(* Title: FOL/ex/prolog.ML ID: $Id: Prolog.ML,v 1.4 2005/09/03 15:15:52 wenzelm Exp $ 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();