| author | Christian Urban <urbanc@in.tum.de> |
| Thu, 23 Jun 2011 12:28:25 +0100 | |
| changeset 2889 | 0435c4dfd6f6 |
| parent 2617 | e44551d067e6 |
| child 2891 | 304dfe6cc83a |
| permissions | -rw-r--r-- |
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1792
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
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1 |
theory Classical |
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9ffee4eb1ae1
renamed NewParser to Nominal2
Christian Urban <urbanc@in.tum.de>
parents:
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diff
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2 |
imports "../Nominal2" |
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1792
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
3 |
begin |
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c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
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4 |
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2617
e44551d067e6
properly exported strong exhaust theorem; cleaned up some examples
Christian Urban <urbanc@in.tum.de>
parents:
2454
diff
changeset
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5 |
(* example from Urban's PhD *) |
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1792
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
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6 |
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c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
7 |
atom_decl name |
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c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
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8 |
atom_decl coname |
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c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
9 |
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c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
10 |
nominal_datatype trm = |
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Ax "name" "coname" |
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| Cut n::"coname" t1::"trm" c::"coname" t2::"trm" bind n in t1, bind c in t2 |
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("Cut <_>._ '(_')._" [100,100,100,100] 100)
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| NotR n::"name" t::"trm" "coname" bind n in t |
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("NotR '(_')._ _" [100,100,100] 100)
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| NotL c::"coname" t::"trm" "name" bind c in t |
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("NotL <_>._ _" [100,100,100] 100)
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| AndR c1::"coname" t1::"trm" c2::"coname" t2::"trm" "coname" bind c1 in t1, bind c2 in t2 |
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("AndR <_>._ <_>._ _" [100,100,100,100,100] 100)
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| AndL1 n::"name" t::"trm" "name" bind n in t |
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("AndL1 '(_')._ _" [100,100,100] 100)
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| AndL2 n::"name" t::"trm" "name" bind n in t |
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("AndL2 '(_')._ _" [100,100,100] 100)
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| OrR1 c::"coname" t::"trm" "coname" bind c in t |
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("OrR1 <_>._ _" [100,100,100] 100)
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| OrR2 c::"coname" t::"trm" "coname" bind c in t |
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("OrR2 <_>._ _" [100,100,100] 100)
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| OrL n1::"name" t1::"trm" n2::"name" t2::"trm" "name" bind n1 in t1, bind n2 in t2 |
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("OrL '(_')._ '(_')._ _" [100,100,100,100,100] 100)
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| ImpL c::"coname" t1::"trm" n::"name" t2::"trm" "name" bind c in t1, bind n in t2 |
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("ImpL <_>._ '(_')._ _" [100,100,100,100,100] 100)
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| ImpR c::"coname" n::"name" t::"trm" "coname" bind n c in t |
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("ImpR '(_').<_>._ _" [100,100,100,100] 100)
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1792
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
34 |
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2436
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
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35 |
thm trm.distinct |
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3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
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36 |
thm trm.induct |
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3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
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37 |
thm trm.exhaust |
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2617
e44551d067e6
properly exported strong exhaust theorem; cleaned up some examples
Christian Urban <urbanc@in.tum.de>
parents:
2454
diff
changeset
|
38 |
thm trm.strong_exhaust |
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e44551d067e6
properly exported strong exhaust theorem; cleaned up some examples
Christian Urban <urbanc@in.tum.de>
parents:
2454
diff
changeset
|
39 |
thm trm.strong_exhaust[simplified] |
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2436
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
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thm trm.fv_defs |
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3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
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41 |
thm trm.bn_defs |
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3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
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thm trm.perm_simps |
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3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
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thm trm.eq_iff |
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3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
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thm trm.fv_bn_eqvt |
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3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
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thm trm.size_eqvt |
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2617
e44551d067e6
properly exported strong exhaust theorem; cleaned up some examples
Christian Urban <urbanc@in.tum.de>
parents:
2454
diff
changeset
|
46 |
thm trm.supp |
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e44551d067e6
properly exported strong exhaust theorem; cleaned up some examples
Christian Urban <urbanc@in.tum.de>
parents:
2454
diff
changeset
|
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thm trm.supp[simplified] |
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1792
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
48 |
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nominal_primrec |
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crename :: "trm \<Rightarrow> coname \<Rightarrow> coname \<Rightarrow> trm" ("_[_\<turnstile>c>_]" [100,100,100] 100)
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where |
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"(Ax x a)[d\<turnstile>c>e] = (if a=d then Ax x e else Ax x a)" |
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| "atom a \<sharp> (d, e) \<Longrightarrow> (Cut <a>.M (x).N)[d\<turnstile>c>e] = Cut <a>.(M[d\<turnstile>c>e]) (x).(N[d\<turnstile>c>e])" |
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| "(NotR (x).M a)[d\<turnstile>c>e] = (if a=d then NotR (x).(M[d\<turnstile>c>e]) e else NotR (x).(M[d\<turnstile>c>e]) a)" |
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| "atom a \<sharp> (d, e) \<Longrightarrow> (NotL <a>.M x)[d\<turnstile>c>e] = (NotL <a>.(M[d\<turnstile>c>e]) x)" |
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| "\<lbrakk>atom a \<sharp> (d, e); atom b \<sharp> (d, e)\<rbrakk> \<Longrightarrow> (AndR <a>.M <b>.N c)[d\<turnstile>c>e] = |
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(if c=d then AndR <a>.(M[d\<turnstile>c>e]) <b>.(N[d \<turnstile>c>e]) e else AndR <a>.(M[d\<turnstile>c>e]) <b>.(N[d\<turnstile>c>e]) c)" |
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| "(AndL1 (x).M y)[d\<turnstile>c>e] = AndL1 (x).(M[d\<turnstile>c>e]) y" |
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| "(AndL2 (x).M y)[d\<turnstile>c>e] = AndL2 (x).(M[d\<turnstile>c>e]) y" |
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| "atom a \<sharp> (d, e) \<Longrightarrow> (OrR1 <a>.M b)[d\<turnstile>c>e] = |
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(if b=d then OrR1 <a>.(M[d\<turnstile>c>e]) e else OrR1 <a>.(M[d\<turnstile>c>e]) b)" |
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| "atom a \<sharp> (d, e) \<Longrightarrow> (OrR2 <a>.M b)[d\<turnstile>c>e] = |
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(if b=d then OrR2 <a>.(M[d\<turnstile>c>e]) e else OrR2 <a>.(M[d\<turnstile>c>e]) b)" |
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| "(OrL (x).M (y).N z)[d\<turnstile>c>e] = OrL (x).(M[d\<turnstile>c>e]) (y).(N[d\<turnstile>c>e]) z" |
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| "atom a \<sharp> (d, e) \<Longrightarrow> (ImpR (x).<a>.M b)[d\<turnstile>c>e] = |
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(if b=d then ImpR (x).<a>.(M[d\<turnstile>c>e]) e else ImpR (x).<a>.(M[d\<turnstile>c>e]) b)" |
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| "atom a \<sharp> (d, e) \<Longrightarrow> (ImpL <a>.M (x).N y)[d\<turnstile>c>e] = ImpL <a>.(M[d\<turnstile>c>e]) (x).(N[d\<turnstile>c>e]) y" |
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apply(simp only: eqvt_def) |
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apply(simp only: crename_graph_def) |
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apply (rule, perm_simp, rule) |
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apply(rule TrueI) |
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-- "covered all cases" |
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apply(case_tac x) |
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apply(rule_tac y="a" and c="(b, c)" in trm.strong_exhaust) |
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apply(simp) |
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apply(blast) |
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apply(simp add: fresh_star_def) |
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apply(blast) |
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apply(simp add: fresh_star_def) |
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apply(blast) |
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apply(simp add: fresh_star_def) |
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apply(blast) |
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apply(simp add: fresh_star_def) |
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apply(blast) |
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apply(simp add: fresh_star_def) |
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apply(blast) |
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apply(simp add: fresh_star_def) |
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apply(blast) |
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apply(simp add: fresh_star_def) |
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apply(blast) |
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apply(simp add: fresh_star_def) |
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apply(blast) |
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apply(simp add: fresh_star_def) |
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apply(metis) |
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apply(simp add: fresh_star_def) |
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apply(metis) |
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apply(simp add: fresh_star_def) |
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apply(metis) |
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-- "clashes" |
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apply(simp_all) |
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oops |
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1792
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
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c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
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103 |
end |
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c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
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c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
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c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
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106 |