src/ZF/IMP/Denotation.ML

better representation of Sigma

(*  Title:      ZF/IMP/Denotation.ML
    ID:         $Id$
    Author:     Heiko Loetzbeyer & Robert Sandner, TUM
    Copyright   1994 TUM
*)

open Denotation;

(** Rewrite Rules for A,B,C **)
Addsimps [A_nat_def,A_loc_def,A_op1_def,A_op2_def];
Addsimps [B_true_def,B_false_def,B_op_def,B_not_def,B_and_def,B_or_def];
Addsimps [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),
             (ALLGOALS Asm_simp_tac),
             (ALLGOALS (fast_tac (claset() 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),
             (ALLGOALS Asm_simp_tac),
             (ALLGOALS (fast_tac (claset() 
                          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),
             (ALLGOALS Asm_simp_tac),
             (ALLGOALS (fast_tac (claset() 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 (claset() 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 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 => [(best_tac (claset() addEs [C_type]) 1)]);

(** End ***)