src/FOL/ex/prolog.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/prolog.ML	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,74 @@
+(*  Title: 	FOL/ex/prolog.ML
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1992  University of Cambridge
+
+For ex/prolog.thy.  First-Order Logic: PROLOG examples
+*)
+
+open Prolog;
+
+goal Prolog.thy "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 Prolog.thy "app(?x, c:d:Nil, a:b:c:d:Nil)";
+by (REPEAT (resolve_tac [appNil,appCons] 1));
+result();
+
+
+goal Prolog.thy "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 Prolog.thy "rev(a:b:c:d:Nil, ?x)";
+val rules = [appNil,appCons,revNil,revCons];
+by (REPEAT (resolve_tac rules 1));
+result();
+
+goal Prolog.thy "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 Prolog.thy "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 Prolog.thy "rev(a:?x:c:?y:Nil, d:?z:b:?u)";
+by prolog_tac;
+result();
+
+(*rev([a..p], ?w) requires 153 inferences *)
+goal Prolog.thy "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 Prolog.thy
+    "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();
+
+writeln"Reached end of file.";