src/FOL/ex/If.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/FOL/ex/If.ML	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,64 @@
+(*  Title: 	FOL/ex/if
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1991  University of Cambridge
+
+For ex/if.thy.  First-Order Logic: the 'if' example
+*)
+
+open If;
+open Cla;    (*in case structure Int is open!*)
+
+val prems = goalw If.thy [if_def]
+    "[| P ==> Q; ~P ==> R |] ==> if(P,Q,R)";
+by (fast_tac (FOL_cs addIs prems) 1);
+val ifI = result();
+
+val major::prems = goalw If.thy [if_def]
+   "[| if(P,Q,R);  [| P; Q |] ==> S; [| ~P; R |] ==> S |] ==> S";
+by (cut_facts_tac [major] 1);
+by (fast_tac (FOL_cs addIs prems) 1);
+val ifE = result();
+
+
+goal If.thy
+    "if(P, if(Q,A,B), if(Q,C,D)) <-> if(Q, if(P,A,C), if(P,B,D))";
+by (resolve_tac [iffI] 1);
+by (eresolve_tac [ifE] 1);
+by (eresolve_tac [ifE] 1);
+by (resolve_tac [ifI] 1);
+by (resolve_tac [ifI] 1);
+
+choplev 0;
+val if_cs = FOL_cs addSIs [ifI] addSEs[ifE];
+by (fast_tac if_cs 1);
+val if_commute = result();
+
+
+goal If.thy "if(if(P,Q,R), A, B) <-> if(P, if(Q,A,B), if(R,A,B))";
+by (fast_tac if_cs 1);
+val nested_ifs = result();
+
+choplev 0;
+by (rewrite_goals_tac [if_def]);
+by (fast_tac FOL_cs 1);
+result();
+
+
+(*An invalid formula.  High-level rules permit a simpler diagnosis*)
+goal If.thy "if(if(P,Q,R), A, B) <-> if(P, if(Q,A,B), if(R,B,A))";
+by (fast_tac if_cs 1) handle ERROR => writeln"Failed, as expected";
+(*Check that subgoals remain: proof failed.*)
+getgoal 1; 
+by (REPEAT (step_tac if_cs 1));
+
+choplev 0;
+by (rewrite_goals_tac [if_def]);
+by (fast_tac FOL_cs 1) handle ERROR => writeln"Failed, as expected";
+(*Check that subgoals remain: proof failed.*)
+getgoal 1; 
+by (REPEAT (step_tac FOL_cs 1));
+
+
+
+writeln"Reached end of file.";