<HTML><HEAD> <META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"> <TITLE>G4ip Prover</TITLE></HEAD><BODY TEXT="#000000" BGCOLOR="#C7C3C7" LINK="#0000EF" VLINK="#51188E" ALINK="#FF0000"><H2>Prover for G4ip (LJT) </H2><A HREF="README">Readme</A><HR><B>Formulae:</B> F ::= <CODE>false</CODE> | A | F <CODE>&</CODE> F | F <CODE>v</CODE> F | F <CODE>-></CODE> F | F <CODE><-></CODE> F | (F)<BR><B>Sequents:</B> <CODE>=></CODE> F or [F,]* F <CODE>=></CODE> F<HR><B>Inference Rules:</B> <A HREF="G4ip.html">html</A>,<A HREF="G4ip.dvi">dvi</A> or <A HREF="G4ip.ps">ps</A>.<HR><B>Start:</B> starts the proof search, <B>Clear:</B> clears the text fields,<BR><B>Next:</B> searches for the next proof,<B>Stop:</B> stops the proof search.<HR><!-- APPLET code="G4ip/ProverApplet.class" width=600 height=100 --><APPLET code="G4ip/ProverApplet.class" archive="G4ip/ProverApplet.jar" width=600 height=100><PARAM name="LHS_size" value="22"><PARAM name="RHS_size" value="37"></APPLET><HR><B>Provable Examples:</B><TT><DL><DD> => (p v (q v r)) <-> ((p v q) v r)</DD><DD> => (p & (q & r)) <-> ((p & q) & r)</DD><DD> => (p & (q v r)) <-> ((p & q) v (p & r))</DD><DD> => (p v (q & r)) <-> ((p v q) & (p v r))</DD><DD> => (p -> p) -> (p -> p)</DD><DD> => (a -> (b -> c)) -> ((a -> b) -> (a -> c))</DD><DD> => a -> ((a -> b) -> a)</DD><DD> => b -> ((a -> b) -> b)</DD><DD> => (a & b) -> (b & a)</DD><DD> => (a -> (a -> b)) -> (a -> b)</DD><DD> => ((((p -> q) -> p) -> p) -> q) -> q</DD><DD> => (a v (a -> b)) -> (((a -> b) -> a)-> a)</DD><DD> => (a -> (b -> false)) -> (b -> (a -> false))</DD><DD> => ((a v (a -> false))-> false)-> false</DD><DD>a & b, c & d => b & c</DD><DD>(a v (a-> false)) -> false => false</DD></DL></TT><B>Non-Provable Examples:</B><TT><DL><DD> => ((a -> b) -> a) -> a</DD><DD> => a v (a -> false)</DD><DD> => (a & b v (((( a-> flase) -> false) -> q) v (b -> q)) -> q) -> q</DD></DL></TT><A HREF="fun.html">Some advanced examples</A><HR><B>Source Code:</B><A HREF="Formulae.pizza">Formulae</A>,<A HREF="Contexts.pizza">Contexts</A>,<A HREF="Sequents.pizza">Sequents</A>,<A HREF="ProofDisplay.pizza">ProofDisplay</A>,<A HREF="Prover.pizza">Prover</A>,<A HREF="Parser.pizza">Parser</A>,<A HREF="ProverApplet.pizza">Applet</A><BR><HR><B>Lambda Prolog Version:</B> The programm <A HREF="G4ip.mod">G4ip.mod</A> can be executed using <A HREF="http://www.cis.upenn.edu/~dale/lProlog/terzo/index.html">Terzo</A>Another implementation of G4ip by Joshua Hodas and Dale Miller written in <A HREF="http://www.cs.hmc.edu/~hodas/research/lolli/">Lolli</a> can be found<A HREF="ftp://ftp.cse.psu.edu/pub/dale/ic94-code/index.html">here</A>.<HR><ADDRESS><A HREF="mailto:Christian.Urban@cl.cam.ac.uk">Christian Urban</A></ADDRESS><P><!-- Created: Tue Mar 4 00:23:25 GMT 1997 --><!-- hhmts start -->Last modified: Sun May 10 18:18:28 GMT 1998<!-- hhmts end --></BODY></HTML>