4549 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4421
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4422
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4423
 2277 4549 a FN(a:D)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4424
FG(\))2457 4507 y FA(def)2465 4549 y FG(=)2609 4549 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4425
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4426
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4427
2609 4549 a FB(N)2609 4549 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4428
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4429
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4430
 2609 4549 a FN(a:\033)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4431
FG(\()p FN(D)r FG(\))2133 4668 y FN(\033)s FG(\()p FF(8)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4432
FN(X)r(:D)r FG(\))2457 4625 y FA(def)2465 4668 y FG(=)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4433
FF(8)p FN(X)r(:\033)s FG(\()p FN(D)r FG(\))523 4825 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4434
FT(with)c(the)h(pro)o(viso)d(that)j(the)f(quanti\002ed)f(names)h(and)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4435
(v)n(ariables)f(are)h(suitably)g(renamed)f(so)h(that)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4436
4924 y(no)33 b(capturing)e(is)j(possible.)e(F)o(or)g(e)o(xample,)g(if)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4437
FK(\033)50 b FH(=)c([)p FK(X)53 b FH(:=)47 b FI(h)p FK(a;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4438
b(Y)k FI(i)p FH(])34 b FT(and)f FK(t)46 b FH(=)g FK(a:X)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4439
b FT(,)33 b(then)p eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4440
%%Page: 7 7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4441
TeXDict begin 7 6 bop 523 369 2882 4 v 523 1776 4 1408
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4442
v 551 489 376 4 v 551 562 a FF(r)22 b(`)f(hi)g(\031)g(hi)943
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4443
508 y FG(\()p FF(\031)p FQ(-unit)p FG(\))1261 453 y FF(r)h(`)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4444
FN(t)1443 461 y FR(1)1499 453 y FF(\031)g FN(t)1608 421
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4445
y Fp(0)1608 466 y FR(1)1717 453 y FF(r)g(`)g FN(t)1898
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4446
461 y FR(2)1954 453 y FF(\031)g FN(t)2063 421 y Fp(0)2063
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4447
466 y FR(2)p 1261 486 836 4 v 1333 562 a FF(r)g(`)g(h)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4448
FN(t)1544 570 y FR(1)1579 562 y FN(;)13 b(t)1641 570
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4449
y FR(2)1675 562 y FF(i)21 b(\031)g(h)p FN(t)1865 530
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4450
y Fp(0)1865 575 y FR(1)1900 562 y FN(;)13 b(t)1962 530
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4451
y Fp(0)1962 575 y FR(2)1996 562 y FF(i)2113 505 y FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4452
FF(\031)p FQ(-pair)p FG(\))2484 466 y FF(r)21 b(`)g FN(t)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4453
FF(\031)f FN(t)2796 434 y Fp(0)p 2432 486 438 4 v 2432
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4454
562 a FF(r)g(`)g Fx(f)13 b FN(t)22 b FF(\031)f Fx(f)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4455
b FN(t)2848 530 y Fp(0)2886 505 y FG(\()p FF(\031)p FQ(-fun.)18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4456
b(symbol)p FG(\))750 703 y FF(r)j(`)g FN(t)g FF(\031)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4457
FN(t)1062 671 y Fp(0)p 688 723 458 4 v 688 799 a FF(r)f(`)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4458
FN(a:t)g FF(\031)h FN(a:t)1124 767 y Fp(0)1187 742 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4459
FG(\()p FF(\031)p FQ(-abs-1)p FG(\))1661 684 y FN(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4460
FF(6)p FG(=)f FN(a)1846 653 y Fp(0)1942 684 y FF(r)h(`)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4461
FN(t)g FF(\031)g FG(\()p FN(a)12 b(a)2350 653 y Fp(0)2372
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4462
684 y FG(\))p Fz(\001)p FN(t)2455 653 y Fp(0)2552 684
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4463
y FF(r)21 b(`)g FN(a)g FG(#)h FN(t)2881 653 y Fp(0)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4464
1661 723 1242 4 v 2042 799 a FF(r)f(`)h FN(a:t)f FF(\031)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4465
FN(a)2429 767 y Fp(0)2451 799 y FN(:t)2500 767 y Fp(0)2944
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4466
742 y FG(\()p FF(\031)p FQ(-abs-2)p FG(\))p 726 967 338
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4467
4 v 726 1036 a FF(r)g(`)g FN(a)g FF(\031)h FN(a)1105
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4468
986 y FG(\()p FF(\031)p FQ(-name)p FG(\))1621 921 y(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4469
FN(a)e FG(#)i FN(X)6 b FG(\))21 b FF(2)h(r)f FQ(for)e(all)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4470
FN(a)g FF(2)g Ft(ds)7 b FG(\()p FN(\031)s(;)13 b(\031)2647
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4471
889 y Fp(0)2669 921 y FG(\))p 1621 960 1079 4 v 1880
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4472
1036 a FF(r)21 b(`)g FN(\031)s Fz(\001)p FN(X)27 b FF(\031)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4473
b FN(\031)2323 1004 y Fp(0)2345 1036 y Fz(\001)p FN(X)2740
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4474
978 y FG(\()p FF(\031)p FQ(-suspension)p FG(\))p 598
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4475
1185 361 4 v 598 1258 a FF(r)h(`)f FN(a)g FG(#)g FF(hi)975
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4476
1204 y FG(\(#)p FQ(-unit)p FG(\))1298 1150 y FF(r)g(`)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4477
FN(a)g FG(#)h FN(t)1627 1158 y FR(1)1736 1150 y FF(r)f(`)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4478
FN(a)g FG(#)h FN(t)2065 1158 y FR(2)p 1298 1185 802 4
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4479
v 1439 1258 a FF(r)f(`)g FN(a)g FG(#)h FF(h)p FN(t)1798
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4480
1266 y FR(1)1832 1258 y FN(;)13 b(t)1894 1266 y FR(2)1928
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4481
1258 y FF(i)2115 1204 y FG(\(#)p FQ(-pair)p FG(\))2464
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4482
1155 y FF(r)21 b(`)g FN(a)g FG(#)h FN(t)p 2438 1189 381
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4483
4 v 2438 1258 a FF(r)f(`)g FN(a)g FG(#)h Fx(f)13 b FN(t)2834
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4484
1208 y FG(\(#)p FQ(-fun.)19 b(symbol)p FG(\))p 1012 1422
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4485
391 4 v 1012 1490 a FF(r)j(`)f FN(a)g FG(#)g FN(a:t)1444
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4486
1440 y FG(\(#)p FQ(-abs-1)p FG(\))1965 1380 y FN(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4487
FF(6)p FG(=)g FN(a)2149 1348 y Fp(0)2245 1380 y FF(r)h(`)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4488
FN(a)g FG(#)g FN(t)p 1965 1414 610 4 v 2063 1490 a FF(r)g(`)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4489
FN(a)g FG(#)h FN(a)2405 1459 y Fp(0)2427 1490 y FN(:t)2616
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4490
1433 y FG(\(#)p FQ(-abs-2)p FG(\))1032 1614 y FN(a)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4491
FF(6)p FG(=)g FN(a)1216 1582 y Fp(0)p 953 1648 364 4
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4492
v 953 1724 a FF(r)h(`)f FN(a)g FG(#)g FN(a)1295 1692
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4493
y Fp(0)1359 1667 y FG(\(#)p FQ(-name)p FG(\))1879 1617
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4494
y(\()p FN(\031)1956 1585 y Fp(\000)p FR(1)2038 1617 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4495
Fz(\001)p FN(a)g FG(#)g FN(X)6 b FG(\))21 b FF(2)h(r)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4496
1879 1656 588 4 v 1952 1724 a(r)g(`)f FN(a)g FG(#)g FN(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4497
Fz(\001)o FN(X)2508 1674 y FG(\(#)p FQ(-suspension)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4498
FG(\))p 3402 1776 4 1408 v 523 1779 2882 4 v 668 1923
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4499
a FO(Fig)o(.)12 b(3.)19 b FQ(Inducti)n(v)o(e)h(de\002nitions)f(for)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4500
FF(\031)f FQ(and)i FG(#)p FQ(.)e(The)h(reader)g(is)g(referred)g(to)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4501
([9])g(for)f(more)i(details.)523 2215 y FK(\033)s FH(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4502
FK(t)p FH(\))32 b(=)f FK(a:)p FI(h)p FK(a;)14 b(Y)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4503
b FI(i)p FT(,)25 b(b)n(ut)g(if)g FK(D)33 b FH(=)1584
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4504
2215 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4505
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4506
 1584 2215 a FD(N)1584 2215 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4507
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4508
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4509
 1584 2215 a FK(a:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4510
FI(8)p FK(Y)5 b(:)p Fm(?)p FK(=)p FI(>)14 b(\033)e FK(A)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4511
FH(\()p FK(a;)i(Y)5 b(;)14 b(X)7 b FH(\))25 b FT(then)f(forming)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4512
FK(\033)s FH(\()p FK(D)r FH(\))j FT(gi)n(v)o(es)e(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4513
2314 y(formula)866 2314 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4514
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4515
 866 2314 a FD(N)866 2314 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4516
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4517
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4518
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4519
866 2314 a FK(a)910 2284 y Fv(0)934 2314 y FK(:)p FI(8)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4520
FK(Y)1069 2284 y Fv(0)1093 2314 y FK(:)p Fm(?)p FK(=)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4521
FI(>)14 b(\033)e FK(A)p FH(\()p FK(a)1517 2284 y Fv(0)1540
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4522
2314 y FK(;)i(Y)1644 2284 y Fv(0)1667 2314 y FK(;)g FI(h)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4523
FK(a;)g(Y)19 b FI(i)p FH(\))p FT(.)i(W)-7 b(e)21 b(use)f(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4524
(notation)d FK(\033)s FH(\()p FI(r)p FH(\))k FT(to)e(mean)g(that)g(e)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4525
(v-)523 2414 y(ery)g(freshness)f(constraint)h FK(a)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4526
FH(#)g FK(X)k FT(in)20 b FI(r)h FT(is)g(replaced)e(by)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4527
FK(a)j FH(#)g FK(\033)s FH(\()p FK(X)7 b FH(\))p FT(.)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4528
2516 y(It)34 b(is)i(crucial)e(for)f(programming)e(in)k
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4529
FK(\013)p FT(Prolog)f(that)g(abstractions)g FK(a:)p FH(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4530
FI(\000)p FH(\))h FT(ha)n(v)o(e)f(concrete)523 2615 y(names.)d(This)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4531
(allo)n(ws)f(us)g(to)g(formulate)f(the)h FJ(type)p FT(-clause)f(for)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4532
(lambda-abstractions)e(in)j(the)523 2715 y(usual)25 b(f)o(ashion)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4533
(whereby)g(the)h(abstracted)f(name)h FJ(x)g FT(and)g(its)h(type)f(is)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4534
(just)f(added)f(to)i(the)f(conte)o(xt)523 2815 y FJ(Gamma)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4535
FT(.)c(Furthermore,)d(the)j(w)o(ork)g(reported)e(in)j([9])e(pro)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4536
(vides)g(us)h(with)h(a)f(simple)g(algorithm)f(for)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4537
2914 y(unifying)g(nominal)h(terms.)h(This)h(uni\002cation)e(algorithm)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4538
(does)h(not)g(calculate)g(uni\002ers)f(to)i(mak)o(e)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4539
3014 y(nominal)29 b(terms)i(syntactically)f(equal,)g(b)n(ut)g(equal)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4540
(modulo)f(an)i(equi)n(v)n(alence)d(relation)i FI(\031)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4541
FT(.)h(F)o(or)523 3114 y(e)o(xample)23 b(when)h(unifying)e(the)i(tw)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4542
(o)h(terms)f FK(a:a)31 b FI(\031)o FH(?)g FK(b:X)7 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4543
FT(,)24 b(the)g(nominal)f(uni\002cation)g(algorithm)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4544
3213 y(produces)i(the)h(uni\002er)f FH([)p FK(X)41 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4545
FH(:=)34 b FK(b)p FH(])p FT(.)26 b(While)h(the)f(relation)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4546
FI(\031)i FT(is)g(intended)e(to)h(capture)f(the)h(\(tradi-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4547
3313 y(tional\))h(notion)f(of)i FK(\013)p FT(-equi)n(v)n(alence,)d(it)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4548
(is)h(in)f(f)o(act)f(a)h(more)f(general)g(relation.)f(F)o(or)h(e)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4549
(xample,)f FI(\031)523 3413 y FT(is)g(not)f(just)g(a)g(relation)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4550
(between)h(tw)o(o)g(nominal)e(terms,)i(b)n(ut)g(a)g(relation)g(that)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4551
(depends)e(on)i(some)523 3512 y(freshness)18 b(constraints)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4552
FI(r)p FT(.)h(Figure)f(3)h(gi)n(v)o(es)f(a)h(syntax-directed)d(inducti)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4553
n(v)o(e)h(de\002nition)h(for)g(judge-)523 3612 y(ments)i(of)h(the)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4554
(form)f FI(r)24 b(`)f FH(\()p FI(\000)p FH(\))h FI(\031)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4555
FH(\()p FI(\000)p FH(\))p FT(,)e(which)f(asserts)h(that)g(tw)o(o)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4556
(terms)f(are)g FI(\031)p FT(-equal)f(under)g(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4557
3711 y(hypotheses)h FI(r)p FT(;)i(the)g(de\002nition)e(depends)h(on)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4558
(the)h(auxiliary)e(relation)h FI(r)26 b(`)f FH(\()p FI(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4559
FH(\))h(#)g(\()p FI(\000)p FH(\))p FT(,)c(which)523 3811
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4560
y(de\002nes)17 b(when)g(a)h(name)f(is)i FE(fr)m(esh)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4561
FT(for)f(a)h(term)f(under)g(some)g(hypotheses.)f(This)h(de\002nition)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4562
(depends)523 3911 y(on)k(the)g(auxiliary)e(notion)h(of)h(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4563
(disagreement)e(set,)j FK(ds)p FT(,)f(between)f(tw)o(o)h(permutations)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4564
(\(the)i(set)h(of)523 4010 y(names)e(on)g(which)f(the)i(permutations)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4565
(disagree\))h(gi)n(v)o(en)g(by:)h FI(f)p FK(a)i FI(j)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4566
FK(\031)2515 4022 y FS(1)2553 4010 y Fu(\001)o FK(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4567
FI(6)p FH(=)g FK(\031)2781 4022 y FS(2)2818 4010 y Fu(\001)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4568
FK(a)p FI(g)p FT(.)648 4104 y(W)-7 b(e)21 b(can)f(e)o(xtend)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4569
FI(\031)h FT(to)g FE(quanti\002er)n(-fr)m(ee)f FK(G)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4570
FT(-formulae)f(as)j(follo)n(ws:)p 610 4292 376 4 v 610
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4571
4360 a FF(r)h(`)f(>)g(\031)g(>)1252 4264 y(r)g(`)h FN(t)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4572
FF(\031)g FN(t)1564 4233 y Fp(0)p 1154 4284 531 4 v 1154
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4573
4360 a FF(r)g(`)g FN(p)p FG(\()p FN(t)p FG(\))g FF(\031)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4574
FN(p)p FG(\()p FN(t)1633 4329 y Fp(0)1654 4360 y FG(\))1852
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4575
4264 y FF(r)h(`)f FN(G)2066 4272 y FR(1)2122 4264 y FF(\031)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4576
FN(G)2263 4272 y FR(3)2372 4264 y FF(r)h(`)f FN(G)2586
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4577
4272 y FR(2)2642 4264 y FF(\031)g FN(G)2783 4272 y FR(4)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4578
1852 4292 966 4 v 1945 4360 a FF(r)g(`)h FN(G)2159 4368
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4579
y FR(1)2211 4360 y FN(?)17 b(G)2326 4368 y FR(2)2382
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4580
4360 y FF(\031)k FN(G)2523 4368 y FR(3)2575 4360 y FN(?)c(G)2690
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4581
4368 y FR(4)2902 4310 y FQ(for)22 b FN(?)f FG(::=)h FF(^j_)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4582
4526 y FT(The)28 b(adv)n(antage)e(of)i(setting)g(up)g(the)h(formalism)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4583
(in)h(this)h(w)o(ay)f(is)h(that)g(the)f FI(\031)p FT(-equi)n(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4584
(alence)d(has)523 4625 y(a)h(number)d(of)i(good)f(properties,)f(which)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4585
(will)h(play)f(an)g(important)f(rle)h(in)g(our)g(proof)f(for)g(sho)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4586
(w-)523 4725 y(ing)30 b(that)g(the)h FK(\031)s FT(-rule)e(can)h(be)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4587
(eliminated.)e(F)o(or)h(e)o(xample,)e FI(\031)j FT(is)g(preserv)o(ed)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4588
(under)h(\(possibly-)523 4825 y(capturing\))f(substitutions)i(and)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4589
(beha)n(v)o(es)f(well)i(with)g(respect)f(to)g(the)g(permutation)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4590
(operation.)523 4924 y(This)20 b(is)i(made)d(precise)h(in)g(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4591
(follo)n(wing)d(lemma.)p eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4592
%%Page: 8 8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4593
TeXDict begin 8 7 bop 523 369 2882 4 v 523 1244 4 875
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4594
v 551 521 335 4 v 551 590 a FF(r)p FG(;)13 b FN(\000)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4595
b FF(\))21 b(>)902 543 y(>)962 551 y Fn(R)1070 479 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4596
FF(r)p FG(;)13 b FN(\000)32 b FF(\))21 b FN(G)75 b FF(r)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4597
FG(;)13 b FN(\000)32 b FF(\))21 b FN(G)1815 448 y Fp(0)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4598
1070 514 768 4 v 1220 590 a FF(r)p FG(;)13 b FN(\000)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4599
b FF(\))21 b FN(G)p FF(^)p FN(G)1666 558 y Fp(0)1854
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4600
530 y FF(^)1905 539 y Fn(R)2090 488 y FF(r)p FG(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4601
b FN(\000)31 b FF(\))22 b FN(G)2426 496 y Fn(i)p 2013
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4602
522 516 4 v 2013 590 a FF(r)p FG(;)13 b FN(\000)32 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4603
FF(\))21 b FN(G)2348 598 y FR(1)2383 590 y FF(_)p FN(G)2494
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4604
598 y FR(2)2545 539 y FF(_)2596 547 y Fn(R)t(i)2731 479
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4605
y FF(r)p FG(;)13 b FN(D)r(;)h(\000)3027 436 y Fn(D)3008
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4606
479 y FF(\000)-36 b(!)21 b FN(p)p FG(\()p FN(t)p FG(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4607
2731 517 525 4 v 2743 590 a FF(r)p FG(;)13 b FN(D)r(;)h(\000)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4608
b FF(\))21 b FN(p)p FG(\()p FN(t)p FG(\))3297 542 y FQ(Sel)1006
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4609
760 y FF(r)g(`)g FN(t)1187 729 y Fp(0)1231 760 y FF(\031)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4610
FN(t)p 923 780 501 4 v 923 898 a FF(r)p FG(;)13 b FN(\000)1119
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4611
849 y Fn(p)p FR(\()p Fn(t)1199 828 y Fl(0)1221 849 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4612
FR(\))1100 898 y FF(\000)-33 b(\000)-17 b(\000)-31 b(!)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4613
b FN(p)p FG(\()p FN(t)p FG(\))1464 805 y FQ(Ax)1649 742
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4614
y FF(r)g(`)h(r)1867 710 y Fp(0)1964 742 y FF(r)p FG(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4615
b FN(\000)32 b FF(\))21 b FN(G)75 b FF(r)p FG(;)13 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4616
FN(\000)2570 693 y Fn(p)p FR(\()p Fn(t)2650 672 y Fl(0)2672
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4617
693 y FR(\))2551 742 y FF(\000)-33 b(\000)-17 b(\000)-31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4618
b(!)21 b FN(p)p FG(\()p FN(t)p FG(\))p 1649 780 1225
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4619
4 v 1911 898 a FF(r)p FG(;)13 b FN(\000)2107 849 y Fp(r)2158
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4620
828 y Fl(0)2181 849 y Fn(=G)p Fp(\033)p Fn(p)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4621
Fn(t)2388 828 y Fl(0)2410 849 y FR(\))2088 898 y FF(\000)-39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4622
b(\000)-17 b(\000)g(\000)f(\000)h(\000)g(\000)f(\000)-37
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4623
b(!)21 b FN(p)p FG(\()p FN(t)p FG(\))2915 797 y FF(\033)2975
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4624
805 y Fn(L)728 1050 y FF(r)p FG(;)13 b FN(\000)924 1002
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4625
y Fn(D)r FR([)p Fn(X)t FR(:=)p Fn(t)1137 981 y Fl(0)1157
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4626
1002 y FR(])905 1050 y FF(\000)-34 b(\000)-18 b(\000)h(\000)g(\000)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4627
(\000)-33 b(!)21 b FN(p)p FG(\()p FN(t)p FG(\))p 728
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4628
1089 625 4 v 775 1191 a FF(r)p FG(;)13 b FN(\000)971
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4629
1149 y Fp(8)p Fn(X)q(:D)952 1191 y FF(\000)-39 b(\000)-17
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4630
b(\000)g(\000)-38 b(!)21 b FN(p)p FG(\()p FN(t)p FG(\))1394
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4631
1111 y FF(8)1437 1119 y Fn(L)1576 1043 y FN(b)g FG(#)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4632
Ft(Xs)7 b FN(;)13 b FF(r)p FG(;)g FN(\000)2041 994 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4633
FR(\()p Fn(a)d(b)p FR(\))p Fk(\001)p Fn(D)2021 1043 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4634
FF(\000)-21 b(\000)k(\000)f(\000)e(!)21 b FN(p)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4635
FN(t)p FG(\))p 1576 1082 834 4 v 1733 1191 a FF(r)p FG(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4636
b FN(\000)1971 1149 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4637
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4638
 1971 1149 a Fj(N)1971 1149 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4639
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4640
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4641
 1971
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4642
1149 a Fn(a:D)1910 1191 y FF(\000)-23 b(\000)-17 b(\000)-22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4643
b(!)21 b FN(p)p FG(\()p FN(t)p FG(\))2505 1104 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4644
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4645
 2505
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4646
1104 a FB(N)2505 1104 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4647
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4648
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4649
 2505 1104 a 9 x Fn(L)2644 1051
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4650
y FF(r)p FG(;)14 b FN(\000)2841 1008 y Fn(\031)r Fk(\001)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4651
Fn(D)2821 1051 y FF(\000)-19 b(\000)h(!)21 b FN(p)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4652
FN(t)p FG(\))p 2644 1090 484 4 v 2674 1191 a FF(r)p FG(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4653
b FN(\000)2870 1149 y Fn(D)2851 1191 y FF(\000)-36 b(!)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4654
b FN(p)p FG(\()p FN(t)p FG(\))3170 1106 y FN(\031)p 3402
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4655
1244 4 875 v 523 1247 2882 4 v 523 1390 a FO(Fig)o(.)12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4656
b(4.)19 b FQ(Proof-search)g(rules)g(of)g FN(\013)p FQ(Prolog.)f(In)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4657
(the)g(ne)n(w-left)g(rule)g(it)f(is)g(assumed)i(that)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4658
FN(b)g FQ(is)f(a)h(fresh)g(name)g(not)523 1481 y(occurring)h(in)f(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4659
(conclusion)h(and)g Ft(Xs)25 b FQ(are)19 b(all)f(free)h(v)n(ariables)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4660
(in)e FN(\000)30 b FQ(and)19 b FN(p)p FG(\()p FN(t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4661
FG(\))p FQ(.)523 1762 y Fi(Lemma)i(1.)41 b FE(The)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4662
b(permutation)f(and)g(substitution)g(oper)o(ations)g(pr)m(eserve)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4663
FI(\031)h FE(in)f(the)g(sense)h(that)544 1929 y(\(i\))41
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4664
b(if)21 b FI(r)i(`)g FK(t)g FI(\031)g FK(t)1068 1899
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4665
y Fv(0)1112 1929 y FE(then)d FI(r)j(`)g FK(\031)s Fu(\001)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4666
FK(t)g FI(\031)g FK(\031)s Fu(\001)p FK(t)1766 1899 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4667
Fv(0)1810 1929 y FE(for)e(all)f(permutations)f FK(\031)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4668
b FE(and)521 2070 y(\(ii\))41 b(if)28 b FI(r)37 b(`)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4669
FK(t)h FI(\031)f FK(t)1129 2040 y Fv(0)1152 2070 y FE(,)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4670
b(then)f FI(r)1441 2040 y Fv(0)1501 2070 y FI(`)36 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4671
FK(\033)s FH(\()p FK(t)p FH(\))h FI(\031)f FK(\033)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4672
FH(\()p FK(t)1982 2040 y Fv(0)2006 2070 y FH(\))29 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4673
FE(for)f(all)f(substitutions)g FK(\033)32 b FE(with)c
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4674
FI(r)3074 2040 y Fv(0)3134 2070 y FI(`)36 b FK(\033)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4675
FH(\()p FI(r)p FH(\))664 2170 y FE(\(wher)m(eby)20 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4676
FI(r)1060 2140 y Fv(0)1106 2170 y FI(`)j FK(\033)s FH(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4677
FI(r)p FH(\))f FE(means)e(that)g FI(r)1837 2140 y Fv(0)1883
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4678
2170 y FI(`)j FK(a)g FH(#)g FK(\033)s FH(\()p FK(X)7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4679
b FH(\))21 b FE(holds)f(for)h(eac)o(h)e FH(\()p FK(a)k
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4680
FH(#)g FK(X)7 b FH(\))23 b FI(2)h(r)p FE(\).)523 2340
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4681
y FT(The)19 b(proof)e(of)h(these)h(tw)o(o)h(f)o(acts)f(are)g(a)g(minor)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4682
f(e)o(xtension)f(of)i(the)g(proofs)e(gi)n(v)o(en)h(for)g([9];)g(the)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4683
(y)g(hold)523 2439 y(because)24 b(permutations)f(are)i(bijections)g(on)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4684
f(names,)h(and)f(substitutions)g(act)i(on)e(v)n(ariables)g(only)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4685
2539 y(\(not)k(names\).)g(The)h(properties)f(stated)h(in)g(Lemma)f(1)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4686
(should)e(be)h(compared)d(with)k(the)f(notion)523 2639
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4687
y(of)j FK(\013)p FT(-equi)n(v)n(alence)e(we)i(imposed)f(\(on)g(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4688
(meta-le)n(v)o(el\))f(on)g(quanti\002ed)g FK(D)r FT(-formulae.)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4689
(There,)523 2738 y(whene)n(v)o(er)f(a)j(permutation)d(or)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4690
(substitution)f(is)i(pushed)e(under)g(a)h(binder)m(,)f(we)h(might)g(ha)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4691
n(v)o(e)f(to)523 2838 y(rename)19 b(its)i(binder)e(in)i(order)d(to)j(a)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4692
n(v)n(oid)f(possible)g(capture.)648 2929 y(Ne)o(xt)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4693
b(we)h(introduce)e(the)h(inference)f(rules)i(on)f(which)g(proof-search)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4694
e(is)j(based)f(in)h FK(\013)p FT(Prolog)523 3051 y(\(see)f(Figure)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4695
(4\).)f(Sequents)h(are)f(of)h(the)g(form)f FI(r)p FH(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4696
b FK(\000)46 b FI(\))34 b FK(G)27 b FT(or)e FI(r)p FH(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4697
b FK(\000)2640 3003 y FC(D)2619 3051 y FI(\000)-39 b(!)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4698
b FK(p)p FH(\()p FK(t)p FH(\))27 b FT(where)e(the)h(for)n(-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4699
3142 y(mer)18 b(models)g FE(goal-dir)m(ected)e(pr)l(oof-sear)m(c)o(h)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4700
FT(and)g(the)i(latter)f(models)g FE(focused)g(bac)n(kc)o(haining)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4701
FT(\(the)523 3233 y(formula)21 b(abo)o(v)o(e)g(the)i(sequent)f(arro)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4702
(w)g(is)h(usually)f(called)h(the)g FE(stoup)p FT(-formula\).)c(These)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4703
(inference)523 3324 y(rules)j(are)f(adapted)f(from)h(a)h(standard)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4704
(focusing)g(approach)g(to)i(\002rst-order)e(logic)h(programming)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4705
3416 y(\(for)j(e)o(xample)g([4]\).)1132 3386 y FA(4)1192
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4706
3416 y FT(The)h(main)g(no)o(v)o(elty)e(of)i(these)g(rules)g(is)h(the)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4707
(presence)f(of)h(the)g(freshness-)523 3507 y(constraints)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4708
b FI(r)p FT(.)g(T)m(raditionally)f(axiom)g(rules)h(are)g(formulated)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4709
(as)p 893 3660 486 4 v 893 3736 a FN(p)p FG(\()p FN(t)990
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4710
3704 y Fp(0)1012 3736 y FG(\))p FN(;)13 b(\000)31 b FF(\))22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4711
b FN(p)p FG(\()p FN(t)p FG(\))1420 3685 y FQ(Ax)1511
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4712
3736 y FN(;)88 b FT(or)20 b(in)g(focusing)f(proofs)g(as)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4713
2479 3619 402 4 v 75 w FN(\000)2577 3687 y Fn(p)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4714
Fn(t)2657 3667 y Fl(0)2679 3687 y FR(\))2558 3736 y FF(\000)-33
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4715
b(\000)-17 b(\000)-31 b(!)21 b FN(p)p FG(\()p FN(t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4716
FG(\))2922 3644 y FQ(Ax)3014 3736 y FN(;)523 3887 y FT(where)h(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4717
(terms)g FK(t)g FT(and)f FK(t)1308 3857 y Fv(0)1355 3887
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4718
y FT(need)g(to)h(be)f(syntactically)g(equal.)g(In)h FK(\013)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4719
FT(Prolog)f(this)h(requirement)e(is)523 3979 y(relax)o(ed:)j(terms)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4720
(only)g(need)f(to)i(be)f(being)f(equal)h(modulo)e FI(\031)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4721
FT(.)i(Ho)n(we)n(v)o(er)m(,)e FI(\031)j FT(only)e(mak)o(es)h(sense)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4722
4070 y(in)d(the)f(conte)o(xt)f(of)h(some)g(freshness)g(constraints.)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4723
(Consequently)-5 b(,)19 b(in)j FK(\013)p FT(Prolog)o(,)f(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4724
(axiom-rule)523 4161 y(tak)o(es)f(the)f(form)1731 4230
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4725
y FF(r)h(`)g FN(t)1912 4198 y Fp(0)1956 4230 y FF(\031)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4726
FN(t)p 1648 4250 501 4 v 1648 4368 a FF(r)p FG(;)13 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4727
FN(\000)1844 4319 y Fn(p)p FR(\()p Fn(t)1924 4298 y Fl(0)1946
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4728
4319 y FR(\))1825 4368 y FF(\000)-33 b(\000)-17 b(\000)-32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4729
b(!)22 b FN(p)p FG(\()p FN(t)p FG(\))2189 4275 y FQ(Ax)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4730
4495 y FT(where)g(the)h(conte)o(xt)f FI(r)h FT(e)o(xplicitly)f(records)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4731
g(all)h(freshness)g(constraints)f(in)h(a)g(sequent.)f(The)g(only)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4732
4595 y(inference)i(rule)g(which)h(adds)g(ne)n(w)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4733
(freshness-constraints)f(to)j(this)f(conte)o(xt)f(is)i(the)3075
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4734
4595 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4735
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4736
 3075 4595 a FD(N)3075 4595 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4737
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4738
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4739
 3075 4595 a FT(-rule;)e(that)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4740
523 4654 473 4 v 558 4710 a Fy(4)606 4742 y FQ(The)h(question)g(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4741
(establishing)g(the)g(precise)f(relation)h(between)g(the)g(inference)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4742
(rules)g(gi)n(v)o(en)g(here)g(and)606 4833 y(nominal)j(logic)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4743
(introduced)h(in)f([8])g(is)f(be)o(yond)j(the)e(scope)g(of)g(this)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4744
(paper)m(,)g(b)o(ut)g(will)f(appear)i(in)e(a)h(full)606
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4745
4924 y(v)o(ersion)20 b(\(some)f(results)g(concerning)h(this)f(question)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4746
h(ha)o(v)o(e)f(already)h(been)f(presented)h(in)f([5]\).)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4747
eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4748
%%Page: 9 9
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4749
TeXDict begin 9 8 bop 523 448 a FT(is)33 b(whene)n(v)o(er)e(a)1093
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4750
448 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4751
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4752
 1093 448 a FD(N)1093 448 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4753
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4754
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4755
 1093 448 a FT(-quanti\002er)g(is)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4756
(analysed,)e(a)i(ne)n(w)f(name)g(is)h(chosen)e(and)h(some)g(freshness-)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4757
523 548 y(constraints)20 b(are)g(added)f(to)h FI(r)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4758
FT(in)f(order)f(to)i(enforce)d(the)i(\223freshness\224)g(of)g(this)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4759
(name.)648 648 y(The)h FI(\033)864 660 y FC(L)914 648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4760
y FT(-rule)g(includes)g(the)h(judgement)e FI(r)27 b(`)f(r)2131
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4761
617 y Fv(0)2177 648 y FT(where)21 b FI(r)2471 617 y Fv(0)2517
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4762
648 y FT(is)i(the)f(set)h(of)f(freshness)f(con-)523 747
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4763
y(straints)29 b(associated)g(with)f(the)h FK(D)r FT(-formula)e(in)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4764
(the)f(stoup.)g(This)h(judgement)e(requires)g(that)i(all)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4765
847 y(constraints)22 b(in)g FI(r)1062 817 y Fv(0)1109
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4766
847 y FT(\(being)f(of)h(the)g(form)g FK(a)27 b FH(#)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4767
FK(t)p FT(\))c(are)f(satis\002ed)h(by)f(the)h FI(r)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4768
FT(,)g(that)f(is)i(for)d(all)i FK(a)28 b FH(#)f FK(t)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4769
946 y FT(the)20 b(judgement)f FI(r)k(`)g FK(a)g FH(#)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4770
FK(t)d FT(de\002ned)g(in)g(Fig.)g(3)h(holds.)648 1046
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4771
y(Of)15 b(most)h(interest)g(in)f(this)h(paper)f(is)h(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4772
FK(\031)s FT(-rule.)f(In)g(a)h(\223root-\002rst\224)f(proof-search,)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4773
(this)k(rule)g(is)g(a)523 1178 y(source)h(of)g(non-determinism.)d(F)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4774
(or)j(e)o(xample,)f(if)i(we)g(w)o(ant)f(to)h(pro)o(v)o(e)d(the)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4775
(sequent)f Fm(?)p FH(;)3065 1124 y FC(p)p FS(\()p FC(a)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4776
FS(\))3044 1178 y FI(\000)-19 b(\000)g(!)23 b FK(p)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4777
FH(\()p FK(b)p FH(\))p FT(,)523 1278 y(we)32 b(need)f(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4778
FK(\031)s FT(-rule)g(in)g(order)e(to)i(mak)o(e)g(the)g(terms)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4779
FK(a)i FT(and)e FK(b)h FI(\031)p FT(-equi)n(v)n(alent\227in)d(this)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4780
(case,)523 1378 y(only)19 b(after)h(applying)e(a)i(permutation)e(such)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4781
(as)g FH(\()p FK(a)14 b(b)p FH(\))21 b FT(to)f FK(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4782
FT(may)g(the)g(axiom-rule)d(be)j(used.)g(Prima)523 1477
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4783
y(f)o(acie)d(the)g FK(\031)s FT(-rule)g(is)h(innocuous,)d(ho)n(we)n(v)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4784
(er)m(,)f(the)j(problem)f(of)g(simultaneously)g(unifying)f(nominal)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4785
1577 y(terms)j(and)g(\002nding)f(a)i FK(\031)j FT(is,)d(as)h(mentioned)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4786
c(earlier)m(,)h(an)i(NP-hard)e(decision)g(problem.)g(In)h(the)g(ne)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4787
(xt)523 1677 y(section)g(we)g(shall)h(sho)n(w)f(that)g(such)g(problems)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4788
e(ne)n(v)o(er)h(need)h(to)g(be)g(solv)o(ed)f(pro)o(vided)f(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4789
(program)523 1776 y(clauses)j(are)f(well-formed.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4790
2015 y FL(3)99 b(Elimination)25 b(of)g(the)h Fh(\031)t
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4791
FL(-Rule)523 2180 y FT(W)-7 b(e)18 b(implemented)c FK(\013)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4792
FT(Prolog)i(using)g(the)g(nominal)g(uni\002cation)f(algorithm.)f(W)m
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4793
(ith)j(this)g(implemen-)523 2271 y(tation)22 b(we)h(were)g(able)f(to)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4794
(calculate)f(the)h(e)o(xpected)e(results)i(for)e(programs)g(such)i(as)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4795
FJ(subst)f FT(and)523 2362 y FJ(type)p FT(.)16 b(The)f(reason)h(for)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4796
(this)i(is,)g(roughly)d(speaking,)g(that)j(the)f(name)f(we)i(used)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4797
(for)h(specifying)e(the)523 2454 y(clauses)26 b(dealing)f(with)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4798
FK(\025)p FT(-abstractions)f(does)h(not)g(matter)-5 b(.)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4799
b(When)h(using)f(nominal)g(uni\002cation,)523 2545 y(the)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4800
b(follo)n(wing)f(renamed)f(clauses)j(\(where)e FJ(a)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4801
FT(and)e FJ(x)i FT(are)f(renamed)f(to)h FJ(b)h FT(and)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4802
FJ(y)p FT(,)i(respecti)n(v)o(ely\))527 2675 y FP
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4803
(subst\(lam\(b.M\),X,T,lam\(b.M'\)\))-16 b(:-)23 b(b)12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4804
b(#)g(T,)g(b)h(#)f(X,)g(subst\(M,X,T,M'\).)527 2790 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4805
(type\(Gamma,lam\(y.M\),arr\(S,T\)\))-16 b(:-)23 b(y)12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4806
b(#)g(Gamma,)g(type\([\(y,S\)|Gamma],M,T\).)523 2922
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4807
y FT(beha)n(v)o(e)25 b(just)h(the)g(same)g(as)g(the)g(original)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4808
(clauses,)h(in)g(the)f(sense)i(that)f(all)g(queries)f(successfully)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4809
3013 y(solv)o(ed)30 b(by)h(the)g(original)f(v)o(ersions)g(are)h(solv)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4810
(ed)f(by)g(the)h(renamed)f(v)o(ersions.)g(In)g(contrast,)g(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4811
3105 y(name)19 b FJ(a)i FT(in)f(the)g(clauses)g FJ(p\(a\))13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4812
b FT(,)44 b FJ(q\(a.X,X\))e FT(and)19 b FJ(r\(X\))13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4813
b(:-)h(id\(X,a\))19 b FT(determines)g(which)523 3196
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4814
y(queries)k(can)h(be)g(solv)o(ed)g(successfully)f(using)h(nominal)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4815
(uni\002cation)f(and)i(which)g(cannot:)f(gi)n(v)o(en)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4816
3287 y(our)k(inference)g(rules,)h(which)g(choose)f(a)h(fresh)g(name)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4817
(for)f FJ(a)p FT(,)i(there)e(are)h(some)g(queries)g(whose)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4818
3379 y(answers)18 b(can)g(only)g(be)g(found)e(using)i(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4819
FK(\031)s FT(-rule,)g(and)f(this)i(means)f(the)o(y)f(cannot)h(be)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4820
(solv)o(ed)f(using)523 3470 y(nominal)i(uni\002cation.)g(Consider)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4821
(for)h(e)o(xample)f(the)h(follo)n(wing)e(deduction.)1500
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4822
3730 y FN(:)13 b(:)g(:)1856 3592 y Fq(?)21 b FF(`)h FN(c)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4823
FF(\031)g FN(c)p 1813 3619 405 4 v 1813 3730 a Fq(?)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4824
FG(;)1927 3681 y Fn(p)p FR(\()p Fn(c)p FR(\))1907 3730
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4825
y FF(\000)-20 b(\000)h(!)21 b FN(p)p FG(\()p FN(c)p FG(\))2259
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4826
3644 y FQ(Ax)p 1500 3769 718 4 v 1558 3879 a Fq(?)p FG(;)1671
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4827
3831 y Fg(?)p Fn(=)p Fp(>)11 b(\033)f Fn(p)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4828
Fn(c)p FR(\))1652 3879 y FF(\000)-29 b(\000)-17 b(\000)g(\000)f(\000)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4829
(\000)g(\000)-28 b(!)21 b FN(p)p FG(\()p FN(c)p FG(\))2259
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4830
3785 y FF(\033)2319 3793 y Fn(L)p 1558 3918 601 4 v 1558
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4831
4029 a Fq(?)p FG(;)1672 3980 y Fg(?)p Fn(=)p Fp(>)10
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4832
b(\033)g Fn(p)p FR(\()p Fn(b)p FR(\))1652 4029 y FF(\000)-29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4833
b(\000)-17 b(\000)g(\000)f(\000)h(\000)g(\000)-28 b(!)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4834
b FN(p)p FG(\()p FN(c)p FG(\))2200 3937 y FN(\031)46
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4835
b FG(\()p FN(c)13 b(b)p FG(\))p 1508 4068 702 4 v 1508
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4836
4183 a Fq(?)p FG(;)1663 4134 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4837
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4838
 1663 4134 a Fj(N)1663
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4839
4134 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4840
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4841
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4842
 1663 4134 a Fn(a:)p Fg(?)p Fn(=)p Fp(>)d(\033)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4843
Fn(p)p FR(\()p Fn(a)p FR(\))1602 4183 y FF(\000)-21 b(\000)j(\000)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4844
(\000)g(\000)f(\000)h(\000)g(\000)f(\000)e(!)22 b FN(p)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4845
FG(\()p FN(c)p FG(\))2305 4090 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4846
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4847
 2305 4090 a FB(N)2305
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4848
4090 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4849
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4850
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4851
 2305 4090 a 9 x Fn(L)523 4327 y FT(In)e(this)g(deduction)e(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4852
FK(\031)s FT(-rule,)f(applying)f(the)i(permutation)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4853
FH(\()p FK(c)c(b)p FH(\))20 b FT(\(annotated)e(to)i(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4854
FK(\031)s FT(-rule\),)f(is)523 4426 y(crucial)j(for)g(the)h(sequent)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4855
(being)f(pro)o(v)n(able)g(and)h(it)h(will)h(turn)e(out)g(that)h(it)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4856
(is)h(impossible)e(to)h(elim-)523 4526 y(inate)e(it)h(from)f(this)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4857
(deduction.)e(Consequently)-5 b(,)19 b(a)j(proof-search)c(procedure)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4858
(based)i(on)g(nominal)523 4625 y(uni\002cation)e(will)i(not)f(\002nd)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4859
(this)g(proof.)648 4725 y(If)i(we)h(impose)f(the)h(follo)n(wing)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4860
(well-formedness)g(condition)g(on)h FK(D)r FT(-formulae,)e(we)j(can)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4861
(en-)523 4825 y(sure)18 b(that)h(the)f FK(\031)s FT(-rule)g(can)h(al)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4862
(w)o(ays)f(be)h(eliminated)e(from)h(corresponding)d(deductions)h(and)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4863
(hence)523 4924 y(the)i(nominal)f(uni\002cation)g(algorithm)g(alone)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4864
(is)i(suf)n(\002cient)f(for)g(solving)f(queries.)p eop
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4865
end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4866
%%Page: 10 10
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4867
TeXDict begin 10 9 bop 523 448 a Fi(De\002nition)20 b(1.)41
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4868
b FE(A)25 b(closed)f FK(D)r FE(-formula)1757 448 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4869
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4870
 1757
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4871
448 a FD(N)1757 448 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4872
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4873
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4874
 1757 448 a Fr(as)7 b FK(:)p FI(8)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4875
Fr(Xs)g FK(:)p FI(r)2104 460 y Fs(as)e FC(;)p Fs(Xs)2279
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4876
448 y FK(=G)2386 460 y Fs(as)t FC(;)p Fs(Xs)2574 448
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4877
y FI(\033)14 b FK(A)2715 460 y Fs(as)5 b FC(;)p Fs(Xs)2914
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4878
448 y FE(is)26 b FT(well-formed)523 540 y FE(if)21 b(ther)m(e)f(e)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4879
(xists)i(a)e(substitution)f FK(\033)25 b FE(and)19 b(a)h(permutation)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4880
FK(\031)24 b FE(suc)o(h)19 b(that)552 679 y FM(\(i\))41
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4881
b Ft(bs)28 b FG(#)22 b Ft(Xs)6 b FN(;)13 b FF(r)1036
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4882
687 y Ff(as)t Fn(;)p Ff(Xs)1210 679 y FF(`)21 b FN(\033)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4883
FG(\()p FN(A)1413 688 y Ff(bs)s Fn(;)p Ff(Xs)1562 679
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4884
y FG(\))g FF(\031)g FN(A)1752 687 y Ff(as)t Fn(;)p Ff(Xs)1923
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4885
679 y FM(and)531 766 y(\(ii\))41 b Ft(bs)28 b FG(#)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4886
b Ft(Xs)6 b FN(;)13 b FF(r)1036 774 y Ff(as)t Fn(;)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4887
Ff(Xs)1210 766 y FF(`)21 b FN(\033)s FG(\()p FN(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4888
Fz(\001)o FN(G)1486 775 y Ff(bs)t Fn(;)p Ff(Xs)1635 766
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4889
y FG(\))h FF(\031)f FN(G)1828 774 y Ff(as)t Fn(;)p Ff(Xs)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4890
918 y FE(wher)m(e)g(the)f Fr(bs)28 b FE(ar)m(e)20 b(some)g(fr)m(esh)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4891
(names)f(\(dif)o(fer)m(ent)f(fr)l(om)i Fr(as)7 b FE(\).)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4892
1065 y FT(Let)20 b(us)h(illustrate)f(this)h(condition)d(with)i(some)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4893
(e)o(xamples.)f(Clauses)h(without)g(names)g(clearly)f(sat-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4894
1156 y(isfy)h(the)h(condition.)d(F)o(or)i(e)o(xample)e(the)j(\002rst)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4895
FJ(subst)p FT(-clause)f(in)i(Fig.)f(1)691 1299 y Fq(?)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4896
FF(`)g FN(\033)s FG(\()p FN(S)t FG(\()p Fx(var)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4897
FN(X)6 b FG(\))p FN(;)13 b(X)r(;)h(T)6 b(;)13 b(T)e FG(\)\))42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4898
b FF(\031)g FN(S)t FG(\()p Fx(var)q FG(\()p FN(X)6 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4899
FG(\))p FN(;)13 b(X)r(;)g(T)6 b(;)14 b(T)d FG(\))84 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4900
FT(and)h Fq(?)21 b FF(`)g FN(\033)s FG(\()p FN(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4901
Fz(\001)o FF(>)p FG(\))42 b FF(\031)g(>)523 1442 y FT(tri)n(vially)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4902
b(satis\002es)i(the)f(condition)e(by)h(taking)f(for)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4903
FK(\033)32 b FT(the)27 b(identity)g(substitution)g(and)g(for)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4904
FK(\031)k FT(the)523 1533 y(empty)17 b(permutation.)f(More)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4905
(complicated)e(is)j(the)g(case)f(of)g(the)g(second)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4906
FJ(subst)p FT(-clause)f(in)h(Fig.)g(1)789 1675 y FF(r)j(`)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4907
FN(\033)s FG(\()p FN(S)t FG(\()p Fx(lam)p FG(\()p FN(b:M)8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4908
b FG(\))p FN(;)13 b(X)r(;)g(T)6 b(;)14 b Fx(lam)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4909
FN(b:M)1916 1643 y Fp(0)1939 1675 y FG(\)\))42 b FF(\031)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4910
FN(S)t FG(\()p Fx(lam)p FG(\()p FN(a:M)8 b FG(\))p FN(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4911
b(X)r(;)f(T)6 b(;)13 b Fx(lam)q FG(\()p FN(a:M)3057 1643
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4912
y Fp(0)3079 1675 y FG(\)\))789 1766 y FF(r)21 b(`)h FN(\033)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4913
FG(\()p FN(\031)s Fz(\001)n FN(S)t FG(\()p FN(M)t(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4914
b(X)r(;)h(T)6 b(;)13 b(M)1550 1735 y Fp(0)1572 1766 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4915
FG(\)\))43 b FF(\031)f FN(S)t FG(\()p FN(M)t(;)13 b(X)r(;)h(T)6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4916
b(;)13 b(M)2237 1735 y Fp(0)2260 1766 y FG(\))523 1916
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4917
y FT(where)20 b FI(r)h FT(is)g FI(f)p FK(b)h FH(#)h FK(M)t(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4918
b(b)23 b FH(#)g FK(X)r(;)14 b(b)22 b FH(#)h FK(T)7 b(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4919
b(b)22 b FH(#)i FK(M)1970 1886 y Fv(0)1993 1916 y FK(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4920
b(a)22 b FH(#)i FK(X)r(;)14 b(a)22 b FH(#)h FK(T)12 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4921
FI(g)p FT(.)20 b(In)f(this)i(case)651 2072 y FN(\033)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4922
FG(=)d([)p FN(M)30 b FG(:=)21 b(\()p FN(a)12 b(b)p FG(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4923
Fz(\001)p FN(M)t(;)h(X)27 b FG(:=)22 b(\()p FN(a)12 b(b)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4924
FG(\))p Fz(\001)o FN(X)r(;)i(T)31 b FG(:=)22 b(\()p FN(a)12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4925
b(b)p FG(\))p Fz(\001)o FN(T)6 b(;)14 b(M)2290 2040 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4926
Fp(0)2334 2072 y FG(:=)21 b(\()p FN(a)13 b(b)p FG(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4927
Fz(\001)o FN(M)2689 2040 y Fp(0)2711 2072 y FG(])66 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4928
FT(and)d FN(\031)24 b FG(=)d(\()p FN(a)13 b(b)p FG(\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4929
2236 y FT(v)o(erify)19 b(that)h(the)g(clause)h(is)g(well-formed.)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4930
2327 y(Before)k(we)h(formally)e(sho)n(w)i(that)g(all)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4931
FK(\031)s FT(-rules)g(can)f(be)h(eliminated)f(from)f(deductions)g(con-)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4932
523 2419 y(sisting)31 b(of)f(well-formed)e(clauses)i(only)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4933
b(,)29 b(we)h(outline)g(our)f(proof-plan)e(with)k(some)f(e)o(xamples.)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4934
523 2510 y(Consider)25 b(the)g(follo)n(wing)e(deduction,)g(which)i(has)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4935
g(a)h FK(\031)s FT(-rule)e(on)h(the)g(top)g(right-hand)e(side.)i(The)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4936
523 2601 y(corresponding)17 b(permutation)h FH(\()p FK(e)c(d)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4937
FH(\))21 b FT(transforms)e FK(p)p FH(\()p FK(b:d)p FH(\))i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4938
FT(into)f FK(p)p FH(\()p FK(b:e)p FH(\))h FT(so)g(that)f(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4939
(axiom-rule)f(is)523 2692 y(applicable.)1349 3051 y FN(:)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4940
b(:)g(:)1743 2771 y FF(`)21 b FN(b:e)h FF(\031)f FN(d:e)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4941
1664 2791 516 4 v 1664 2901 a Fq(?)p FG(;)1777 2853 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4942
Fn(p)p FR(\()p Fn(b:e)p FR(\))1758 2901 y FF(\000)-39
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4943
b(\000)-17 b(\000)f(\000)-38 b(!)21 b FN(p)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4944
FN(d:e)p FG(\))2221 2816 y FQ(Ax)p 1663 2940 518 4 v
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4945
1663 3051 a Fq(?)p FG(;)1776 3002 y Fn(p)p FR(\()p Fn(b:d)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4946
FR(\))1757 3051 y FF(\000)-38 b(\000)-17 b(\000)f(\000)-36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4947
b(!)21 b FN(p)p FG(\()p FN(d:e)p FG(\))2222 2959 y FN(\031)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4948
FG(\()p FN(e)13 b(d)p FG(\))p 1349 3089 832 4 v 1418
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4949
3200 a Fq(?)p FG(;)1531 3152 y Fg(?)p Fn(=)p Fp(>\033)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4950
Fn(p)p FR(\()p Fn(b:d)p FR(\))1512 3200 y FF(\000)-35
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4951
b(\000)-18 b(\000)h(\000)g(\000)f(\000)h(\000)g(\000)-34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4952
b(!)21 b FN(p)p FG(\()p FN(d:e)p FG(\))2222 3106 y FF(\033)2282
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4953
3114 y Fn(L)p 1355 3239 820 4 v 1355 3350 a Fq(?)p FG(;)1468
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4954
3301 y Fp(8)p Fn(X)q(:)p Fg(?)p Fn(=)p Fp(>\033)o Fn(p)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4955
FR(\()p Fn(b:X)t FR(\))1449 3350 y FF(\000)-36 b(\000)-18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4956
b(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)-35
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4957
b(!)21 b FN(p)p FG(\()p FN(d:e)p FG(\))2216 3258 y FF(8)2259
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4958
3266 y Fn(L)2348 3258 y FG([)p FN(X)28 b FG(:=)21 b FN(d)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4959
FG(])p 1305 3388 921 4 v 1305 3504 a Fq(?)p FG(;)1460
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4960
3455 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4961
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4962
 1460 3455 a Fj(N)1460 3455 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4963
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4964
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4965
 1460 3455 a Fn(a:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4966
Fp(8)p Fn(X)q(:)p Fg(?)p Fn(=)p Fp(>\033)o Fn(p)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4967
Fn(a:X)t FR(\))1398 3504 y FF(\000)-28 b(\000)-17 b(\000)f(\000)h(\000)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4968
g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)-27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4969
b(!)21 b FN(p)p FG(\()p FN(d:e)p FG(\))2321 3407 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4970
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4971
 2321
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4972
3407 a FB(N)2321 3407 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4973
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4974
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4975
 2321 3407 a 8 x Fn(L)2388 3407
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4976
y FG(\()p FN(a)13 b(b)p FG(\))523 3629 y FT(Observ)o(e)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4977
b(that)i(the)f(\223choice\224)g(of)g(the)g(fresh)g(name)g(\(namely)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4978
FK(b)p FT(\))h(introduced)e(by)i(the)3065 3629 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4979
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4980
 3065
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4981
3629 a FD(N)3065 3629 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4982
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4983
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4984
 3065 3629 a 12 x FC(L)3115 3629
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4985
y FT(-rule)f(has)523 3729 y(no)i(ef)n(fect)f(on)h(whether)f(this)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4986
(sequent)e(is)i(deri)n(v)n(able,)e(since)h(this)h(binder)e(will)h(not)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4987
(bind)g(an)o(ything)523 3828 y(inside)g(the)h(abstraction.)e(The)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4988
(annotated)f(substitution)h FH([)p FK(X)35 b FH(:=)29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4989
b FK(d)p FH(])24 b FT(ho)n(we)n(v)o(er)e(is)i(important)e(with)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4990
3928 y(respect)h(to)h(the)f FK(\031)s FT(-rule)g(we)h(are)g(trying)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4991
(to)i(eliminate.)e(If)i(we)f(had)g(instead)h(substituted)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4992
FK(e)i FT(for)f FK(X)7 b FT(,)523 4028 y(then)20 b(the)g(axiom)f(is)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4993
(applicable)e FE(without)j FT(the)e FK(\031)s FT(-rule.)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4994
4127 y(Note,)31 b(ho)n(we)n(v)o(er)m(,)e(that)i(changing)f(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4995
(instantiation)g(of)g FI(8)p FT(-quanti\002ers)f(might)h(ha)n(v)o(e)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4996
(some)523 4227 y(\223non-local\224)18 b(consequences)g(in)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4997
(deductions.)d(Consider)i(for)f(e)o(xample)g(the)i(deduction)d(in)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4998
(Fig.)h(5.)523 4327 y(In)j(this)i(deduction,)c(the)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  4999
FK(\031)s FT(-rule)f(\(mark)o(ed)f(by)i FI(\017)p FT(\))f(sw)o(aps)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5000
(the)e(names)h FK(z)j FT(and)c FK(y)s FT(.)h(If)g(we)g(eliminate)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5001
4426 y(this)e FK(\031)s FT(-rule)g(by)f(applying)f(the)i(sw)o(apping)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5002
(to)g(the)h(terms)g(instantiated)f(for)g(the)h(v)n(ariables)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5003
FK(M)9 b FT(,)23 b FK(X)7 b FT(,)523 4526 y FK(T)29 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5004
FT(and)17 b FK(M)829 4496 y Fv(0)852 4526 y FT(,)h(then)f(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5005
FK(\031)s FT(-rule)f(is)i(not)e(needed,)f(b)n(ut)i(at)g(the)g(same)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5006
(time)f(the)h(subgoal)f(\(mark)o(ed)f(by)h FK(?)p FT(\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5007
4625 y(is)26 b(changed.)d(The)i(well-formedness)e(condition)h(ensures)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5008
(that)i(the)f(modi\002cation)e(of)i(the)g(terms)523 4725
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5009
y(introduced)18 b(by)i(the)g FI(8)1171 4737 y FC(L)1221
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5010
4725 y FT(-rules)f(does)h(not)g(af)n(fect)g(the)g(pro)o(v)n(ability)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5011
(of)i(the)g(sequent.)648 4825 y(T)-7 b(o)18 b(sho)n(w)f(that)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5012
FK(\031)s FT(-rules)g(can)f(be)h(eliminated)f(from)g(deri)n(v)n(ations)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5013
f(in)m(v)n(olving)g(well-formed)g(pro-)523 4924 y(grams,)j(we)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5014
(\002rst)g(pro)o(v)o(e)d(some)i(auxiliary)f(f)o(acts.)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5015
eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5016
%%Page: 11 11
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5017
TeXDict begin 11 10 bop 523 369 2882 4 v 523 1436 4 1068
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5018
v 616 752 a FN(::)973 611 y FQ(.)973 644 y(.)973 677
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5019
y(.)p 708 698 548 4 v 708 752 a Fp(\))p Fn(s)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5020
Fe(v)p FR(\()p Fn(z)r FR(\))p Fn(;z)r(;)p Fe(v)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5021
Fn(y)r FR(\))p Fn(;)p Fe(v)p FR(\()p Fn(y)r FR(\)\))1272
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5022
715 y FN(?)1491 459 y Fn(::)p Fp(`h)p Fe(l)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5023
Fn(b:)p Fe(v)p FR(\()p Fn(y)r FR(\)\))p Fn(;y)r(;)p Fe(v)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5024
FR(\()p Fn(z)r FR(\))p Fn(;)p Fe(l)p FR(\()p Fn(b:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5025
Fe(v)p FR(\()p Fn(z)r FR(\)\))p Fp(i\031h)p Fe(l)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5026
Fn(x:)p Fe(v)p FR(\()p Fn(y)r FR(\)\))p Fn(;y)r(;)p Fe(v)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5027
FR(\()p Fn(z)r FR(\))p Fn(;)p Fe(l)p FR(\()p Fn(x:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5028
Fe(v)p FR(\()p Fn(z)r FR(\)\))p Fp(i)p 1334 492 1858
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5029
4 v 1334 603 a FN(::)p FG(;)1430 554 y Fn(s)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5030
Fe(l)p FR(\()p Fn(b:)p Fe(v)p FR(\()p Fn(y)r FR(\)\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5031
Fn(;y)r(;)p Fe(v)p FR(\()p Fn(z)r FR(\))p Fn(;)p Fe(l)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5032
FR(\()p Fn(b:)p Fe(v)p FR(\()p Fn(z)r FR(\)\)\))1410
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5033
603 y FF(\000)-29 b(\000)-18 b(\000)h(\000)g(\000)f(\000)h(\000)g(\000)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5034
f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)f(\000)-29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5035
b(!)22 b FN(s)p FG(\()p Fx(l)p FG(\()p FN(x:)p Fx(v)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5036
FG(\()p FN(y)s FG(\)\))p FN(;)12 b(y)s(;)g Fx(v)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5037
FN(z)s FG(\))p FN(;)h Fx(l)p FG(\()p FN(x:)p Fx(v)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5038
FN(z)s FG(\)\)\))3194 517 y FQ(Ax)p 1334 641 V 1334 752
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5039
a FN(::)p FG(;)1430 703 y Fn(s)p FR(\()p Fe(l)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5040
Fn(b:)p Fe(v)p FR(\()p Fn(z)r FR(\)\))p Fn(;z)r(;)p Fe(v)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5041
FR(\()p Fn(y)r FR(\))p Fn(;)p Fe(l)p FR(\()p Fn(b:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5042
Fe(v)p FR(\()p Fn(y)r FR(\)\)\))1410 752 y FF(\000)-29
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5043
b(\000)-18 b(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5044
(\000)f(\000)h(\000)g(\000)f(\000)h(\000)f(\000)-29 b(!)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5045
b FN(s)p FG(\()p Fx(l)p FG(\()p FN(x:)p Fx(v)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5046
FN(y)s FG(\)\))p FN(;)12 b(y)s(;)g Fx(v)p FG(\()p FN(z)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5047
FG(\))p FN(;)h Fx(l)p FG(\()p FN(x:)p Fx(v)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5048
FN(z)s FG(\)\)\))3207 669 y FN(\031)3254 637 y Fp(\017)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5049
616 791 2575 4 v 666 901 a FN(::)p FG(;)762 853 y Fp(r)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5050
Fn(=s)p FR(\()p Fe(v)p FR(\()p Fn(z)r FR(\))p Fn(;z)r(;)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5051
Fe(v)p FR(\()p Fn(y)r FR(\))p Fn(;)p Fe(v)p FR(\()p Fn(y)r
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5052
FR(\)\))p Fp(\033)o Fn(s)p FR(\()p Fe(l)p FR(\()p Fn(b:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5053
Fe(v)p FR(\()p Fn(z)r FR(\)\))p Fn(;z)r(;)p Fe(v)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5054
Fn(y)r FR(\))p Fn(;)p Fe(l)p FR(\()p Fn(b:)p Fe(v)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5055
Fn(y)r FR(\)\)\))743 901 y FF(\000)-20 b(\000)j(\000)f(\000)h(\000)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5056
(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5057
(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5058
(\000)g(\000)f(\000)h(\000)g(\000)f(\000)g(!)21 b FN(s)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5059
FG(\()p Fx(l)p FG(\()p FN(x:)p Fx(v)p FG(\()p FN(y)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5060
FG(\)\))p FN(;)12 b(y)s(;)h Fx(v)p FG(\()p FN(z)s FG(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5061
FN(;)g Fx(l)p FG(\()p FN(x:)p Fx(v)p FG(\()p FN(z)s FG(\)\)\))3194
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5062
807 y FF(\033)3254 815 y Fn(L)p 666 940 2476 4 v 1509
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5063
1014 a FQ(.)1509 1047 y(.)1509 1080 y(.)284 b FG([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5064
FN(M)29 b FG(:=)22 b Fx(v)p FG(\()p FN(z)s FG(\))p FN(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5065
b(X)28 b FG(:=)21 b FN(z)s(;)13 b(T)32 b FG(:=)21 b Fx(v)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5066
FG(\()p FN(y)s FG(\))p FN(;)13 b(M)2912 1049 y Fp(0)2956
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5067
1080 y FG(:=)21 b Fx(v)p FG(\()p FN(y)s FG(\)])3157 962
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5068
y FF(8)3200 970 y Fn(L)p 638 1119 2532 4 v 638 1236 a
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5069
FN(::)p FG(;)712 1188 y Fp(8)p Fn(M)r(;X)q(;T)5 b(;M)1019
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5070
1167 y Fl(0)1031 1188 y Fn(:)p Fp(r)-11 b Fn(=s)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5071
Fn(M)r(;X)q(;T)5 b(;M)1447 1167 y Fl(0)1470 1188 y FR(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5072
Fp(\033)p Fn(s)p FR(\()p Fe(l)p FR(\()p Fn(b:M)g FR(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5073
Fn(;X)q(;T)g(;)p Fe(l)p FR(\()p Fn(b:M)2086 1167 y Fl(0)2110
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5074
1188 y FR(\)\))715 1236 y FF(\000)-35 b(\000)-17 b(\000)g(\000)f(\000)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5075
(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5076
(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5077
(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)-33
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5078
b(!)21 b FN(s)p FG(\()p Fx(l)p FG(\()p FN(x:)p Fx(v)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5079
FG(\()p FN(y)s FG(\)\))p FN(;)12 b(y)s(;)h Fx(v)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5080
FN(z)s FG(\))p FN(;)g Fx(l)p FG(\()p FN(x:)p Fx(v)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5081
FN(z)s FG(\)\)\))3185 1141 y FF(8)3228 1149 y Fn(L)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5082
590 1275 2629 4 v 590 1393 a FN(::)p FG(;)696 1344 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5083
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5084
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5085
696 1344 a Fj(N)696 1344 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5086
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5087
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5088
 696 1344 a Fn(a:)p Fp(8)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5089
Fn(M)r(;X)q(;T)5 b(;M)1056 1323 y Fl(0)1067 1344 y Fn(:)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5090
Fp(r)-11 b Fn(=s)p FR(\()p Fn(M)r(;X)q(;T)5 b(;M)1483
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5091
1323 y Fl(0)1506 1344 y FR(\))p Fp(\033)p Fn(s)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5092
Fe(l)p FR(\()p Fn(a:M)g FR(\))p Fn(;X)q(;T)g(;)p Fe(l)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5093
FR(\()p Fn(a:M)2136 1323 y Fl(0)2158 1344 y FR(\)\))666
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5094
1393 y FF(\000)-28 b(\000)-18 b(\000)h(\000)g(\000)f(\000)h(\000)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5095
(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5096
(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5097
(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)-28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5098
b(!)21 b FN(s)p FG(\()p Fx(l)p FG(\()p FN(x:)p Fx(v)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5099
FG(\()p FN(y)s FG(\)\))p FN(;)12 b(y)s(;)h Fx(v)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5100
FN(z)s FG(\))p FN(;)g Fx(l)p FG(\()p FN(x:)p Fx(v)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5101
FN(z)s FG(\)\)\))3263 1292 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5102
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5103
 3263 1292 a Fj(N)3263 1292
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5104
y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5105
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5106
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5107
 3263 1292 a 8 x Fn(L)p 3402 1436 4 1068 v 523 1439
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5108
2882 4 v 523 1582 a FO(Fig)o(.)f(5.)31 b FQ(Deduction)g(pro)o(ving)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5109
(the)f(f)o(act)g FN(s)p FP(\(l\(x.v\(y\)\),y,v\(z\),l\(x.v\(z\)\)\))26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5110
b FQ(where)31 b FP(l)g FQ(and)g FP(v)523 1674 y FQ(stand)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5111
b(for)g(lambda-abstractions)i(and)e(v)n(ariables,)h(respecti)n(v)o(ely)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5112
-5 b(.)523 1971 y Fi(Lemma)21 b(2.)41 b FE(F)-9 b(or)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5113
b(all)h(permutations)e FK(\031)s FE(,)i(the)f(sequent)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5114
FI(r)p FH(;)14 b FK(\000)46 b FI(\))34 b FK(\031)s Fu(\001)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5115
FK(G)27 b FE(is)g(derivable)f(only)f(if)i(the)523 2071
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5116
y(sequent)19 b FI(r)p FH(;)14 b FK(\031)953 2041 y Fv(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5117
FS(1)1043 2071 y Fu(\001)p FK(\000)34 b FI(\))23 b FK(G)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5118
FE(is)f(derivable)e(\(wher)m(e)h(we)h(use)g(the)f(notation)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5119
FK(\031)s Fu(\001)p FK(\000)32 b FE(to)20 b(indicate)g(that)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5120
FK(\031)523 2171 y FE(is)h(applied)e(to)h(e)o(very)h(formula)e(in)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5121
FK(\000)12 b FE(\).)523 2364 y(Pr)l(oof)o(.)40 b FT(By)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5122
b(induction)d(on)h(the)h(structure)f(of)h(deductions.)e(It)i(mak)o(es)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5123
(use)i(of)e(the)h(property)e(of)h FI(\031)523 2464 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5124
FT(that)c FI(r)k(`)g FK(t)g FI(\031)g FK(\031)s Fu(\001)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5125
FK(t)1081 2433 y Fv(0)1123 2464 y FT(holds)c(only)f(if)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5126
FI(r)k(`)g FK(\031)1776 2433 y Fv(\000)p FS(1)1865 2464
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5127
y Fu(\001)p FK(t)g FI(\031)g FK(t)2063 2433 y Fv(0)2105
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5128
2464 y FT(holds.)18 b(By)i(inspection)e(we)h(can)g(further)e(see)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5129
2563 y(that)j(no)g(additional)f FK(\031)s FT(-rule)h(is)h(necessary)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5130
(to)i(sho)n(w)f(the)g(pro)o(v)n(ability)e(in)i(both)f(directions.)191
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5131
b FI(u)-55 b(t)523 2757 y FT(The)31 b(follo)n(wing)f(corollary)g(is)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5132
(a)f(simple)f(consequence)e(of)j(this)g(lemma)f(by)g(the)h(f)o(act)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5133
(that)h(for)523 2856 y(closed)20 b FK(D)r FT(-formulae)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5134
FK(\031)s Fu(\001)p FK(D)25 b FH(=)e FK(D)f FT(holds.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5135
3055 y Fi(Cor)o(ollary)c(1.)41 b FE(F)-9 b(or)25 b(all)g(permutations)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5136
FK(\031)29 b FE(and)23 b(conte)n(xts)i FK(\000)37 b FE(consisting)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5137
b(of)i(closed)f FK(D)r FE(-formulae)523 3154 y(only)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5138
b(,)20 b FI(r)p FH(;)14 b FK(\000)35 b FI(\))23 b FK(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5139
Fu(\001)p FK(G)e FE(is)g(derivable)e(only)h(if)h FI(r)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5140
FH(;)14 b FK(\000)34 b FI(\))24 b FK(G)d FE(is)g(derivable)o(.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5141
3348 y Fi(Lemma)g(3.)41 b FE(If)23 b(the)h(sequent)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5142
FI(r)p FH(;)14 b FK(\000)41 b FI(\))28 b FK(G)d FE(is)f(derivable)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5143
(and)h FI(r)29 b(`)f FK(G)i FI(\031)e FK(G)2791 3317
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5144
y Fv(0)2814 3348 y FE(,)c(then)f(the)g(sequent)523 3447
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5145
y FI(r)p FH(;)14 b FK(\000)35 b FI(\))23 b FK(G)886 3417
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5146
y Fv(0)930 3447 y FE(is)e(derivable)o(.)523 3641 y(Pr)l(oof)o(.)40
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5147
b FT(Since)21 b FI(r)i(`)g FK(G)g FI(\031)g FK(G)1382
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5148
3611 y Fv(0)1426 3641 y FT(is)e(inducti)n(v)o(ely)d(de\002ned)i(e)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5149
(xtending)e(the)i FI(\031)p FT(-equality)e(of)i(the)g(terms)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5150
3740 y(occurring)i(in)i FK(G)h FT(and)f FK(G)1255 3710
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5151
y Fv(0)1279 3740 y FT(,)g(we)h(can)f(pro)o(v)o(e)e(this)j(lemma)e(by)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5152
(inspection)f(of)h(the)g(inference-rules,)523 3840 y(noting)c(that)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5153
(in)g(the)g FH(\()p FI(\000)p FH(\))1241 3852 y FC(L)1291
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5154
3840 y FT(-rules)f(the)h(right-hand)e(side)i(of)f(sequents)h(is)h(al)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5155
(w)o(ays)f(of)g(the)g(form)f FK(p)p FH(\()p FK(t)p FH(\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5156
3940 y FT(and)g(the)g(lemma)g(for)f(axioms)h(follo)n(ws)g(from)f(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5157
(transiti)n(vity)f(of)h FI(\031)p FT(.)648 4133 y(F)o(or)25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5158
b(sho)n(wing)f(our)h(main)h(result,)f(it)i(is)f(con)m(v)o(enient)d(to)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5159
(restrict)g(attention)f(to)h(some)f(speci\002c)523 4233
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5160
y(instances)17 b(of)f(the)g FK(\031)s FT(-rule.)g(The)g(ne)o(xt)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5161
(lemma)g(sho)n(ws)h(that)g(we)g(only)e(need)h(to)h(consider)e(unmo)o(v)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5162
n(able)523 4332 y(instances)20 b(of)g(the)g FK(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5163
FT(-rule.)523 4530 y Fi(De\002nition)g(2.)41 b FE(A)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5164
b FK(\031)s FE(-rule)h(is)g FT(mo)o(v)n(able)d FE(pr)l(o)o(vided)h(it)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5165
(is)h(not)f(dir)m(ectly)g(under)f(an)h(axiom,)f(otherwise)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5166
4630 y(it)j(is)g(said)f(to)h(be)f FT(unmo)o(v)n(able)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5167
FE(.)523 4824 y Fi(Lemma)h(4.)41 b FE(All)33 b(mo)o(vable)f(instances)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5168
(of)g(the)g FK(\031)s FE(-rules)g(can)g(be)g(r)m(eplaced)f(by)h(unmo)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5169
(vable)e(in-)523 4923 y(stances.)p eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5170
%%Page: 12 12
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5171
TeXDict begin 12 11 bop 523 448 a FE(Pr)l(oof)o(.)40
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5172
b FT(W)-7 b(e)25 b(call)f(a)g(deri)n(v)n(ation)d FK(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5173
FT(-normalised)h(if)i(all)f(instances)h(of)f(the)g FK(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5174
FT(-rule)g(are)h(unmo)o(v)n(able.)523 569 y(W)-7 b(e)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5175
b(\002rst)f(sho)n(w)g(that)g(if)g FK(\000)1351 522 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5176
FC(\031)r Fd(\001)o FC(D)1330 569 y FI(\000)-21 b(\000)g(!)32
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5177
b FK(A)26 b FT(has)f(a)g FK(\031)s FT(-normalised)e(deri)n(v)n(ation,)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5178
(then)h(we)h(can)g(construct)523 684 y(a)i FK(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5179
FT(-normalised)e(deri)n(v)n(ation)g(of)h FK(\000)1636
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5180
637 y FC(D)1615 684 y FI(\000)-39 b(!)35 b FK(A)p FT(.)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5181
b(Using)g(this)g(construction,)e(we)i(can)f(eliminate)g(the)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5182
784 y(mo)o(v)n(able)18 b FK(\031)s FT(-rules)i(from)g(an)o(y)f(deri)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5183
(v)n(ation)f(one)i(at)h(a)f(time.)648 883 y(There)f(is)i(one)f(case)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5184
(for)g(each)g(left-rule.)f(F)o(or)g FK(Ax)p FT(,)j(we)e(ha)n(v)o(e)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5185
1217 1092 482 4 v 1217 1194 a FF(r)p FG(;)14 b FN(\000)1414
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5186
1151 y Fn(\031)r Fk(\001)o Fn(A)1394 1194 y FF(\000)-21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5187
b(\000)g(!)21 b FN(\031)s Fz(\001)o FN(A)1740 1118 y(Ax)1864
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5188
1123 y FF(\000)-13 b(!)p 2059 956 V 2059 1058 a(r)p FG(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5189
b FN(\000)2255 1015 y Fn(\031)r Fk(\001)p Fn(A)2236 1058
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5190
y FF(\000)-22 b(\000)h(!)21 b FN(\031)s Fz(\001)o FN(A)2581
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5191
981 y(Ax)p 2059 1092 V 2088 1194 a FF(r)p FG(;)13 b FN(\000)2284
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5192
1151 y Fn(A)2265 1194 y FF(\000)-41 b(!)21 b FN(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5193
Fz(\001)o FN(A)2581 1124 y(\031)2628 1092 y Fp(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5194
FR(1)523 1327 y FT(since)k FK(\031)769 1296 y Fv(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5195
FS(1)858 1327 y Fu(\001)p FK(\031)s Fu(\001)p FK(A)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5196
b FH(=)g FK(A)p FT(.)25 b(A)h FK(\031)s FT(-normalised)d(deri)n(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5197
(ation)g(ending)g(in)i(a)g FK(\031)2628 1296 y Fv(0)2651
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5198
1327 y FT(-rule)f(must)h(be)g(immedi-)523 1426 y(ately)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5199
b(follo)n(wed)f(by)h FK(Ax)p FT(,)h(we)g(can)f(deri)n(v)o(e)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5200
1007 1505 656 4 v 1007 1617 a FF(r)p FG(;)13 b FN(\000)1203
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5201
1574 y Fn(\031)1241 1553 y Fl(0)1264 1574 y Fk(\001)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5202
Fn(\031)r Fk(\001)p Fn(A)1184 1617 y FF(\000)-24 b(\000)-18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5203
b(\000)h(\000)-23 b(!)21 b FN(\031)1487 1585 y Fp(0)1509
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5204
1617 y Fz(\001)p FN(\031)s Fz(\001)o FN(A)1704 1531 y(Ax)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5205
1007 1651 V 1047 1753 a FF(r)p FG(;)13 b FN(\000)1244
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5206
1710 y Fn(\031)r Fk(\001)o Fn(A)1224 1753 y FF(\000)-22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5207
b(\000)i(!)21 b FN(\031)1447 1721 y Fp(0)1469 1753 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5208
Fz(\001)o FN(\031)s Fz(\001)o FN(A)1704 1681 y(\031)1751
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5209
1649 y Fp(0)1828 1682 y FF(\000)-13 b(!)p 2023 1505 682
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5210
4 v 2023 1617 a(r)p FG(;)13 b FN(\000)2219 1574 y Fn(\031)2257
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5211
1553 y Fl(0)2279 1574 y FR(@)p Fn(\031)r Fk(\001)p Fn(A)2200
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5212
1617 y FF(\000)-33 b(\000)-17 b(\000)g(\000)f(\000)-31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5213
b(!)21 b FN(\031)2529 1585 y Fp(0)2551 1617 y Fz(\001)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5214
FN(\031)s Fz(\001)o FN(A)2746 1531 y(Ax)p 2023 1651 V
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5215
2105 1753 a FF(r)p FG(;)13 b FN(\000)2302 1710 y Fn(A)2282
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5216
1753 y FF(\000)-41 b(!)21 b FN(\031)2446 1721 y Fp(0)2468
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5217
1753 y Fz(\001)p FN(\031)s Fz(\001)o FN(A)2746 1681 y(\031)2793
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5218
1649 y Fp(0)2815 1681 y FG(@)p FN(\031)523 1881 y FT(since)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5219
FK(\031)766 1851 y Fv(0)790 1881 y Fu(\001)o FK(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5220
Fu(\001)p FK(A)k FH(=)g FK(\031)1122 1851 y Fv(0)1146
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5221
1881 y FH(@)p FK(\031)s Fu(\001)o FK(A)p FT(.)d(F)o(or)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5222
FI(8)1575 1893 y FC(L)1625 1881 y FT(,)h(since)g FK(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5223
Fu(\001)p FI(8)p FK(X)r(:D)28 b FH(=)e FI(8)p FK(X)r(:\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5224
Fu(\001)2482 1896 y Fv(f)p FC(X)5 b Fv(g)2613 1881 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5225
FK(D)25 b FT(and)c FH(\()p FK(\031)s Fu(\001)2958 1896
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5226
y Fv(f)p FC(X)5 b Fv(g)3089 1881 y FK(D)r FH(\)[)p FK(X)33
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5227
b FH(:=)523 1980 y FK(t)p FH(])23 b(=)g FK(\031)s Fu(\001)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5228
FH(\()p FK(D)r FH([)p FK(X)29 b FH(:=)23 b FK(\031)1149
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5229
1950 y Fv(\000)p FS(1)1238 1980 y Fu(\001)p FK(t)p FH(]\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5230
FT(,)e(so)f(we)h(ha)n(v)o(e)1013 2143 y FF(r)p FG(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5231
b FN(\000)1209 2082 y FR(\()p Fn(\031)r Fk(\001)1292
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5232
2096 y Fl(f)p Fc(X)s Fl(g)1406 2082 y Fn(D)r FR(\)[)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5233
Fn(X)t FR(:=)p Fn(t)p FR(])1190 2143 y FF(\000)-20 b(\000)i(\000)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5234
(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)e(!)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5235
b FN(A)p 1013 2177 755 4 v 1073 2297 a FF(r)p FG(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5236
b FN(\000)1269 2237 y Fp(8)p Fn(X)q(:\031)r Fk(\001)1432
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5237
2251 y Fl(f)p Fc(X)s Fl(g)1547 2237 y Fn(D)1250 2297
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5238
y FF(\000)-38 b(\000)-17 b(\000)g(\000)f(\000)h(\000)g(\000)f(\000)-36
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5239
b(!)21 b FN(A)1809 2199 y FF(8)1852 2207 y Fn(L)1921
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5240
2226 y FF(\000)-13 b(!)2115 2160 y(r)p FG(;)13 b FN(\000)2312
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5241
2112 y Fn(D)r FR([)p Fn(X)t FR(:=)p Fn(\031)2539 2091
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5242
y Fl(\000)p Fb(1)2614 2112 y Fk(\001)o Fn(t)p FR(])2292
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5243
2160 y FF(\000)-20 b(\000)j(\000)g(\000)f(\000)h(\000)g(\000)f(\000)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5244
(!)21 b FN(A)p 2115 2195 670 4 v 2219 2297 a FF(r)p FG(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5245
b FN(\000)2416 2254 y Fp(8)p Fn(X)q(:D)2396 2297 y FF(\000)-38
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5246
b(\000)-18 b(\000)h(\000)-38 b(!)21 b FN(A)2826 2217
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5247
y FF(8)2869 2225 y Fn(L)523 2478 y FT(where)f(by)g(induction)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5248
FI(r)p FH(;)14 b FK(\000)1399 2423 y FC(D)r FS([)p FC(X)5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5249
b FS(:=)p FC(\031)1644 2398 y Fl(\000)p Fb(1)1721 2423
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5250
y Fd(\001)o FC(t)p FS(])1378 2478 y FI(\000)-24 b(\000)-19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5251
b(\000)g(\000)g(\000)g(\000)g(\000)g(\000)-25 b(!)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5252
b FK(A)d FT(has)g(a)g FK(\031)s FT(-normalised)e(deri)n(v)n(ation)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5253
(obtained)g(from)523 2619 y(that)28 b(of)g FI(r)p FH(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5254
b FK(\000)1000 2565 y FC(\031)r Fd(\001)p FC(D)r FS([)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5255
FC(X)5 b FS(:=)p FC(\031)1308 2540 y Fl(\000)p Fb(1)1385
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5256
2565 y Fd(\001)o FC(t)p FS(])979 2619 y FI(\000)-39 b(\000)-19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5257
b(\000)g(\000)g(\000)g(\000)h(\000)f(\000)g(\000)g(\000)-40
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5258
b(!)37 b FK(A)29 b FT(.)f(The)g(cases)g(for)f FI(^)2201
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5259
2631 y FC(L)2279 2619 y FT(and)2487 2619 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5260
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5261
 2487 2619
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5262
a FD(N)2487 2619 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5263
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5264
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5265
 2487 2619 a 12 x FC(L)2565 2619 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5266
FT(are)h(straightforw)o(ard)d(since)523 2719 y FK(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5267
Fu(\001)600 2731 y Fv(B)649 2719 y FH(\()p FI(\000)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5268
FH(\))c FT(commutes)e(with)i FI(^)g FT(and)1606 2719
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5269
y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5270
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5271
 1606 2719 a FD(N)1606 2719 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5272
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5273
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5274
 1606 2719 a FT(.)g(F)o(or)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5275
FI(\033)1847 2731 y FC(L)1918 2719 y FT(we)g(ha)n(v)o(e)567
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5276
2860 y FF(r)h(`)g(r)75 b(r)p FG(;)13 b FN(\000)32 b FF(\))21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5277
b FN(\031)s Fz(\001)o FN(G)75 b FF(r)p FG(;)13 b FN(\000)1537
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5278
2817 y Fn(\031)r Fk(\001)o Fn(A)1517 2860 y FF(\000)-22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5279
b(\000)h(!)22 b FN(A)1751 2828 y Fp(0)p 567 2894 1206
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5280
4 v 787 3005 a FF(r)p FG(;)13 b FN(\000)983 2957 y Fp(r)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5281
Fn(=)p FR(\()p Fn(\031)r Fk(\001)p Fn(G)p FR(\))p Fp(\033)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5282
FR(\()p Fn(\031)r Fk(\001)p Fn(A)p FR(\))964 3005 y FF(\000)-26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5283
b(\000)-17 b(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)-25
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5284
b(!)21 b FN(A)1530 2974 y Fp(0)1814 2911 y FF(\033)1874
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5285
2919 y Fn(L)1943 2934 y FF(\000)-13 b(!)2138 2860 y(r)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5286
b(`)g(r)75 b(r)p FG(;)13 b FN(\000)32 b FF(\))21 b FN(G)75
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5287
b FF(r)p FG(;)13 b FN(\000)3036 2817 y Fn(A)3017 2860
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5288
y FF(\000)-41 b(!)21 b FN(A)3192 2828 y Fp(0)p 2138 2894
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5289
1077 4 v 2399 3005 a FF(r)p FG(;)14 b FN(\000)2596 2957
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5290
y Fp(r)p Fn(=G)p Fp(\033)p Fn(A)2577 3005 y FF(\000)-26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5291
b(\000)-18 b(\000)h(\000)g(\000)-25 b(!)21 b FN(A)2930
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5292
2974 y Fp(0)3255 2911 y FF(\033)3315 2919 y Fn(L)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5293
3127 y FT(using)i(Lemma)f(3)h(to)h(deri)n(v)o(e)e FI(r)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5294
FH(;)14 b FK(\000)40 b FI(\))29 b FK(G)24 b FT(from)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5295
FI(r)p FH(;)14 b FK(\000)40 b FI(\))29 b FK(\031)s Fu(\001)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5296
FK(G)24 b FT(and)f(the)g(induction)e(hypothesis)523 3249
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5297
y(to)f(obtain)g(a)g FK(\031)s FT(-normalised)f(deri)n(v)n(ation)f(of)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5298
FI(r)p FH(;)14 b FK(\000)2018 3202 y FC(A)1997 3249 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5299
FI(\000)-45 b(!)23 b FK(A)2185 3219 y Fv(0)2229 3249
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5300
y FT(from)c(that)i(of)e FI(r)p FH(;)14 b FK(\000)2859
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5301
3202 y FC(\031)r Fd(\001)o FC(A)2838 3249 y FI(\000)-23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5302
b(\000)e(!)24 b FK(A)3089 3219 y Fv(0)3112 3249 y FT(.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5303
3384 y Fi(Theor)o(em)c(1.)41 b FE(If)22 b FK(\000)34
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5304
b FE(consists)22 b(of)h(well-formed)e(clauses)h(and)f(the)h(sequent)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5305
FI(r)p FH(;)14 b FK(\000)38 b FI(\))26 b FK(G)d FE(is)g(deriv-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5306
3484 y(able)o(,)d(then)f(it)i(is)g(derivable)f(without)g(using)f(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5307
FK(\031)s FE(-rule)o(.)523 3611 y(Pr)l(oof)o(.)40 b FT(Since)26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5308
b FK(\000)39 b FT(consists)26 b(of)g(well-formed)e(clauses)i(only)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5309
b(,)24 b(all)j FK(\000)12 b FT(')-5 b(s)26 b(in)g(the)g(deduction)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5310
(consist)523 3703 y(of)29 b(well-formed)e(clauses)i(\(formulae)e(on)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5311
(the)h(left-hand)f(side)h(are)g(analysed)f(only)g(if)h(the)o(y)g(are)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5312
523 3794 y(selected)e(to)g(be)g(in)h(the)f(stoup-position\).)d(By)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5313
(Lemma)g(4,)g(we)g(can)g(replace)f(this)i(deduction)d(by)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5314
3885 y(one)j(in)h(which)g(all)g FK(\031)s FT(-rules)g(are)g(unmo)o(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5315
(able.)d(So)j(we)g(need)g(to)g(consider)e(ho)n(w)i(unmo)o(v)n(able)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5316
FK(\031)s FT(-)523 3977 y(rules)20 b(can)g(be)g(eliminated.)f(Recall)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5317
(that)f(unmo)o(v)n(able)e FK(\031)s FT(-rules)i(occur)f(in)h(se)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5318
(gments)g(of)g(the)g(form)1061 4339 y FG(:)847 4415 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5319
FF(r)911 4383 y Fp(00)911 4431 y Ff(bs)971 4415 y FN(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5320
b FF(r)1069 4383 y Fp(0)1112 4415 y FF(`)22 b(r)1245
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5321
4423 y Ff(ts)1703 4339 y FG(:)1393 4415 y FF(r)1457 4383
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5322
y Fp(00)1457 4431 y Ff(bs)1516 4415 y FN(;)13 b FF(r)1614
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5323
4383 y Fp(0)1637 4415 y FG(;)g FN(\000)32 b FF(\))21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5324
b FN(G)1908 4424 y Ff(bs)t Fn(;)p Ff(ts)2197 4102 y FF(r)2261
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5325
4070 y Fp(00)2261 4117 y Ff(bs)2320 4102 y FN(;)14 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5326
FF(r)2419 4070 y Fp(0)2462 4102 y FF(`)22 b FN(\031)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5327
Fz(\001)o FN(s)2638 4111 y Ff(bs)t Fn(;)p Ff(ts)2785
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5328
4102 y FF(\031)f FN(t)p 2130 4140 831 4 v 2130 4258 a
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5329
FF(r)2194 4227 y Fp(00)2194 4274 y Ff(bs)2254 4258 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5330
FN(;)13 b FF(r)2352 4227 y Fp(0)2374 4258 y FG(;)g FN(\000)2507
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5331
4203 y Fn(\031)r Fk(\001)o Fn(p)p FR(\()p Fn(s)2650 4215
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5332
y Fa(bs)s Fc(;)p Fa(ts)2759 4203 y FR(\))2487 4258 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5333
FF(\000)-21 b(\000)k(\000)f(\000)h(\000)g(\000)d(!)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5334
b FN(p)p FG(\()p FN(t)p FG(\))2989 4165 y FQ(Ax)p 2130
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5335
4297 V 2159 4415 a FF(r)2223 4383 y Fp(00)2223 4431 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5336
Ff(bs)2283 4415 y FN(;)13 b FF(r)2381 4383 y Fp(0)2403
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5337
4415 y FG(;)g FN(\000)2536 4359 y Fn(p)p FR(\()p Fn(s)2621
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5338
4371 y Fa(bs)s Fc(;)p Fa(ts)2730 4359 y FR(\))2516 4415
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5339
y FF(\000)-29 b(\000)-17 b(\000)g(\000)f(\000)-28 b(!)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5340
b FN(p)p FG(\()p FN(t)p FG(\))2989 4313 y FN(\031)p 847
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5341
4454 2085 4 v 1338 4572 a FF(r)1402 4540 y Fp(00)1402
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5342
4587 y Ff(bs)1461 4572 y FN(;)13 b FF(r)1559 4540 y Fp(0)1581
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5343
4572 y FG(;)h FN(\000)1714 4516 y Fp(r)1765 4524 y Fa(ts)1809
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5344
4516 y Fn(=G)1888 4528 y Fa(bs)s Fc(;)p Fa(ts)1998 4516
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5345
y Fp(\033)p Fn(p)p FR(\()p Fn(s)2131 4528 y Fa(bs)s Fc(;)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5346
Fa(ts)2240 4516 y FR(\))1694 4572 y FF(\000)-33 b(\000)-18
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5347
b(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5348
(\000)-33 b(!)21 b FN(p)p FG(\()p FN(t)p FG(\))2973 4470
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5349
y FF(\033)3033 4478 y Fn(L)1810 4663 y FG(:)473 b FF(g)2409
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5350
4663 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5351
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5352
 2409 4663 a FB(N)2409 4663 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5353
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5354
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5355
 2409 4663 a FF(8)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5356
1260 4702 1259 4 v 1260 4824 a(r)1324 4792 y Fp(0)1347
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5357
4824 y FG(;)13 b FN(\000)1521 4769 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5358
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5359
 1521 4769 a Fj(N)1521
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5360
4769 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5361
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5362
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5363
 1521 4769 a Fn(as:)p Fp(8)p Ff(Xs)t Fn(:)p Fp(r)1779
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5364
4780 y Fa(Xs)1843 4769 y Fn(=G)1922 4780 y Fa(as)s Fc(;)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5365
Fa(Xs)2053 4769 y Fp(\033)p Fn(p)p FR(\()p Fn(s)2186
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5366
4780 y Fa(as)s Fc(;)p Fa(Xs)2317 4769 y FR(\))1460 4824
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5367
y FF(\000)-27 b(\000)-18 b(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5368
(\000)h(\000)g(\000)f(\000)h(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5369
(\000)f(\000)-26 b(!)21 b FN(p)p FG(\()p FN(t)p FG(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5370
1260 4862 1259 4 v 1678 4938 a FF(r)1742 4907 y Fp(0)1764
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5371
4938 y FG(;)13 b FN(\000)32 b FF(\))21 b FN(p)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5372
FN(t)p FG(\))2560 4887 y FQ(Sel)3318 4523 y(\(4\))p eop
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5373
end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5374
%%Page: 13 13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5375
TeXDict begin 13 12 bop 523 448 a FT(where)23 b(the)936
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5376
448 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5377
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5378
 936 448 a FD(N)936 448 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5379
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5380
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5381
 936 448 a FT(-quanti\002er)f(introduces)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5382
g(the)i(names)g Fr(bs)31 b FT(and)23 b(the)h FI(8)p FT(-quanti\002ers)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5383
(replace)h(the)h(v)n(ari-)523 548 y(ables)g Fr(Xs)31
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5384
b FT(with)24 b(the)g(terms)g Fr(ts)7 b FT(.)24 b(W)-7
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5385
b(e)25 b(indicate)f(this)g(by)g(using)f(the)h(notation)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5386
FK(G)2831 560 y Fs(as)5 b FC(;)p Fs(Xs)3030 548 y FT(and)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5387
b FK(G)3240 560 y Fs(bs)t FC(;)p Fs(ts)3384 548 y FT(.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5388
648 y(The)19 b(freshness)f(constraints)g FI(r)1448 617
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5389
y Fv(00)1448 671 y Fs(bs)1537 648 y FT(stand)g(for)h(the)g(constraints)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5390
f(introduced)f(by)h(the)3006 648 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5391
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5392
 3006 648 a FD(N)3006
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5393
648 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5394
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5395
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5396
 3006 648 a FT(-quanti\002ers,)523 747 y(that)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5397
b(is)h FK(b)36 b FH(#)g FK(F)12 b(V)19 b FH(\()p FK(t)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5398
FH(\))28 b FT(for)f(each)g FK(b)g FT(in)h Fr(bs)7 b FT(.)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5399
b(Let)h FK(\033)j FT(be)c(the)g(substitution)f(of)h(the)h(terms)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5400
Fr(ts)34 b FT(for)26 b(the)523 847 y(v)n(ariables)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5401
b Fr(Xs)7 b FT(,)20 b(that)h(is)g(the)f(terms)g(introduced)e(by)i(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5402
FI(8)p FT(-quanti\002ers.)648 939 y(Belo)n(w)31 b(we)g(gi)n(v)o(e)g(a)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5403
(deduction)f(without)g(the)h FK(\031)s FT(-rule)g(where)f(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5404
Fr(bs)38 b FT(and)31 b Fr(ts)38 b FT(are)31 b(suitably)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5405
1030 y(changed.)17 b(F)o(or)i(this)h(we)g(choose)e(\002rst)i(some)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5406
(fresh)g(names)g Fr(cs)27 b FT(with)19 b(the)h(pro)o(viso)d(that)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5407
FK(\031)s Fu(\001)p Fr(cs)30 b FH(=)22 b FK(cs)p FT(,)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5408
1121 y(which)29 b(means)h(the)o(y)f(are)g(unaf)n(fected)f(by)h(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5409
(permutation)d(introduced)h(by)h(the)h FK(\031)s FT(-rule)f(\(such)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5410
1213 y(fresh)15 b(names)h(al)o(w)o(ays)g(e)o(xist\).)f(From)h(the)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5411
(well-formedness)f(of)i(the)f(clause)h(in)g(the)g(stoup-position,)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5412
1304 y(we)21 b(kno)n(w)e(that)h(there)g(is)h(a)f(substitution)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5413
FK(\033)1768 1274 y Fv(0)1812 1304 y FT(and)g(a)h(permutation)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5414
FK(\031)2483 1274 y Fv(0)2527 1304 y FT(such)i(that)1296
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5415
1466 y Ft(cs)28 b FG(#)22 b Ft(Xs)6 b FN(;)13 b FF(r)1668
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5416
1474 y Ff(Xs)1765 1466 y FF(`)21 b FN(\033)1880 1434
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5417
y Fp(0)1902 1466 y FG(\()p FN(p)p FG(\()p FN(s)2037 1474
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5418
y Ff(cs)t Fn(;)p Ff(Xs)2186 1466 y FG(\)\))g FF(\031)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5419
FN(p)p FG(\()p FN(s)2453 1475 y Ff(bs)s Fn(;)p Ff(Xs)2602
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5420
1466 y FG(\))1296 1557 y Ft(cs)28 b FG(#)22 b Ft(Xs)6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5421
b FN(;)13 b FF(r)1668 1565 y Ff(Xs)1765 1557 y FF(`)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5422
b FN(\033)1880 1525 y Fp(0)1902 1557 y FG(\()p FN(\031)1979
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5423
1525 y Fp(0)2001 1557 y Fz(\001)p FN(G)2086 1565 y Ff(cs)t
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5424
Fn(;)p Ff(Xs)2235 1557 y FG(\))h FF(\031)f FN(G)2428
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5425
1566 y Ff(bs)t Fn(;)p Ff(Xs)3318 1512 y FQ(\(5\))523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5426
1723 y FT(hold)g(where)h(we)g(use)h(the)f(short-hand)e(notation)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5427
Fr(cs)33 b FH(#)27 b Fr(Xs)j FT(to)22 b(refer)f(the)i(sets)g(of)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5428
(freshness)f(con-)523 1814 y(straints)h FK(c)821 1826
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5429
y FC(i)875 1814 y FH(#)k FK(X)1039 1826 y FS(1)1077 1814
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5430
y FK(;)14 b(:)g(:)g(:)f(;)h(c)1297 1826 y FC(i)1351 1814
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5431
y FH(#)26 b FK(X)1515 1826 y FC(n)1583 1814 y FT(for)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5432
b(all)h(names)g FK(c)2078 1826 y FC(i)2128 1814 y FT(in)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5433
Fr(cs)7 b FT(.)22 b(By)g(Lemma)f(1)p FE(\(ii\))p FT(,)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5434
FI(\031)g FT(is)g(preserv)o(ed)523 1905 y(under)d(substitutions,)g(so)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5435
(we)f(can)g(infer)g(from)f(\(5\))g(that)1247 2064 y Ft(cs)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5436
b FG(#)22 b Ft(Xs)27 b FF(`)22 b FN(\033)d FF(\016)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5437
FN(\033)1777 2032 y Fp(0)1799 2064 y FG(\()p FN(p)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5438
FN(s)1934 2072 y Ff(cs)s Fn(;)p Ff(Xs)2082 2064 y FG(\)\))j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5439
FF(\031)g FN(\033)s FG(\()p FN(p)p FG(\()p FN(s)2426
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5440
2073 y Ff(bs)s Fn(;)p Ff(Xs)2575 2064 y FG(\)\))1247
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5441
2155 y Ft(cs)28 b FG(#)22 b Ft(Xs)27 b FF(`)22 b FN(\033)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5442
FF(\016)f FN(\033)1777 2124 y Fp(0)1799 2155 y FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5443
FN(\031)1876 2124 y Fp(0)1898 2155 y Fz(\001)o FN(G)1982
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5444
2163 y Ff(cs)t Fn(;)p Ff(Xs)2132 2155 y FG(\))j FF(\031)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5445
FN(\033)s FG(\()p FN(G)2401 2164 y Ff(bs)t Fn(;)p Ff(Xs)2550
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5446
2155 y FG(\))3318 2110 y FQ(\(6\))523 2326 y FT(hold)16
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5447
b(where)f(the)i(right-hand)d(sides)j(are)f FK(p)p FH(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5448
FK(s)1803 2338 y Fs(bs)t FC(;)p Fs(ts)1947 2326 y FH(\))h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5449
FT(and)f FK(G)2198 2338 y Fs(bs)5 b FC(;)p Fs(ts)2342
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5450
2326 y FT(,)17 b(respecti)n(v)o(ely)-5 b(.)14 b(Note)j(that)f(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5451
FI(r)3317 2338 y Fs(Xs)523 2417 y FT(\223v)n(anish\224)j(because)h(we)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5452
(ha)n(v)o(e)g(that)g Fr(cs)30 b FH(#)23 b Fr(Xs)30 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5453
FI(`)23 b FK(\033)s FH(\()p FI(r)2098 2429 y Fs(Xs)2186
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5454
2417 y FH(\))p FT(.)e(From)e(\(6\))h(we)g(can)g(further)f(infer)h(that)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5455
1257 2580 y Ft(cs)29 b FG(#)21 b Ft(Xs)28 b FF(`)21 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5456
FN(\031)s Fz(\001)o FN(\033)f FF(\016)d FN(\033)1858
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5457
2544 y Fp(0)1880 2580 y FG(\()p FN(p)p FG(\()p FN(s)2015
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5458
2588 y Ff(cs)s Fn(;)p Ff(Xs)2164 2580 y FG(\)\))k FF(\031)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5459
FN(\031)s Fz(\001)o FG(\()p FN(p)p FG(\()p FN(s)2532
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5460
2589 y Ff(bs)s Fn(;)p Ff(ts)2657 2580 y FG(\)\))601 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5461
FQ(\(7\))1257 2696 y Ft(cs)29 b FG(#)21 b Ft(Xs)28 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5462
FF(`)21 b FN(\031)s Fz(\001)o FN(\033)f FF(\016)d FN(\033)1858
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5463
2660 y Fp(0)1880 2696 y FG(\()p FN(\031)1957 2660 y Fp(0)1979
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5464
2696 y Fz(\001)p FN(G)2064 2704 y Ff(cs)t Fn(;)p Ff(Xs)2213
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5465
2696 y FG(\))k FF(\031)g FN(\031)s Fz(\001)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5466
FN(G)2507 2705 y Ff(bs)t Fn(;)p Ff(ts)2633 2696 y FG(\))655
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5467
b FQ(\(8\))523 2860 y FT(hold)25 b(by)g(Lemma)g(1)p FE(\(i\))g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5468
FT(asserting)g(that)h FI(\031)f FT(is)i(preserv)o(ed)d(under)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5469
(permutations.)f(Recall)j(that)g(we)523 2951 y(chosen)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5470
b(the)g Fr(cs)28 b FT(so)21 b(that)g FK(\031)j FT(does)d(not)f(af)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5471
(fect)g(them.)g(So)g(if)h(we)g(apply)f(the)g(substitution)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5472
FK(\033)i FI(\016)c FK(\033)3240 2921 y Fv(0)3285 2951
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5473
y FT(and)523 3042 y(the)i(permutation)e FK(\031)25 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5474
FT(to)20 b(the)g(left-hand)f(side)h(of)g(\(7\))g(we)h(ha)n(v)o(e)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5475
FK(\031)s Fu(\001)p FK(\033)j FI(\016)c FK(\033)2577
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5476
3012 y Fv(0)2601 3042 y FH(\()p FK(p)p FH(\()p FK(s)2746
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5477
3054 y Fs(cs)5 b FC(;)p Fs(Xs)2917 3042 y FH(\)\))24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5478
b(=)f FK(p)p FH(\()p FK(s)3206 3054 y Fs(cs)t FC(;)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5479
Fs(ts)3346 3038 y Fl(0)3373 3042 y FH(\))523 3134 y FT(for)f(some)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5480
(terms)h Fr(ts)1117 3103 y Fv(0)1140 3134 y FT(.)g(Moreo)o(v)o(er)d(we)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5481
j(ha)n(v)o(e)f Fr(cs)34 b FH(#)28 b Fr(Xs)33 b FI(`)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5482
b FK(s)2278 3146 y Fs(cs)5 b FC(;)p Fs(ts)2418 3129 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5483
Fl(0)2472 3134 y FI(\031)27 b FK(\031)s Fu(\001)p FK(s)2680
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5484
3146 y Fs(bs)t FC(;)p Fs(ts)2847 3134 y FT(which)22 b(means)g(we)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5485
3225 y(can)e(replace)f(in)g(the)h(deduction)e(\(4\))h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5486
FK(\031)s Fu(\001)p FK(s)1706 3237 y Fs(bs)t FC(;)p Fs(ts)1870
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5487
3225 y FT(by)h FK(s)2013 3237 y Fs(cs)t FC(;)p Fs(ts)2153
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5488
3221 y Fl(0)2200 3225 y FT(and)f(get)h(by)f(transiti)n(vity)g(of)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5489
FI(\031)h FT(a)g(correct)523 3316 y(instance)g(of)g(the)g(axiom.)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5490
(Thus)h(we)g(can)g(form)g(the)g(deduction:)1056 3479
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5491
y FQ(.)1056 3513 y(.)1056 3546 y(.)829 3623 y FF(r)893
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5492
3591 y Fp(00)893 3636 y Ff(cs)952 3623 y FN(;)14 b FF(r)1051
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5493
3591 y Fp(0)1094 3623 y FF(`)22 b(r)1227 3635 y Ff(ts)1274
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5494
3620 y Fl(0)1720 3479 y FQ(.)1720 3513 y(.)1720 3546
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5495
y(.)1397 3623 y FF(r)1461 3591 y Fp(00)1461 3636 y Ff(cs)1520
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5496
3623 y FN(;)14 b FF(r)1619 3591 y Fp(0)1641 3623 y FG(;)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5497
FN(\000)32 b FF(\))21 b FN(G)1912 3635 y Ff(cs)t Fn(;)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5498
Ff(ts)2034 3621 y Fl(0)2230 3457 y FF(r)2294 3425 y Fp(00)2294
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5499
3470 y Ff(cs)2353 3457 y FN(;)14 b FF(r)2452 3425 y Fp(0)2495
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5500
3457 y FF(`)22 b FN(s)2600 3469 y Ff(cs)t Fn(;)p Ff(ts)2721
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5501
3455 y Fl(0)2769 3457 y FF(\031)f FN(t)p 2157 3498 795
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5502
4 v 2157 3623 a FF(r)2221 3591 y Fp(00)2221 3636 y Ff(cs)2280
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5503
3623 y FN(;)13 b FF(r)2378 3591 y Fp(0)2401 3623 y FG(;)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5504
FN(\000)2533 3560 y Fn(p)p FR(\()p Fn(s)2618 3579 y Fa(cs)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5505
Fc(;)p Fa(ts)2723 3567 y Fl(0)2750 3560 y FR(\))2514
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5506
3623 y FF(\000)-39 b(\000)-18 b(\000)h(\000)g(\000)f(\000)-38
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5507
b(!)21 b FN(p)p FG(\()p FN(t)p FG(\))2980 3523 y FQ(Ax)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5508
829 3664 2123 4 v 1305 3789 a FF(r)1369 3757 y Fp(00)1369
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5509
3802 y Ff(cs)1428 3789 y FN(;)13 b FF(r)1526 3757 y Fp(0)1549
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5510
3789 y FG(;)g FN(\000)1681 3726 y Fp(r)1732 3744 y Fa(ts)1772
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5511
3732 y Fl(0)1799 3726 y Fn(=G)1878 3744 y Fa(cs)s Fc(;)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5512
Fa(ts)1983 3732 y Fl(0)2010 3726 y Fp(\033)p Fn(p)p FR(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5513
Fn(s)2143 3744 y Fa(cs)s Fc(;)p Fa(ts)2248 3732 y Fl(0)2274
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5514
3726 y FR(\))1662 3789 y FF(\000)-22 b(\000)-17 b(\000)f(\000)h(\000)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5515
(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)d(!)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5516
b FN(p)p FG(\()p FN(t)p FG(\))2993 3680 y FF(\033)3053
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5517
3689 y Fn(L)1811 3880 y FG(:)472 b FF(g)2410 3880 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5518
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5519
 2410
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5520
3880 a FB(N)2410 3880 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5521
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5522
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5523
 2410 3880 a FF(8)p 1261 3919
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5524
1259 4 v 1261 4041 a(r)1325 4009 y Fp(0)1348 4041 y FG(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5525
b FN(\000)1522 3985 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5526
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5527
 1522 3985 a Fj(N)1522 3985 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5528
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5529
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5530
 1522
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5531
3985 a Fn(as:)p Fp(8)p Ff(Xs)t Fn(:)p Fp(r)1780 3996
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5532
y Fa(Xs)1844 3985 y Fn(=G)1923 3996 y Fa(as)s Fc(;)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5533
Fa(Xs)2054 3985 y Fp(\033)p Fn(p)p FR(\()p Fn(s)2187
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5534
3996 y Fa(as)s Fc(;)p Fa(Xs)2318 3985 y FR(\))1461 4041
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5535
y FF(\000)-28 b(\000)-17 b(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5536
(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g(\000)f(\000)h(\000)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5537
(\000)f(\000)-26 b(!)21 b FN(p)p FG(\()p FN(t)p FG(\))p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5538
1261 4079 1259 4 v 1678 4155 a FF(r)1742 4123 y Fp(0)1765
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5539
4155 y FG(;)13 b FN(\000)32 b FF(\))21 b FN(p)p FG(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5540
FN(t)p FG(\))2561 4104 y FQ(Sel)523 4327 y FT(without)k(the)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5541
FK(\031)s FT(-rule.)g(W)-7 b(e)26 b(still)h(need)e(to)g(ensure)g(that)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5542
FI(r)2205 4296 y Fv(00)2205 4347 y Fs(cs)2273 4327 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5543
FK(;)14 b FI(r)2379 4296 y Fv(0)2403 4327 y FH(;)g FK(\000)44
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5544
b FI(\))33 b FK(G)2716 4339 y Fs(cs)t FC(;)p Fs(ts)2856
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5545
4322 y Fl(0)2908 4327 y FT(and)25 b FI(r)3123 4296 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5546
Fv(00)3123 4347 y Fs(cs)3192 4327 y FK(;)14 b FI(r)3298
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5547
4296 y Fv(0)3354 4327 y FI(`)523 4426 y(r)592 4438 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5548
Fs(ts)648 4422 y Fl(0)699 4426 y FT(are)23 b(deri)n(v)n(able.)f(The)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5549
(second)g(sequent)g(is)i(deri)n(v)n(able)d(because)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5550
Fr(cs)37 b FH(#)29 b Fr(Xs)36 b FI(`)29 b FK(\033)s FH(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5551
FI(r)3125 4438 y Fs(Xs)3214 4426 y FH(\))p FT(.)24 b(F)o(or)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5552
4526 y(the)j(\002rst)h(sequent)f(we)g(can)g(infer)g(from)f(the)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5553
(original)e(\(sub\)deduction)e FI(r)2743 4496 y Fv(00)2743
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5554
4549 y Fs(bs)2811 4526 y FK(;)14 b FI(r)2917 4496 y Fv(0)2941
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5555
4526 y FH(;)g FK(\000)47 b FI(\))36 b FK(G)3260 4538
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5556
y Fs(bs)5 b FC(;)p Fs(ts)523 4625 y FT(by)28 b(Corollary)f(1)h(that)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5557
FI(r)1275 4595 y Fv(00)1275 4649 y Fs(bs)1343 4625 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5558
FK(;)14 b FI(r)1449 4595 y Fv(0)1473 4625 y FH(;)g FK(\000)49
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5559
b FI(\))38 b FK(\031)s Fu(\001)p FK(G)1873 4637 y Fs(bs)5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5560
b FC(;)p Fs(ts)2046 4625 y FT(is)30 b(deri)n(v)n(able)c(\(this)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5561
(deduction)d(does)i(not)g(in-)523 4725 y(troduce)33 b(an)o(y)h(ne)n(w)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5562
FK(\031)s FT(-rules\).)f(In)h(\(8\))f(we)h(can)f(pull)h(out)f(the)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5563
(permutation)e FK(\031)2905 4695 y Fv(0)2964 4725 y FT(and)h(we)h(ha)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5564
(v)o(e)523 4825 y FK(\031)s Fu(\001)p FK(\033)28 b FI(\016)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5565
FK(\033)792 4795 y Fv(0)816 4825 y FH(\()p FK(\031)898
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5566
4795 y Fv(0)922 4825 y Fu(\001)o FK(G)1013 4837 y Fs(cs)5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5567
b FC(;)p Fs(Xs)1185 4825 y FH(\))40 b(=)f FK(\031)s FH(@)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5568
FK(\031)1526 4795 y Fv(0)1550 4825 y Fu(\001)o FH(\()p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5569
FK(\033)29 b FI(\016)c FK(\033)1801 4795 y Fv(0)1825
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5570
4825 y FH(\()p FK(G)1922 4837 y Fs(cs)5 b FC(;)p Fs(Xs)2094
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5571
4825 y FH(\)\))p FT(.)30 b(Therefore)d(applying)g(the)i(substitution)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5572
523 4924 y(to)22 b FK(G)675 4936 y Fs(cs)5 b FC(;)p Fs(Xs)869
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5573
4924 y FT(gi)n(v)o(es)21 b FK(\031)s FH(@)p FK(\031)1228
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5574
4894 y Fv(0)1252 4924 y Fu(\001)o FH(\()p FK(\033)j FI(\016)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5575
b FK(\033)1492 4894 y Fv(0)1516 4924 y FH(\()p FK(G)1613
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5576
4936 y Fs(cs)5 b FC(;)p Fs(Xs)1785 4924 y FH(\)\))26
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5577
b(=)g FK(\031)s FH(@)p FK(\031)2131 4894 y Fv(0)2154
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5578
4924 y Fu(\001)p FK(G)2246 4936 y Fs(cs)5 b FC(;)p Fs(ts)2386
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5579
4920 y Fl(0)2435 4924 y FT(\(taking)21 b(the)h Fr(ts)2885
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5580
4894 y Fv(0)2931 4924 y FT(we)g(introduced)p eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5581
%%Page: 14 14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5582
TeXDict begin 14 13 bop 523 448 a FT(for)21 b FK(s)681
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5583
460 y Fs(cs)t FC(;)p Fs(ts)820 444 y Fl(0)869 448 y FT(earlier\).)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5584
(Thus)h(by)f(Lemma)h(3)g(we)h(can)f(sho)n(w)f(that)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5585
FI(r)2448 418 y Fv(00)2448 469 y Fs(cs)2516 448 y FK(;)14
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5586
b FI(r)2622 418 y Fv(0)2646 448 y FH(;)g FK(\000)36 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5587
FI(\))25 b FK(G)2943 460 y Fs(cs)5 b FC(;)p Fs(ts)3083
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5588
444 y Fl(0)3132 448 y FT(is)22 b(deri)n(v-)523 548 y(able.)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5589
651 y(Each)16 b(transformation)f(decreases)i(the)g(number)e(of)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5590
FK(\031)s FT(-rules)g(in)h(a)f(deduction)e(by)i(one)g(and)g(thus)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5591
751 y(by)j(repeated)f(application)f(we)j(will)g(e)n(v)o(entually)d(end)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5592
i(up)g(with)g(a)h FK(\031)s FT(-free)e(proof.)500 b FI(u)-55
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5593
b(t)523 940 y FT(W)-7 b(e)28 b(ha)n(v)o(e)e(sho)n(wn)g(that)h(when)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5594
(all)i(the)f(formulas)e(in)i FK(\000)39 b FT(are)27 b(well-formed,)d(e)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5595
n(v)o(ery)i(deduction)f(of)523 1039 y FK(\000)57 b FI(\))45
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5596
b FK(G)33 b FT(containing)d FK(\031)s FT(-rules)i(can)g(be)g(replaced)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5597
(by)h(one)g(without)f FK(\031)s FT(-rules.)h(Consequently)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5598
b(,)523 1139 y(nominal)19 b(uni\002cation)g(is)i(suf)n(\002cient)f(for)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5599
f(e)o(x)o(ecuting)f(well-formed)g FK(\013)p FT(Prolog)o(-programs.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5600
1423 y FL(4)99 b(V)-10 b(eri\002cation)26 b(of)f(W)-6
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5601
b(ell-F)n(ormedness)24 b(Using)g(Nominal)h(Matching)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5602
1632 y FT(In)19 b(this)h(section)f(we)g(consider)f(the)h(question)f(of)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5603
h(ho)n(w)g(to)g(v)o(erify)f(the)h(well-formedness)e(condition)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5604
1724 y(gi)n(v)o(en)k(in)g(De\002nition)g(1.)h(F)o(or)f(a)i(clause)1742
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5605
1724 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5606
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5607
 1742 1724 a FD(N)1742 1724 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5608
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5609
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5610
 1742 1724 a Fr(as)8
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5611
b FK(:)p FI(8)p Fr(Xs)e FK(:)p FI(r)2089 1736 y Fs(as)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5612
FC(;)p Fs(Xs)2264 1724 y FK(=G)2371 1736 y Fs(as)g FC(;)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5613
Fs(Xs)2546 1724 y FI(\033)o FK(A)2672 1736 y Fs(as)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5614
FC(;)p Fs(Xs)2848 1724 y FT(,)22 b(we)g(need)f(to)h(\002nd)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5615
1815 y(a)f(substitution)e FK(\033)24 b FT(and)c(permutation)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5616
FK(\031)24 b FT(which)19 b(mak)o(e)h(the)g(tw)o(o)h(judgements)541
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5617
1987 y Ft(bs)28 b FG(#)21 b Ft(Xs)6 b FN(;)14 b FF(r)913
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5618
1995 y Ff(as)t Fn(;)p Ff(Xs)1086 1987 y FF(`)22 b FN(\033)s
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5619
FG(\()p FN(A)1290 1996 y Ff(bs)s Fn(;)p Ff(Xs)1438 1987
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5620
y FG(\))f FF(\031)g FN(A)1628 1995 y Ff(as)t Fn(;)p Ff(Xs)1866
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5621
1987 y FT(and)84 b Ft(bs)28 b FG(#)22 b Ft(Xs)6 b FN(;)13
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5622
b FF(r)2443 1995 y Ff(as)t Fn(;)p Ff(Xs)2617 1987 y FF(`)21
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5623
b FN(\033)s FG(\()p FN(\031)s Fz(\001)o FN(G)2893 1996
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5624
y Ff(bs)t Fn(;)p Ff(Xs)3043 1987 y FG(\))g FF(\031)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5625
FN(G)3235 1995 y Ff(as)t Fn(;)p Ff(Xs)523 2164 y FT(hold.)f(F)o(or)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5626
(the)g(\002rst)h(judgement,)d FK(\033)25 b FT(can)c(be)g(found)f(by)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5627
(nominal)e(matching.)h(But)i(for)e(the)h(second)523 2264
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5628
y(judgement,)j(\002nding)i(both)f(substitution)h FK(\033)k
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5629
FT(and)c(permutation)e FK(\031)30 b FT(requires)c(solving)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5630
(\(NP-hard\))523 2363 y(equi)n(v)n(ariant)13 b(matching)h(problems.)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5631
(This)h(seemingly)f(ne)o(gati)n(v)o(e)f(result)j(should,)e(ho)n(we)n(v)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5632
o(er)m(,)e(be)j(seen)523 2463 y(in)29 b(the)f(conte)o(xt)g(that)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5633
(well-formedness)f(only)g(needs)h(to)h(be)g(v)o(eri\002ed)e(once)h(per)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5634
g(clause,)g(rather)523 2563 y(than)20 b(repeatedly)e(during)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5635
(proof-search.)e(Thus,)i(the)h(one-time)f(cost)i(of)e(performing)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5636
(equi)n(v)n(ariant)523 2662 y(uni\002cation)h(in)i(checking)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5637
(well-formedness)f(is)j(ne)o(gligible)e(compared)g(to)h(the)h(cost)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5638
(of)f(perform-)523 2762 y(ing)j(equi)n(v)n(ariant)f(uni\002cation)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5639
(throughout)d(computation.)i(Furthermore,)f(as)j(can)g(be)g(seen)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5640
(from)523 2862 y(the)h(e)o(xamples,)e(the)i(number)e(of)i(names)f(in)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5641
(a)g(clause)g(is)h(usually)e(small.)h(T)-7 b(aking)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5642
b(the)h(follo)n(wing)523 2961 y(proposition)18 b(\(whose)i(proof)e(we)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5643
(omit\))523 3154 y Fi(Pr)o(oposition)e(1.)41 b FE(If)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5644
b FK(G)1193 3166 y Fs(bs)t FC(;)p Fs(Xs)1385 3154 y FE(equivariantly)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5645
(matc)o(hes)h(with)i FK(G)2368 3166 y Fs(as)5 b FC(;)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5646
Fs(Xs)2543 3154 y FE(,)20 b(then)f(a)h(matc)o(hing)e(e)n(xists)j(in)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5647
3254 y(whic)o(h)f(the)g(permutation)f FK(\031)24 b FE(consists)c(of)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5648
(swappings)e FH(\()p FK(a)2177 3266 y FC(i)2219 3254
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5649
y FK(b)2255 3266 y FC(i)2282 3254 y FH(\))i FE(only)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5650
b(.)523 3442 y FT(into)27 b(account,)e(we)j(can)f(just)g(enumerate)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5651
(all)h(possible)g(cases)h(\()p FH(2)2458 3412 y FC(n)2530
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5652
3442 y FT(gi)n(v)o(en)e FK(n)h FT(names\))f(and)h(solv)o(e)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5653
3542 y(each)22 b(of)f(the)h(nominal)e(matching)h(problems.)f(If)i(one)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5654
(problem)f(can)i(be)g(solv)o(ed,)e(then)i(we)g(ha)n(v)o(e)f(a)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5655
3642 y FK(\033)j FT(and)c(a)g FK(\031)25 b FT(as)20 b(required)f(by)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5656
(the)g(condition.)523 3926 y FL(5)99 b(Conclusion)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5657
4122 y FT(W)-7 b(e)22 b(ha)n(v)o(e)f(sho)n(wn)g(that)g(for)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5658
(well-formed)e FK(\013)p FT(Prolog)h(programs,)g(all)h(instances)h(of)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5659
(the)g FK(\031)s FT(-rule)g(can)523 4221 y(be)j(remo)o(v)o(ed)d(from)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5660
(deductions.)f(As)i(a)h(result,)e(proof)g(search)g(using)g(only)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5661
(nominal)g(uni\002cation)523 4321 y(is)k(complete)e(for)h(such)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5662
(programs,)e(which)h(coincides)h(with)g(our)g(e)o(xperimental)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5663
(results)k(gained)523 4421 y(from)17 b(our)g(implementation)f(of)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5664
FK(\013)p FT(Prolog)o(.)h(This)g(is)h(a)g(signi\002cant)e(result,)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5665
(because)f(the)h(alternati)n(v)o(e)523 4520 y(is)j(to)g(use)f(an)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5666
(NP-hard)f(equi)n(v)n(ariant)f(uni\002cation)h(algorithm)g(for)g(proof)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5667
g(search.)648 4615 y(In)e(order)g(to)h(be)g(well-formed,)d(the)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5668
FJ(type)p FT(-program)d(gi)n(v)o(en)h(in)i(the)g(Introduction)d(needs)j
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5669
(to)g(be)523 4706 y(stated)i(as)h(follo)n(ws)800 4861
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5670
y FP(type\(Gamma,lam\(x.M\),arr\(S,T\)\))40 b(:-)1272
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5671
4953 y(x)13 b(#)f(Gamma,)f(x#S,)h(x#T,)g(type\([\(x,S\)|Gamma],M,T\).)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5672
eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5673
%%Page: 15 15
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5674
TeXDict begin 15 14 bop 523 448 a FT(e)o(xplicitly)24
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5675
b(gi)n(ving)g(the)i(freshness)e(constraints)h FJ(x#S)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5676
FT(and)g FJ(x#T)p FT(.)g(These)g(constraints)g(do)g(not)g(af-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5677
548 y(fect)f(the)f(meaning)f(of)h(the)h(program)d(because)i(term)h(v)n
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5678
(ariables)e(are)i(e)o(xpected)e(\(by)h(programmer)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5679
648 y(con)m(v)o(ention\))e(not)i(to)i(appear)e(in)h(types.)f(In)h(f)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5680
(act,)g(our)g(implementation)d(of)j FK(\013)p FT(Prolog)g(is)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5681
(strongly)523 747 y(typed)i(and)h(therefore)e(can)i(determine)e
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5682
(automatically)h(from)g(type)g(information)f(that)i(lambda-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5683
847 y(term)19 b(v)n(ariables)f(can)i(ne)n(v)o(er)d(occur)i(in)g(types.)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5684
g(Thus,)f(our)h(analysis)g(could)g(be)g(made)f(more)h(precise)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5685
946 y(by)h(taking)f(type)h(information)e(into)i(account.)648
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5686
1046 y(Let)i(us)i(brie\003y)e(mention)f(whether)h(our)f(result)i(can)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5687
(be)f(strengthened.)e(The)j(logic)f(program-)523 1146
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5688
y(ming)j(language)f FK(\025)p FT(Prolog)h([7])g(has)h(con)m(vincingly)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5689
(demonstrated)h(the)i(usefulness)f(of)g(implica-)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5690
1245 y(tions)f(in)h FK(G)p FT(-formulae)e(\(that)h(is)h(e)o(xtending)d
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5691
(logic)i(programming)d(to)k(the)f(setting)h(of)f(Hereditary)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5692
1345 y(Harrop)j(formulae\).)f(In)h FK(\013)p FT(Prolog)h(we)g(w)o(ould)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5693
g(lik)o(e)g(to)g(allo)n(w)g(implications)f(in)i FK(G)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5694
FT(-formulae)d(as)523 1445 y(well.)20 b(Whether)f(our)f(result)i(e)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5695
(xtends)e(to)i(such)f(formulae)f(is)i(still)h(open.)d(It)i(seems)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5696
(that)f(our)g(de\002ni-)523 1544 y(tion)f(of)f FK(G)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5697
FT(-formulae)f(can)i(be)g(e)o(xtended)e(to)i(include)f(e)o(xistential)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5698
(and)h(uni)n(v)o(ersal)e(formulae.)g(Ho)n(w-)523 1644
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5699
y(e)n(v)o(er)m(,)f(our)h(pro)o(ving)e(technique)h(for)h(sho)n(wing)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5700
(this)i(w)o(ould)f(require)f(some)h(subtle)h(modi\002cations\227)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5701
1743 y(for)k(e)o(xample)e(we)j(w)o(ould)e(need)h(to)g(de\002ne)f(when)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5702
(tw)o(o)g(formulae)f(with)h(quanti\002ers)f(are)h FI(\031)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5703
FT(-equal,)523 1843 y(which)j(is)i(non-tri)n(vial.)d(Ho)n(we)n(v)o(er)m
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5704
(,)f(we)j(e)o(xpect)f(that)h(this)h(can)e(be)h(done.)e(What)j(is)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5705
(impossible)g(is)523 1943 y(to)20 b(allo)n(w)871 1943
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5706
y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5707
 currentpoint currentpoint translate -1 1 scale neg exch neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5708
 871 1943 a FD(N)871 1943 y
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5709
 currentpoint currentpoint translate 1 -1 div 1 1 div scale neg exch
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5710
neg exch translate
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5711
 871 1943 a FT(-quanti\002ers)f(in)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5712
(goal-formulae.)d(Such)j(formulae)e(really)i(need)f(equi)n(v)n(ariant)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5713
(uni\002ca-)523 2042 y(tion.)523 2150 y FO(Ackno)o(wledgements:)28
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5714
b FQ(This)14 b(research)h(w)o(as)g(supported)h(by)f(a)f(fello)n(wship)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5715
(for)f(Urban)h(from)f(the)h(Ale)o(xander)o(-)523 2249
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5716
y(v)o(on-Humboldt)20 b(foundation.)523 2515 y FL(Refer)n(ences)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5717
2706 y FQ(1.)42 b(J.)22 b(Chene)o(y)-5 b(.)41 b(The)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5718
b(comple)o(xity)i(of)f(equi)n(v)n(ariant)h(uni\002cation.)40
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5719
b(In)23 b FM(Pr)m(oc.)f(of)h(International)h(Colloquium)621
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5720
2797 y(on)19 b(A)o(utomata,)f(Langua)o(g)o(es)k(and)d(Pr)m(o)o(gr)o
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5721
(amming)p FQ(,)h(v)o(olume)f(3142)h(of)f FM(LNCS)p FQ(,)f(pages)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5722
(332\226344,)h(2004.)523 2889 y(2.)42 b(J.)18 b(Chene)o(y)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5723
b(.)28 b FM(Nominal)19 b(Lo)o(gic)g(Pr)m(o)o(gr)o(amming)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5724
FQ(.)28 b(PhD)18 b(thesis,)h(Cornell)g(Uni)n(v)o(ersity)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5725
b(,)19 b(Ithaca,)g(NY)-10 b(,)18 b(2004.)523 2980 y(3.)42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5726
b(J.)18 b(Chene)o(y)i(and)g(C.)e(Urban.)28 b(Alpha-prolog:)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5727
b(A)f(logic)h(programming)g(language)h(with)d(names,)i(binding,)621
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5728
3071 y(and)e FN(\013)p FQ(-equi)n(v)n(alence.)26 b(In)17
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5729
b(B.)g(Demoen)i(and)f(V)-10 b(.)17 b(Lifschitz,)g(editors,)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5730
FM(Pr)m(oc.)g(of)h(International)g(Confer)m(ence)621
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5731
3163 y(on)h(Lo)o(gic)g(Pr)m(o)o(gr)o(amming)p FQ(,)h(v)o(olume)f(3132)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5732
(of)f FM(LNCS)p FQ(,)f(pages)i(269\226283,)h(2004.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5733
3254 y(4.)42 b(R.)14 b(Dyckhof)n(f)j(and)f(L.)e(Pinto.)19
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5734
b(Proof)c(Search)g(in)g(Constructi)n(v)o(e)h(Logic.)j(In)d(S.)e(Barry)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5735
(Cooper)h(and)g(John)g(K.)621 3345 y(T)m(russ,)28 b(editors,)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5736
FM(Pr)m(oc.)g(of)h(the)f(Lo)o(gic)h(Colloquium)g(1997)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5737
FQ(,)g(v)o(olume)g(258)h(of)e FM(London)i(Mathematical)621
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5738
3437 y(Society)19 b(Lectur)m(e)g(Note)g(Series)p FQ(,)g(pages)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5739
(53\22665.)g(Cambridge)g(Uni)n(v)o(ersity)f(Press,)f(1997.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5740
3528 y(5.)42 b(M.)25 b(J.)h(Gabbay)h(and)f(J.)g(Chene)o(y)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5741
b(.)50 b(A)25 b(proof)i(theory)f(for)g(nominal)h(logic.)49
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5742
b(In)26 b FM(Pr)m(oc.)f(of)h(Annual)g(IEEE)621 3619 y(Symposium)20
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5743
b(on)f(Lo)o(gic)g(in)g(Computer)h(Science)p FQ(,)f(pages)h(139\226148,)
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5744
h(2004.)523 3710 y(6.)42 b(J.)18 b(C.)g(Mitchell.)27
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5745
b FM(Concepts)20 b(in)f(Pr)m(o)o(gr)o(amming)g(Langua)o(g)o(es)p
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5746
FQ(.)29 b(CUP)18 b(Press,)g(2003.)523 3802 y(7.)42 b(G.)22
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5747
b(Nadathur)i(and)f(D.)g(Miller)l(.)39 b(Higher)o(-order)23
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5748
b(logic)g(programming.)42 b(In)23 b(D.)f(M.)h(Gabbay)-5
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5749
b(,)24 b(C.)e(J.)g(Hog-)621 3893 y(ger)m(,)28 b(and)g(J.)g(A.)g
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5750
(Robinson,)h(editors,)f FM(Handbook)i(of)e(Lo)o(gics)h(for)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5751
(Arti\002cial)f(Intellig)o(ence)i(and)g(Lo)o(gic)621
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5752
3984 y(Pr)m(o)o(gr)o(amming)p FQ(,)19 b(v)o(olume)g(5,)g(pages)h
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5753
(499\226590.)h(Clarendon)f(Press,)e(1998.)523 4076 y(8.)42
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5754
b(A.)28 b(M.)i(Pitts.)59 b(Nominal)29 b(logic,)g(a)h(\002rst)e(order)i
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5755
(theory)g(of)f(names)h(and)g(binding.)62 b FM(Information)30
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5756
b(and)621 4167 y(Computation)p FQ(,)19 b(186:165\226193,)j(2003.)523
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5757
4258 y(9.)42 b(C.)16 b(Urban,)h(A.)f(M.)g(Pitts,)g(and)h(M.)g(J.)f
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5758
(Gabbay)-5 b(.)24 b(Nominal)17 b(uni\002cation.)22 b
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5759
FM(Theor)m(etical)c(Computer)f(Science)p FQ(,)621 4350
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5760
y(323\(1-2\):473\226497,)22 b(2004.)p eop end
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5761
%%Trailer
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5762
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5763
userdict /end-hook known{end-hook}if
Christian Urban <urbanc@in.tum.de>
parents:
diff changeset
  5764
%%EOF