(* Title: HOL/IOA/NTP/Correctness.ML
ID: $Id$
Author: Tobias Nipkow & Konrad Slind
Copyright 1994 TU Muenchen
The main correctness proof: Impl implements Spec
*)
(* repeated from Traces.ML *)
claset_ref() := claset() delSWrapper "split_all_tac";
val hom_ioas = [Spec.ioa_def, Spec.trans_def,
Sender.sender_trans_def,Receiver.receiver_trans_def]
@ impl_ioas;
val impl_asigs = [Sender.sender_asig_def,Receiver.receiver_asig_def,
Abschannel.srch_asig_def,Abschannel.rsch_asig_def];
(* Two simpsets: - simpset() is basic, ss' unfolds hom_ioas *)
Delsimps [split_paired_All];
val ss' = (simpset() addsimps hom_ioas);
(* A lemma about restricting the action signature of the implementation
* to that of the specification.
****************************)
goal Correctness.thy
"a:externals(asig_of(restrict impl_ioa (externals spec_sig))) = \
\ (case a of \
\ S_msg(m) => True \
\ | R_msg(m) => True \
\ | S_pkt(pkt) => False \
\ | R_pkt(pkt) => False \
\ | S_ack(b) => False \
\ | R_ack(b) => False \
\ | C_m_s => False \
\ | C_m_r => False \
\ | C_r_s => False \
\ | C_r_r(m) => False)";
by (simp_tac (simpset() addsimps ([externals_def, restrict_def,
restrict_asig_def, Spec.sig_def]
@asig_projections)) 1);
by (Action.action.induct_tac "a" 1);
by (ALLGOALS(simp_tac (simpset() addsimps [actions_def]@asig_projections)));
(* 2 *)
by (simp_tac (simpset() addsimps impl_ioas) 1);
by (simp_tac (simpset() addsimps impl_asigs) 1);
by (simp_tac (simpset() addsimps
[asig_of_par, asig_comp_def]@asig_projections) 1);
by (simp_tac rename_ss 1);
(* 1 *)
by (simp_tac (simpset() addsimps impl_ioas) 1);
by (simp_tac (simpset() addsimps impl_asigs) 1);
by (simp_tac (simpset() addsimps
[asig_of_par, asig_comp_def]@asig_projections) 1);
qed "externals_lemma";
val sels = [Sender.sbit_def, Sender.sq_def, Sender.ssending_def,
Receiver.rbit_def, Receiver.rq_def, Receiver.rsending_def];
(* Proof of correctness *)
goalw Correctness.thy [Spec.ioa_def, is_weak_ref_map_def]
"is_weak_ref_map hom (restrict impl_ioa (externals spec_sig)) spec_ioa";
by (simp_tac (simpset() delsplits [split_if] addsimps
[Correctness.hom_def, cancel_restrict, externals_lemma]) 1);
by (rtac conjI 1);
by (simp_tac ss' 1);
by (asm_simp_tac (simpset() addsimps sels) 1);
by (REPEAT(rtac allI 1));
by (rtac imp_conj_lemma 1); (* from lemmas.ML *)
by (Action.action.induct_tac "a" 1);
by (asm_simp_tac (ss' addsplits [split_if]) 1);
by (forward_tac [inv4] 1);
by (fast_tac (claset() addss (simpset() addsimps [neq_Nil_conv])) 1);
by (simp_tac ss' 1);
by (simp_tac ss' 1);
by (simp_tac ss' 1);
by (simp_tac ss' 1);
by (simp_tac ss' 1);
by (simp_tac ss' 1);
by (simp_tac ss' 1);
by (asm_simp_tac ss' 1);
by (forward_tac [inv4] 1);
by (forward_tac [inv2] 1);
by (etac disjE 1);
by (Asm_simp_tac 1);
by (fast_tac (claset() addss (simpset() addsimps [neq_Nil_conv])) 1);
by (asm_simp_tac ss' 1);
by (forward_tac [inv2] 1);
by (etac disjE 1);
by (forward_tac [inv3] 1);
by (case_tac "sq(sen(s))=[]" 1);
by (asm_full_simp_tac ss' 1);
by (fast_tac (claset() addSDs [add_leD1 RS leD]) 1);
by (case_tac "m = hd(sq(sen(s)))" 1);
by (fast_tac (claset() addss (simpset() addsimps [neq_Nil_conv])) 1);
by (Asm_full_simp_tac 1);
by (fast_tac (claset() addSDs [add_leD1 RS leD]) 1);
by (Asm_full_simp_tac 1);
qed"ntp_correct";