src/FOL/ex/Prolog.ML

-(*  Title:      FOL/ex/prolog.ML
-    ID:         $Id$
-    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
-    Copyright   1992  University of Cambridge
-*)
-
-Goal "app(a:b:c:Nil, d:e:Nil, ?x)";
-by (resolve_tac [appNil,appCons] 1);
-by (resolve_tac [appNil,appCons] 1);
-by (resolve_tac [appNil,appCons] 1);
-by (resolve_tac [appNil,appCons] 1);
-prth (result());
-
-Goal "app(?x, c:d:Nil, a:b:c:d:Nil)";
-by (REPEAT (resolve_tac [appNil,appCons] 1));
-result();
-
-
-Goal "app(?x, ?y, a:b:c:d:Nil)";
-by (REPEAT (resolve_tac [appNil,appCons] 1));
-back();
-back();
-back();
-back();
-result();
-
-
-(*app([x1,...,xn], y, ?z) requires (n+1) inferences*)
-(*rev([x1,...,xn], ?y) requires (n+1)(n+2)/2 inferences*)
-
-Goal "rev(a:b:c:d:Nil, ?x)";
-val rules = [appNil,appCons,revNil,revCons];
-by (REPEAT (resolve_tac rules 1));
-result();
-
-Goal "rev(a:b:c:d:e:f:g:h:i:j:k:l:m:n:Nil, ?w)";
-by (REPEAT (resolve_tac rules 1));
-result();
-
-Goal "rev(?x, a:b:c:Nil)";
-by (REPEAT (resolve_tac rules 1)); (*does not solve it directly!*)
-back();
-back();
-
-(*backtracking version*)
-val prolog_tac = DEPTH_FIRST (has_fewer_prems 1) (resolve_tac rules 1);
-
-choplev 0;
-by prolog_tac;
-result();
-
-Goal "rev(a:?x:c:?y:Nil, d:?z:b:?u)";
-by prolog_tac;
-result();
-
-(*rev([a..p], ?w) requires 153 inferences *)
-Goal "rev(a:b:c:d:e:f:g:h:i:j:k:l:m:n:o:p:Nil, ?w)";
-by (DEPTH_SOLVE (resolve_tac ([refl,conjI]@rules) 1));
-(*Poly/ML: 4 secs >> 38 lips*)
-result();
-
-(*?x has 16, ?y has 32;  rev(?y,?w) requires 561 (rather large) inferences;
-  total inferences = 2 + 1 + 17 + 561 = 581*)
-Goal
-    "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)";
-by (DEPTH_SOLVE (resolve_tac ([refl,conjI]@rules) 1));
-(*Poly/ML: 29 secs >> 20 lips*)
-result();