(* Title: ZF/IMP/Denotation.ML
ID: $Id$
Author: Heiko Loetzbeyer & Robert Sandner, TUM
Copyright 1994 TUM
*)
open Denotation;
(**** Rewrite Rules fuer A,B,C ****)
val A_rewrite_rules =
[A_nat_def,A_loc_def,A_op1_def,A_op2_def];
val B_rewrite_rules =
[B_true_def,B_false_def,B_op_def,B_not_def,B_and_def,B_or_def]
val C_rewrite_rules =
[C_skip_def,C_assign_def,C_comp_def,C_if_def,C_while_def];
(**** Type_intr for A ****)
val A_type = prove_goal Denotation.thy
"!!a.[|a:aexp; sigma:loc->nat|] ==> A(a,sigma):nat"
(fn _ => [(etac Aexp.induct 1),
(rewrite_goals_tac A_rewrite_rules),
(ALLGOALS (fast_tac (ZF_cs addSIs [apply_type])))]);
(**** Type_intr for B ****)
val B_type = prove_goal Denotation.thy
"!!b. [|b:bexp; sigma:loc->nat|] ==> B(b,sigma):bool"
(fn _ => [(etac Bexp.induct 1),
(rewrite_goals_tac B_rewrite_rules),
(ALLGOALS (fast_tac (ZF_cs
addSIs [apply_type,A_type]@bool_typechecks)))]);
(**** C_subset ****)
val C_subset = prove_goal Denotation.thy
"!!c. c:com ==> C(c) <= (loc->nat)*(loc->nat)"
(fn _ => [(etac Com.induct 1),
(rewrite_tac C_rewrite_rules),
(ALLGOALS (fast_tac (comp_cs addDs [lfp_subset RS subsetD])))]);
(**** Type_elims for C ****)
val C_type = prove_goal Denotation.thy
"[| <x,y>:C(c); c:com; \
\ !!c. [| x:loc->nat; y:loc->nat |] ==> R |] \
\ ==> R"
(fn prems => [(cut_facts_tac prems 1),
(fast_tac (ZF_cs addSIs prems
addDs [(C_subset RS subsetD)]) 1)]);
val C_type_fst = prove_goal Denotation.thy
"[| x:C(c); c:com; \
\ !!c. [| fst(x):loc->nat |] ==> R |] \
\ ==> R"
(fn prems => [(cut_facts_tac prems 1),
(resolve_tac prems 1),
(dtac (C_subset RS subsetD) 1),
(atac 1),
(etac SigmaE 1),
(asm_simp_tac ZF_ss 1)]);
(**** bnd_mono (nat->nat*nat->nat,Gamma(b,c) ****)
val Gamma_bnd_mono = prove_goalw Denotation.thy [bnd_mono_def,Gamma_def]
"!!c. c:com ==> bnd_mono ((loc->nat)*(loc->nat),Gamma(b,c))"
(fn prems => [(fast_tac (comp_cs addSIs [compI] addEs [C_type]) 1)]);
(**** End ***)