diff -r f04b33ce250f -r a4dc62a46ee4 IOA/meta_theory/IOA.ML --- a/IOA/meta_theory/IOA.ML Tue Oct 24 14:59:17 1995 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,149 +0,0 @@ -(* Title: HOL/IOA/meta_theory/IOA.ML - ID: $Id$ - Author: Tobias Nipkow & Konrad Slind - Copyright 1994 TU Muenchen - -The I/O automata of Lynch and Tuttle. -*) - -open IOA Asig; - -val ioa_projections = [asig_of_def, starts_of_def, trans_of_def]; - -val exec_rws = [executions_def,is_execution_fragment_def]; - -goal IOA.thy -"asig_of() = x & starts_of() = y & trans_of() = z"; - by (simp_tac (SS addsimps ioa_projections) 1); - qed "ioa_triple_proj"; - -goalw IOA.thy [ioa_def,state_trans_def,actions_def, is_asig_def] - "!!A. [| IOA(A); :trans_of(A) |] ==> a:actions(asig_of(A))"; - by (REPEAT(etac conjE 1)); - by (EVERY1[etac allE, etac impE, atac]); - by (asm_full_simp_tac SS 1); -qed "trans_in_actions"; - - -goal IOA.thy "filter_oseq(p,filter_oseq(p,s)) = filter_oseq(p,s)"; - by (simp_tac (SS addsimps [filter_oseq_def]) 1); - by (rtac ext 1); - by (Option.option.induct_tac "s(i)" 1); - by (simp_tac SS 1); - by (simp_tac (SS setloop (split_tac [expand_if])) 1); -qed "filter_oseq_idemp"; - -goalw IOA.thy [mk_behaviour_def,filter_oseq_def] -"(mk_behaviour(A, s, n) = None) = \ -\ (s(n)=None | (? a. s(n)=Some(a) & a ~: externals(asig_of(A)))) \ -\ & \ -\ (mk_behaviour(A, s, n) = Some(a)) = \ -\ (s(n)=Some(a) & a : externals(asig_of(A)))"; - by (Option.option.induct_tac "s(n)" 1); - by (ALLGOALS (simp_tac (SS setloop (split_tac [expand_if])))); - by (fast_tac HOL_cs 1); -qed "mk_behaviour_thm"; - -goalw IOA.thy [reachable_def] "!!A. s:starts_of(A) ==> reachable(A,s)"; - by (res_inst_tac [("x","<%i.None,%i.s>")] bexI 1); - by (simp_tac SS 1); - by (asm_simp_tac (SS addsimps exec_rws) 1); -qed "reachable_0"; - -goalw IOA.thy (reachable_def::exec_rws) -"!!A. [| reachable(A,s); : trans_of(A) |] ==> reachable(A,t)"; - by(asm_full_simp_tac SS 1); - by(safe_tac set_cs); - by(res_inst_tac [("x","<%i.if(i")] bexI 1); - by(res_inst_tac [("x","Suc(n)")] exI 1); - by(simp_tac SS 1); - by(asm_simp_tac (SS delsimps [less_Suc_eq]) 1); - by(REPEAT(rtac allI 1)); - by(res_inst_tac [("m","na"),("n","n")] (make_elim less_linear) 1); - be disjE 1; - by(asm_simp_tac SS 1); - be disjE 1; - by(asm_simp_tac SS 1); - by(fast_tac HOL_cs 1); - by(forward_tac [less_not_sym] 1); - by(asm_simp_tac (SS addsimps [less_not_refl2]) 1); -qed "reachable_n"; - -val [p1,p2] = goalw IOA.thy [invariant_def] - "[| !!s. s:starts_of(A) ==> P(s); \ -\ !!s t a. [|reachable(A,s); P(s)|] ==> : trans_of(A) --> P(t) |] \ -\ ==> invariant(A,P)"; - by (rewrite_goals_tac(reachable_def::Let_def::exec_rws)); - by (safe_tac set_cs); - by (res_inst_tac [("Q","reachable(A,snd(ex,n))")] conjunct1 1); - by (nat_ind_tac "n" 1); - by (fast_tac (set_cs addIs [p1,reachable_0]) 1); - by (eres_inst_tac[("x","n1")]allE 1); - by (eres_inst_tac[("P","%x.!a.?Q(x,a)"), ("opt","fst(ex,n1)")] optE 1); - by (asm_simp_tac HOL_ss 1); - by (safe_tac HOL_cs); - by (etac (p2 RS mp) 1); - by (ALLGOALS(fast_tac(set_cs addDs [hd Option.option.inject RS iffD1, - reachable_n]))); -qed "invariantI"; - -val [p1,p2] = goal IOA.thy - "[| !!s. s : starts_of(A) ==> P(s); \ -\ !!s t a. reachable(A, s) ==> P(s) --> :trans_of(A) --> P(t) \ -\ |] ==> invariant(A, P)"; - by (fast_tac (HOL_cs addSIs [invariantI] addSDs [p1,p2]) 1); -qed "invariantI1"; - -val [p1,p2] = goalw IOA.thy [invariant_def] -"[| invariant(A,P); reachable(A,s) |] ==> P(s)"; - br(p2 RS (p1 RS spec RS mp))1; -qed "invariantE"; - -goal IOA.thy -"actions(asig_comp(a,b)) = actions(a) Un actions(b)"; - by(simp_tac (prod_ss addsimps - ([actions_def,asig_comp_def]@asig_projections)) 1); - by(fast_tac eq_cs 1); -qed "actions_asig_comp"; - -goal IOA.thy -"starts_of(A || B) = {p. fst(p):starts_of(A) & snd(p):starts_of(B)}"; - by(simp_tac (SS addsimps (par_def::ioa_projections)) 1); -qed "starts_of_par"; - -(* Every state in an execution is reachable *) -goalw IOA.thy [reachable_def] -"!!A. ex:executions(A) ==> !n. reachable(A, snd(ex,n))"; - by (fast_tac set_cs 1); -qed "states_of_exec_reachable"; - - -goal IOA.thy -" : trans_of(A || B || C || D) = \ -\ ((a:actions(asig_of(A)) | a:actions(asig_of(B)) | a:actions(asig_of(C)) | \ -\ a:actions(asig_of(D))) & \ -\ if(a:actions(asig_of(A)), :trans_of(A), fst(t)=fst(s)) & \ -\ if(a:actions(asig_of(B)), :trans_of(B), \ -\ fst(snd(t))=fst(snd(s))) & \ -\ if(a:actions(asig_of(C)), \ -\ :trans_of(C), \ -\ fst(snd(snd(t)))=fst(snd(snd(s)))) & \ -\ if(a:actions(asig_of(D)), \ -\ :trans_of(D), \ -\ snd(snd(snd(t)))=snd(snd(snd(s)))))"; - by(simp_tac (SS addsimps ([par_def,actions_asig_comp,Pair_fst_snd_eq]@ - ioa_projections) - setloop (split_tac [expand_if])) 1); -qed "trans_of_par4"; - -goal IOA.thy "starts_of(restrict(ioa,acts)) = starts_of(ioa) & \ -\ trans_of(restrict(ioa,acts)) = trans_of(ioa) & \ -\ reachable(restrict(ioa,acts),s) = reachable(ioa,s)"; -by(simp_tac (SS addsimps ([is_execution_fragment_def,executions_def, - reachable_def,restrict_def]@ioa_projections)) 1); -qed "cancel_restrict"; - -goal IOA.thy "asig_of(A || B) = asig_comp(asig_of(A),asig_of(B))"; - by(simp_tac (SS addsimps (par_def::ioa_projections)) 1); -qed "asig_of_par";