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(* Title: HOLCF/IOA/meta_theory/LiveIOA.ML
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ID: $Id$
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Author: Olaf M"uller
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Copyright 1997 TU Muenchen
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Live I/O Automata
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*)
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Delsimps [split_paired_Ex];
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Goalw [live_implements_def]
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"!! A. [| live_implements (A,LA) (B,LB); live_implements (B,LB) (C,LC) |] \
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\ ==> live_implements (A,LA) (C,LC)";
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by Auto_tac;
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qed"live_implements_trans";
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section "Correctness of live refmap";
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(* ---------------------------------------------------------------- *)
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(* Correctness of live refmap *)
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(* ---------------------------------------------------------------- *)
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Goal "!! f. [| inp(C)=inp(A); out(C)=out(A); \
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\ is_live_ref_map f (C,M) (A,L) |] \
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\ ==> live_implements (C,M) (A,L)";
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by (asm_full_simp_tac (simpset() addsimps [is_live_ref_map_def, live_implements_def,
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livetraces_def,liveexecutions_def]) 1);
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by (safe_tac set_cs);
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by (res_inst_tac[("x","corresp_ex A f ex")] exI 1);
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by (safe_tac set_cs);
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(* Traces coincide, Lemma 1 *)
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by (pair_tac "ex" 1);
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by (etac (lemma_1 RS spec RS mp) 1);
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by (simp_tac (simpset() addsimps [externals_def])1);
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by (SELECT_GOAL (auto_tac (claset(),simpset()))1);
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by (asm_full_simp_tac (simpset() addsimps [executions_def,reachable.reachable_0]) 1);
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(* corresp_ex is execution, Lemma 2 *)
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by (pair_tac "ex" 1);
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by (asm_full_simp_tac (simpset() addsimps [executions_def]) 1);
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(* start state *)
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by (rtac conjI 1);
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by (asm_full_simp_tac (simpset() addsimps [is_ref_map_def,corresp_ex_def]) 1);
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(* is-execution-fragment *)
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by (etac (lemma_2 RS spec RS mp) 1);
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by (asm_full_simp_tac (simpset() addsimps [reachable.reachable_0]) 1);
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(* Liveness *)
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by Auto_tac;
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qed"live_implements";
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