--- 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,y,z>) = x & starts_of(<x,y,z>) = y & trans_of(<x,y,z>) = 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); <s1,a,s2>: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); <s,a,t> : 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<n,fst(ex,i),if(i=n,Some(a),None)), \
- \ %i.if(i<Suc(n),snd(ex,i),t)>")] 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)|] ==> <s,a,t>: 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) --> <s,a,t>: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
-"<s,a,t> : 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)), <fst(s),a,fst(t)>:trans_of(A), fst(t)=fst(s)) & \
-\ if(a:actions(asig_of(B)), <fst(snd(s)),a,fst(snd(t))>:trans_of(B), \
-\ fst(snd(t))=fst(snd(s))) & \
-\ if(a:actions(asig_of(C)), \
-\ <fst(snd(snd(s))),a,fst(snd(snd(t)))>:trans_of(C), \
-\ fst(snd(snd(t)))=fst(snd(snd(s)))) & \
-\ if(a:actions(asig_of(D)), \
-\ <snd(snd(snd(s))),a,snd(snd(snd(t)))>: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";