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1 <HTML> |
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2 <HEAD> |
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3 <META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"> |
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4 <TITLE>G4ip Prover</TITLE> |
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5 </HEAD> |
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6 <BODY TEXT="#000000" BGCOLOR="#C7C3C7" LINK="#0000EF" VLINK="#51188E" ALINK="#FF0000"> |
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7 |
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8 <H2>Prover for G4ip (LJT) </H2> |
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9 |
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10 <A HREF="README">Readme</A> |
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11 |
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12 |
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13 <HR> |
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14 <B>Formulae:</B> |
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15 F ::= <CODE>false</CODE> |
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16 | A |
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17 | F <CODE>&</CODE> F |
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18 | F <CODE>v</CODE> F |
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19 | F <CODE>-></CODE> F |
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20 | F <CODE><-></CODE> F |
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21 | (F)<BR> |
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22 <B>Sequents:</B> <CODE>=></CODE> F or |
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23 [F,]* F <CODE>=></CODE> F |
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24 |
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25 <HR> |
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26 <B>Inference Rules:</B> |
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27 <A HREF="G4ip.html">html</A>, |
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28 <A HREF="G4ip.dvi">dvi</A> or |
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29 <A HREF="G4ip.ps">ps</A>. |
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30 |
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31 <HR> |
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32 <B>Start:</B> starts the proof search, |
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33 <B>Clear:</B> clears the text fields,<BR> |
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34 <B>Next:</B> searches for the next proof, |
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35 <B>Stop:</B> stops the proof search. |
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36 |
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37 <HR> |
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38 <!-- APPLET code="G4ip/ProverApplet.class" width=600 height=100 --> |
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39 <APPLET code="G4ip/ProverApplet.class" archive="G4ip/ProverApplet.jar" width=600 height=100> |
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40 <PARAM name="LHS_size" value="22"> |
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41 <PARAM name="RHS_size" value="37"> |
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42 </APPLET> |
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43 |
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44 |
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45 <HR> |
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46 <B>Provable Examples:</B> |
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47 <TT> |
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48 <DL> |
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49 <DD> => (p v (q v r)) <-> ((p v q) v r)</DD> |
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50 <DD> => (p & (q & r)) <-> ((p & q) & r)</DD> |
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51 <DD> => (p & (q v r)) <-> ((p & q) v (p & r))</DD> |
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52 <DD> => (p v (q & r)) <-> ((p v q) & (p v r))</DD> |
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53 <DD> => (p -> p) -> (p -> p)</DD> |
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54 <DD> => (a -> (b -> c)) -> ((a -> b) -> (a -> c))</DD> |
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55 <DD> => a -> ((a -> b) -> a)</DD> |
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56 <DD> => b -> ((a -> b) -> b)</DD> |
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57 <DD> => (a & b) -> (b & a)</DD> |
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58 <DD> => (a -> (a -> b)) -> (a -> b)</DD> |
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59 <DD> => ((((p -> q) -> p) -> p) -> q) -> q</DD> |
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60 <DD> => (a v (a -> b)) -> (((a -> b) -> a)-> a)</DD> |
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61 <DD> => (a -> (b -> false)) -> (b -> (a -> false))</DD> |
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62 <DD> => ((a v (a -> false))-> false)-> false</DD> |
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63 <DD>a & b, c & d => b & c</DD> |
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64 <DD>(a v (a-> false)) -> false => false</DD> |
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65 </DL> |
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66 </TT> |
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67 |
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68 <B>Non-Provable Examples:</B> |
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69 <TT> |
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70 <DL> |
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71 <DD> => ((a -> b) -> a) -> a</DD> |
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72 <DD> => a v (a -> false)</DD> |
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73 <DD> => (a & b v (((( a-> flase) -> false) -> q) v (b -> q)) -> q) -> q</DD> |
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74 </DL> |
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75 </TT> |
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76 |
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77 |
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78 <A HREF="fun.html">Some advanced examples</A> |
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79 |
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80 <HR> |
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81 <B>Source Code:</B> |
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82 <A HREF="Formulae.pizza">Formulae</A>, |
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83 <A HREF="Contexts.pizza">Contexts</A>, |
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84 <A HREF="Sequents.pizza">Sequents</A>, |
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85 <A HREF="ProofDisplay.pizza">ProofDisplay</A>, |
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86 <A HREF="Prover.pizza">Prover</A>, |
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87 <A HREF="Parser.pizza">Parser</A>, |
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88 <A HREF="ProverApplet.pizza">Applet</A><BR> |
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89 |
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90 |
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91 <HR> |
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92 <B>Lambda Prolog Version:</B> The programm |
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93 <A HREF="G4ip.mod">G4ip.mod</A> can be executed using |
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94 <A HREF="http://www.cis.upenn.edu/~dale/lProlog/terzo/index.html">Terzo</A> |
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95 Another implementation of G4ip by Joshua Hodas and Dale Miller written in |
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96 <A HREF="http://www.cs.hmc.edu/~hodas/research/lolli/">Lolli</a> can be found |
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97 <A HREF="ftp://ftp.cse.psu.edu/pub/dale/ic94-code/index.html">here</A>. |
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98 |
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99 |
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100 <HR> |
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101 <ADDRESS> |
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102 <A HREF="mailto:Christian.Urban@cl.cam.ac.uk">Christian Urban</A></ADDRESS> |
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103 |
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104 |
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105 <P><!-- Created: Tue Mar 4 00:23:25 GMT 1997 --> |
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106 <!-- hhmts start --> |
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107 Last modified: Sun May 10 18:18:28 GMT 1998 |
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108 <!-- hhmts end --> |
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109 </BODY> |
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110 </HTML> |