author | paulson |
Mon, 28 Dec 1998 16:54:53 +0100 | |
changeset 6047 | f2e0938ba38d |
parent 5268 | 59ef39008514 |
child 6141 | a6922171b396 |
permissions | -rw-r--r-- |
1461 | 1 |
(* Title: ZF/IMP/Equiv.ML |
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ID: $Id$ |
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Author: Heiko Loetzbeyer & Robert Sandner, TUM |
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Copyright 1994 TUM |
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*) |
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Goal "[| a: aexp; sigma: loc -> nat |] ==> \ |
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\ <a,sigma> -a-> n <-> A(a,sigma) = n"; |
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by (res_inst_tac [("x","n")] spec 1); (* quantify n *) |
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by (etac aexp.induct 1); |
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by (ALLGOALS (fast_tac (claset() addSIs evala.intrs |
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addSEs aexp_elim_cases |
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addss (simpset())))); |
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qed "aexp_iff"; |
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val aexp1 = aexp_iff RS iffD1; |
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val aexp2 = aexp_iff RS iffD2; |
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val bexp_elim_cases = |
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[ |
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evalb.mk_cases bexp.con_defs "<true,sigma> -b-> x", |
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evalb.mk_cases bexp.con_defs "<false,sigma> -b-> x", |
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evalb.mk_cases bexp.con_defs "<ROp(f,a0,a1),sigma> -b-> x", |
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evalb.mk_cases bexp.con_defs "<noti(b),sigma> -b-> x", |
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evalb.mk_cases bexp.con_defs "<b0 andi b1,sigma> -b-> x", |
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evalb.mk_cases bexp.con_defs "<b0 ori b1,sigma> -b-> x" |
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]; |
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Goal "[| b: bexp; sigma: loc -> nat |] ==> \ |
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\ <b,sigma> -b-> w <-> B(b,sigma) = w"; |
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by (res_inst_tac [("x","w")] spec 1); |
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by (etac bexp.induct 1); |
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by (ALLGOALS (fast_tac (claset() addSIs evalb.intrs |
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addSEs bexp_elim_cases |
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addss (simpset() addsimps [aexp_iff])))); |
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qed "bexp_iff"; |
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val bexp1 = bexp_iff RS iffD1; |
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val bexp2 = bexp_iff RS iffD2; |
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Goal "<c,sigma> -c-> sigma' ==> <sigma,sigma'> : C(c)"; |
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by (etac evalc.induct 1); |
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by (ALLGOALS (asm_simp_tac (simpset() addsimps [bexp1]))); |
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(* skip *) |
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by (Fast_tac 1); |
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(* assign *) |
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by (asm_full_simp_tac (simpset() addsimps |
6047
f2e0938ba38d
converted to use new primrec section and update operator
paulson
parents:
5268
diff
changeset
|
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[aexp1, update_type] @ op_type_intrs) 1); |
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(* comp *) |
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by (Fast_tac 1); |
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(* while *) |
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by (etac (Gamma_bnd_mono RS lfp_Tarski RS ssubst) 1); |
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by (asm_simp_tac (simpset() addsimps [Gamma_def, bexp1]) 1); |
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by (blast_tac (claset() addSIs [bexp1]@evalb_type_intrs) 1); |
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(* recursive case of while *) |
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by (etac (Gamma_bnd_mono RS lfp_Tarski RS ssubst) 1); |
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by (asm_full_simp_tac (simpset() addsimps [Gamma_def, bexp1]) 1); |
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by (blast_tac (claset() addSIs [bexp1]@evalb_type_intrs) 1); |
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val com1 = result(); |
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AddSIs [aexp2,bexp2,B_type,A_type]; |
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AddIs evalc.intrs; |
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AddEs [C_type,C_type_fst]; |
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Goal "c : com ==> ALL x:C(c). <c,fst(x)> -c-> snd(x)"; |
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by (etac com.induct 1); |
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(* skip *) |
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by (fast_tac (claset() addss (simpset())) 1); |
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(* assign *) |
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by (fast_tac (claset() addss (simpset())) 1); |
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(* comp *) |
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by (best_tac (claset() addss (simpset())) 1); |
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(* while *) |
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by Safe_tac; |
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by (ALLGOALS Asm_full_simp_tac); |
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by (EVERY1 [forward_tac [Gamma_bnd_mono], etac induct, atac]); |
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by (rewtac Gamma_def); |
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by Safe_tac; |
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by (EVERY1 [dtac bspec, atac]); |
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by (ALLGOALS Asm_full_simp_tac); |
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(* while, if *) |
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by (ALLGOALS Blast_tac); |
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val com2 = result(); |
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(**** Proof of Equivalence ****) |
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Goal "ALL c:com. C(c) = {io:(loc->nat)*(loc->nat). <c,fst(io)> -c-> snd(io)}"; |
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by (fast_tac (claset() addIs [C_subset RS subsetD] |
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addEs [com2 RS bspec] |
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addDs [com1] |
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addss (simpset())) 1); |
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val com_equivalence = result(); |