src/FOLP/ex/prop.ML
author clasohm
Thu Sep 16 12:20:38 1993 +0200 (1993-09-16)
changeset 0 a5a9c433f639
child 1459 d12da312eff4
permissions -rw-r--r--
Initial revision
     1 (*  Title: 	FOL/ex/prop
     2     ID:         $Id$
     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1991  University of Cambridge
     5 
     6 First-Order Logic: propositional examples (intuitionistic and classical)
     7 Needs declarations of the theory "thy" and the tactic "tac"
     8 *)
     9 
    10 writeln"File FOL/ex/prop.";
    11 
    12 
    13 writeln"commutative laws of & and | ";
    14 goal thy "?p : P & Q  -->  Q & P";
    15 by tac;
    16 result();
    17 
    18 goal thy "?p : P | Q  -->  Q | P";
    19 by tac;
    20 result();
    21 
    22 
    23 writeln"associative laws of & and | ";
    24 goal thy "?p : (P & Q) & R  -->  P & (Q & R)";
    25 by tac;
    26 result();
    27 
    28 goal thy "?p : (P | Q) | R  -->  P | (Q | R)";
    29 by tac;
    30 result();
    31 
    32 
    33 
    34 writeln"distributive laws of & and | ";
    35 goal thy "?p : (P & Q) | R  --> (P | R) & (Q | R)";
    36 by tac;
    37 result();
    38 
    39 goal thy "?p : (P | R) & (Q | R)  --> (P & Q) | R";
    40 by tac;
    41 result();
    42 
    43 goal thy "?p : (P | Q) & R  --> (P & R) | (Q & R)";
    44 by tac;
    45 result();
    46 
    47 
    48 goal thy "?p : (P & R) | (Q & R)  --> (P | Q) & R";
    49 by tac;
    50 result();
    51 
    52 
    53 writeln"Laws involving implication";
    54 
    55 goal thy "?p : (P-->R) & (Q-->R) <-> (P|Q --> R)";
    56 by tac;
    57 result();
    58 
    59 
    60 goal thy "?p : (P & Q --> R) <-> (P--> (Q-->R))";
    61 by tac;
    62 result();
    63 
    64 
    65 goal thy "?p : ((P-->R)-->R) --> ((Q-->R)-->R) --> (P&Q-->R) --> R";
    66 by tac;
    67 result();
    68 
    69 goal thy "?p : ~(P-->R) --> ~(Q-->R) --> ~(P&Q-->R)";
    70 by tac;
    71 result();
    72 
    73 goal thy "?p : (P --> Q & R) <-> (P-->Q)  &  (P-->R)";
    74 by tac;
    75 result();
    76 
    77 
    78 writeln"Propositions-as-types";
    79 
    80 (*The combinator K*)
    81 goal thy "?p : P --> (Q --> P)";
    82 by tac;
    83 result();
    84 
    85 (*The combinator S*)
    86 goal thy "?p : (P-->Q-->R)  --> (P-->Q) --> (P-->R)";
    87 by tac;
    88 result();
    89 
    90 
    91 (*Converse is classical*)
    92 goal thy "?p : (P-->Q) | (P-->R)  -->  (P --> Q | R)";
    93 by tac;
    94 result();
    95 
    96 goal thy "?p : (P-->Q)  -->  (~Q --> ~P)";
    97 by tac;
    98 result();
    99 
   100 
   101 writeln"Schwichtenberg's examples (via T. Nipkow)";
   102 
   103 (* stab-imp *)
   104 goal thy "?p : (((Q-->R)-->R)-->Q) --> (((P-->Q)-->R)-->R)-->P-->Q";
   105 by tac;
   106 result();
   107 
   108 (* stab-to-peirce *)
   109 goal thy "?p : (((P --> R) --> R) --> P) --> (((Q --> R) --> R) --> Q) \
   110 \	      --> ((P --> Q) --> P) --> P";
   111 by tac;
   112 result();
   113 
   114 (* peirce-imp1 *)
   115 goal thy "?p : (((Q --> R) --> Q) --> Q) \
   116 \	       --> (((P --> Q) --> R) --> P --> Q) --> P --> Q";
   117 by tac;
   118 result();
   119   
   120 (* peirce-imp2 *)
   121 goal thy "?p : (((P --> R) --> P) --> P) --> ((P --> Q --> R) --> P) --> P";
   122 by tac;
   123 result();
   124 
   125 (* mints  *)
   126 goal thy "?p : ((((P --> Q) --> P) --> P) --> Q) --> Q";
   127 by tac;
   128 result();
   129 
   130 (* mints-solovev *)
   131 goal thy "?p : (P --> (Q --> R) --> Q) --> ((P --> Q) --> R) --> R";
   132 by tac;
   133 result();
   134 
   135 (* tatsuta *)
   136 goal thy "?p : (((P7 --> P1) --> P10) --> P4 --> P5) \
   137 \	  --> (((P8 --> P2) --> P9) --> P3 --> P10) \
   138 \	  --> (P1 --> P8) --> P6 --> P7 \
   139 \	  --> (((P3 --> P2) --> P9) --> P4) \
   140 \	  --> (P1 --> P3) --> (((P6 --> P1) --> P2) --> P9) --> P5";
   141 by tac;
   142 result();
   143 
   144 (* tatsuta1 *)
   145 goal thy "?p : (((P8 --> P2) --> P9) --> P3 --> P10) \
   146 \    --> (((P3 --> P2) --> P9) --> P4) \
   147 \    --> (((P6 --> P1) --> P2) --> P9) \
   148 \    --> (((P7 --> P1) --> P10) --> P4 --> P5) \
   149 \    --> (P1 --> P3) --> (P1 --> P8) --> P6 --> P7 --> P5";
   150 by tac;
   151 result();
   152 
   153 writeln"Reached end of file.";