src/FOL/ex/prolog.ML
author clasohm
Thu Sep 16 12:20:38 1993 +0200 (1993-09-16)
changeset 0 a5a9c433f639
permissions -rw-r--r--
Initial revision
     1 (*  Title: 	FOL/ex/prolog.ML
     2     ID:         $Id$
     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1992  University of Cambridge
     5 
     6 For ex/prolog.thy.  First-Order Logic: PROLOG examples
     7 *)
     8 
     9 open Prolog;
    10 
    11 goal Prolog.thy "app(a:b:c:Nil, d:e:Nil, ?x)";
    12 by (resolve_tac [appNil,appCons] 1);
    13 by (resolve_tac [appNil,appCons] 1);
    14 by (resolve_tac [appNil,appCons] 1);
    15 by (resolve_tac [appNil,appCons] 1);
    16 prth (result());
    17 
    18 goal Prolog.thy "app(?x, c:d:Nil, a:b:c:d:Nil)";
    19 by (REPEAT (resolve_tac [appNil,appCons] 1));
    20 result();
    21 
    22 
    23 goal Prolog.thy "app(?x, ?y, a:b:c:d:Nil)";
    24 by (REPEAT (resolve_tac [appNil,appCons] 1));
    25 back();
    26 back();
    27 back();
    28 back();
    29 result();
    30 
    31 
    32 (*app([x1,...,xn], y, ?z) requires (n+1) inferences*)
    33 (*rev([x1,...,xn], ?y) requires (n+1)(n+2)/2 inferences*)
    34 
    35 goal Prolog.thy "rev(a:b:c:d:Nil, ?x)";
    36 val rules = [appNil,appCons,revNil,revCons];
    37 by (REPEAT (resolve_tac rules 1));
    38 result();
    39 
    40 goal Prolog.thy "rev(a:b:c:d:e:f:g:h:i:j:k:l:m:n:Nil, ?w)";
    41 by (REPEAT (resolve_tac rules 1));
    42 result();
    43 
    44 goal Prolog.thy "rev(?x, a:b:c:Nil)";
    45 by (REPEAT (resolve_tac rules 1)); (*does not solve it directly!*)
    46 back();
    47 back();
    48 
    49 (*backtracking version*)
    50 val prolog_tac = DEPTH_FIRST (has_fewer_prems 1) (resolve_tac rules 1);
    51 
    52 choplev 0;
    53 by prolog_tac;
    54 result();
    55 
    56 goal Prolog.thy "rev(a:?x:c:?y:Nil, d:?z:b:?u)";
    57 by prolog_tac;
    58 result();
    59 
    60 (*rev([a..p], ?w) requires 153 inferences *)
    61 goal Prolog.thy "rev(a:b:c:d:e:f:g:h:i:j:k:l:m:n:o:p:Nil, ?w)";
    62 by (DEPTH_SOLVE (resolve_tac ([refl,conjI]@rules) 1));
    63 (*Poly/ML: 4 secs >> 38 lips*)
    64 result();
    65 
    66 (*?x has 16, ?y has 32;  rev(?y,?w) requires 561 (rather large) inferences;
    67   total inferences = 2 + 1 + 17 + 561 = 581*)
    68 goal Prolog.thy
    69     "a:b:c:d:e:f:g:h:i:j:k:l:m:n:o:p:Nil = ?x & app(?x,?x,?y) & rev(?y,?w)";
    70 by (DEPTH_SOLVE (resolve_tac ([refl,conjI]@rules) 1));
    71 (*Poly/ML: 29 secs >> 20 lips*)
    72 result();
    73 
    74 writeln"Reached end of file.";