src/HOLCF/IMP/Denotational.ML
changeset 2798 f84be65745b2
child 2841 c2508f4ab739
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/IMP/Denotational.ML	Mon Mar 17 15:37:41 1997 +0100
@@ -0,0 +1,81 @@
+(*  Title:      HOLCF/IMP/Denotational.ML
+    ID:         $Id$
+    Author:     Tobias Nipkow & Robert Sandner
+    Copyright   1996 TUM
+
+Equivalence of Denotational Semantics in HOLCF and Evaluation Semantics in HOL
+*)
+
+Addsimps [flift1_def];
+
+val prems = goal Lift.thy "[| f`UU = UU; f`x = Def b |] ==> EX a. x = Def a";
+by (cut_facts_tac prems 1);
+by (res_inst_tac [("x","x")] Lift_cases 1);
+ by (fast_tac (HOL_cs addSEs [DefE2]) 1);
+by (fast_tac HOL_cs 1);
+qed "strict_Def";
+
+
+goal thy "D(WHILE b DO c) = D(IF b THEN c;WHILE b DO c ELSE SKIP)";
+by(Simp_tac 1);
+by(EVERY[stac fix_eq 1, Simp_tac 1, IF_UNSOLVED	no_tac]);
+qed "D_While_If";
+
+
+goal thy "D c`UU =UU";
+by (com.induct_tac "c" 1);
+    by (ALLGOALS Asm_simp_tac);
+by (stac fix_eq 1);
+by (Asm_simp_tac 1);
+qed "D_strict";
+
+
+goal thy "!!c. <c,s> -c-> t ==> D c`(Def s) = (Def t)";
+be evalc.induct 1;
+      by (ALLGOALS Asm_simp_tac);
+ by (ALLGOALS (rtac (fix_eq RS ssubst) THEN' Asm_full_simp_tac));
+qed_spec_mp "eval_implies_D";
+
+goal thy "!s t. D c`(Def s) = (Def t) --> <c,s> -c-> t";
+by (com.induct_tac "c" 1);
+    by (fast_tac ((HOL_cs addSIs evalc.intrs) addss !simpset) 1);
+   by (fast_tac ((HOL_cs addSIs evalc.intrs) addss !simpset) 1);
+  by (Simp_tac 1);
+  by (strip_tac 1);
+  by (forward_tac [D_strict RS strict_Def] 1);
+  be exE 1;
+  by (rotate_tac ~1 1);
+  by (Asm_full_simp_tac 1);
+  by (fast_tac (HOL_cs addSIs evalc.intrs) 1);
+ by (REPEAT (rtac allI 1));
+ by (case_tac "bexp s" 1);
+  by (fast_tac ((HOL_cs addSIs evalc.intrs) unsafe_addss !simpset) 1);
+ by (fast_tac ((HOL_cs addIs evalc.intrs) unsafe_addss !simpset) 1);
+by(res_inst_tac [("Q","D (WHILE bexp DO com)`UU = UU")] conjunct1 1);
+by (Simp_tac 1);
+br fix_ind 1;
+  by(fast_tac (HOL_cs addSIs (adm_lemmas@[adm_flatdom,flat_lift])) 1);
+ by (Simp_tac 1);
+br conjI 1;
+ by (REPEAT (rtac allI 1));
+ by (case_tac "bexp s" 1);
+  (* case bexp s *)
+  by (Asm_simp_tac 1);
+  by (strip_tac 1);
+  be conjE 1;
+  bd strict_Def 1;
+   ba 1;
+  be exE 1;
+  by (rotate_tac ~1 1);
+  by (Asm_full_simp_tac 1);
+  by (fast_tac (HOL_cs addIs evalc.intrs) 1);
+ (* case ~bexp s *)
+ by (fast_tac ((HOL_cs addSIs evalc.intrs) unsafe_addss !simpset) 1);
+(* induction step for strictness *)
+by (Asm_full_simp_tac 1);
+qed_spec_mp "D_implies_eval";
+
+
+goal thy "(D c`(Def s) = (Def t)) = (<c,s> -c-> t)";
+by (fast_tac (HOL_cs addSEs [D_implies_eval,eval_implies_D]) 1);
+qed "D_is_eval";