(* Title: HOLCF/IOA/meta_theory/LiveIOA.ML ID: $Id: LiveIOA.ML,v 1.10 2005/09/02 15:24:01 wenzelm Exp $ Author: Olaf Müller *) Delsimps [split_paired_Ex]; Goalw [live_implements_def] "!!LC. [| live_implements (A,LA) (B,LB); live_implements (B,LB) (C,LC) |] \ \ ==> live_implements (A,LA) (C,LC)"; by Auto_tac; qed"live_implements_trans"; section "Correctness of live refmap"; (* ---------------------------------------------------------------- *) (* Correctness of live refmap *) (* ---------------------------------------------------------------- *) Goal "[| inp(C)=inp(A); out(C)=out(A); \ \ is_live_ref_map f (C,M) (A,L) |] \ \ ==> live_implements (C,M) (A,L)"; by (asm_full_simp_tac (simpset() addsimps [is_live_ref_map_def, live_implements_def, livetraces_def,liveexecutions_def]) 1); by (safe_tac set_cs); by (res_inst_tac[("x","corresp_ex A f ex")] exI 1); by (safe_tac set_cs); (* Traces coincide, Lemma 1 *) by (pair_tac "ex" 1); by (etac (lemma_1 RS spec RS mp) 1); by (simp_tac (simpset() addsimps [externals_def])1); by (SELECT_GOAL (auto_tac (claset(),simpset()))1); by (asm_full_simp_tac (simpset() addsimps [executions_def,reachable.reachable_0]) 1); (* corresp_ex is execution, Lemma 2 *) by (pair_tac "ex" 1); by (asm_full_simp_tac (simpset() addsimps [executions_def]) 1); (* start state *) by (rtac conjI 1); by (asm_full_simp_tac (simpset() addsimps [is_ref_map_def,corresp_ex_def]) 1); (* is-execution-fragment *) by (etac (lemma_2 RS spec RS mp) 1); by (asm_full_simp_tac (simpset() addsimps [reachable.reachable_0]) 1); (* Liveness *) by Auto_tac; qed"live_implements";