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<HTML>
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<HEAD>
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<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
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<TITLE>G4ip Prover</TITLE>
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</HEAD>
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<BODY TEXT="#000000" BGCOLOR="#C7C3C7" LINK="#0000EF" VLINK="#51188E" ALINK="#FF0000">
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<H2>Prover for G4ip (LJT) </H2>
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<A HREF="README">Readme</A>
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<HR>
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<B>Formulae:</B>
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F ::= <CODE>false</CODE>
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| A
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| F <CODE>&</CODE> F
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| F <CODE>v</CODE> F
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| F <CODE>-></CODE> F
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| F <CODE><-></CODE> F
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| (F)<BR>
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<B>Sequents:</B> <CODE>=></CODE> F or
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[F,]* F <CODE>=></CODE> F
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<HR>
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<B>Inference Rules:</B>
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<A HREF="G4ip.html">html</A>,
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<A HREF="G4ip.dvi">dvi</A> or
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<A HREF="G4ip.ps">ps</A>.
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<HR>
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<B>Start:</B> starts the proof search,
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<B>Clear:</B> clears the text fields,<BR>
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<B>Next:</B> searches for the next proof,
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<B>Stop:</B> stops the proof search.
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<HR>
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<APPLET code="G4ip/ProverApplet.class" width=600 height=100>
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<PARAM name="LHS_size" value="22">
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<PARAM name="RHS_size" value="37">
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</APPLET>
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<HR>
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<B>Provable Examples:</B>
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<TT>
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<DL>
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<DD> => (p v (q v r)) <-> ((p v q) v r)</DD>
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<DD> => (p & (q & r)) <-> ((p & q) & r)</DD>
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<DD> => (p & (q v r)) <-> ((p & q) v (p & r))</DD>
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<DD> => (p v (q & r)) <-> ((p v q) & (p v r))</DD>
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<DD> => (p -> p) -> (p -> p)</DD>
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<DD> => (a -> (b -> c)) -> ((a -> b) -> (a -> c))</DD>
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<DD> => a -> ((a -> b) -> a)</DD>
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<DD> => b -> ((a -> b) -> b)</DD>
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<DD> => (a & b) -> (b & a)</DD>
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<DD> => (a -> (a -> b)) -> (a -> b)</DD>
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<DD> => ((((p -> q) -> p) -> p) -> q) -> q</DD>
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<DD> => (a v (a -> b)) -> (((a -> b) -> a)-> a)</DD>
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<DD> => (a -> (b -> false)) -> (b -> (a -> false))</DD>
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<DD> => ((a v (a -> false))-> false)-> false</DD>
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<DD>a & b, c & d => b & c</DD>
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<DD>(a v (a-> false)) -> false => false</DD>
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</DL>
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</TT>
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<B>Non-Provable Examples:</B>
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<TT>
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<DL>
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<DD> => ((a -> b) -> a) -> a</DD>
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<DD> => a v (a -> false)</DD>
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<DD> => (a & b v (((( a-> flase) -> false) -> q) v (b -> q)) -> q) -> q</DD>
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</DL>
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</TT>
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<A HREF="fun.html">Some advanced examples</A>
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<HR>
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<B>Source Code:</B>
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<A HREF="Formulae.pizza">Formulae</A>,
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<A HREF="Contexts.pizza">Contexts</A>,
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<A HREF="Sequents.pizza">Sequents</A>,
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<A HREF="ProofDisplay.pizza">ProofDisplay</A>,
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<A HREF="Prover.pizza">Prover</A>,
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<A HREF="Parser.pizza">Parser</A>,
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<A HREF="ProverApplet.pizza">Applet</A><BR>
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<HR>
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<B>Lambda Prolog Version:</B> The programm
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<A HREF="G4ip.mod">G4ip.mod</A> can be executed using
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<A HREF="http://www.cis.upenn.edu/~dale/lProlog/terzo/index.html">Terzo</A>
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Another implementation of G4ip by Joshua Hodas and Dale Miller written in
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<A HREF="http://www.cs.hmc.edu/~hodas/research/lolli/">Lolli</a> can be found
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<A HREF="ftp://ftp.cse.psu.edu/pub/dale/ic94-code/index.html">here</A>.
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<HR>
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<ADDRESS>
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<A HREF="mailto:Christian.Urban@cl.cam.ac.uk">Christian Urban</A></ADDRESS>
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<P><!-- Created: Tue Mar 4 00:23:25 GMT 1997 -->
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<!-- hhmts start -->
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Last modified: Sun May 10 18:18:13 GMT 1998
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<!-- hhmts end -->
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</BODY>
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</HTML>
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