moved to .. (see also new version in HOLCF/IOA/meta_theory);
--- a/src/HOL/IOA/meta_theory/Asig.ML Wed Apr 30 11:53:30 1997 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,19 +0,0 @@
-(* Title: HOL/IOA/meta_theory/Asig.ML
- ID: $Id$
- Author: Tobias Nipkow & Konrad Slind
- Copyright 1994 TU Muenchen
-
-Action signatures
-*)
-
-open Asig;
-
-val asig_projections = [asig_inputs_def, asig_outputs_def, asig_internals_def];
-
-goal Asig.thy "!!a.[| a~:internals(S) ;a~:externals(S)|] ==> a~:actions(S)";
-by (asm_full_simp_tac (!simpset addsimps [externals_def,actions_def]) 1);
-qed"int_and_ext_is_act";
-
-goal Asig.thy "!!a.[|a:externals(S)|] ==> a:actions(S)";
-by (asm_full_simp_tac (!simpset addsimps [externals_def,actions_def]) 1);
-qed"ext_is_act";
--- a/src/HOL/IOA/meta_theory/Asig.thy Wed Apr 30 11:53:30 1997 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,45 +0,0 @@
-(* Title: HOL/IOA/meta_theory/Asig.thy
- ID: $Id$
- Author: Tobias Nipkow & Konrad Slind
- Copyright 1994 TU Muenchen
-
-Action signatures
-*)
-
-Asig = Prod +
-
-types
-
-'a signature = "('a set * 'a set * 'a set)"
-
-consts
- actions,inputs,outputs,internals,externals
- ::"'action signature => 'action set"
- is_asig ::"'action signature => bool"
- mk_ext_asig ::"'action signature => 'action signature"
-
-
-defs
-
-asig_inputs_def "inputs == fst"
-asig_outputs_def "outputs == (fst o snd)"
-asig_internals_def "internals == (snd o snd)"
-
-actions_def
- "actions(asig) == (inputs(asig) Un outputs(asig) Un internals(asig))"
-
-externals_def
- "externals(asig) == (inputs(asig) Un outputs(asig))"
-
-is_asig_def
- "is_asig(triple) ==
- ((inputs(triple) Int outputs(triple) = {}) &
- (outputs(triple) Int internals(triple) = {}) &
- (inputs(triple) Int internals(triple) = {}))"
-
-
-mk_ext_asig_def
- "mk_ext_asig(triple) == (inputs(triple), outputs(triple), {})"
-
-
-end
--- a/src/HOL/IOA/meta_theory/IOA.ML Wed Apr 30 11:53:30 1997 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,176 +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.
-*)
-
-Addsimps [Let_def];
-
-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 (!simpset 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 1);
-qed "trans_in_actions";
-
-
-goal IOA.thy "filter_oseq p (filter_oseq p s) = filter_oseq p s";
- by (simp_tac (!simpset addsimps [filter_oseq_def]) 1);
- by (rtac ext 1);
- by (Option.option.induct_tac "s(i)" 1);
- by (Simp_tac 1);
- by (simp_tac (!simpset setloop (split_tac [expand_if])) 1);
-qed "filter_oseq_idemp";
-
-goalw IOA.thy [mk_trace_def,filter_oseq_def]
-"(mk_trace A s n = None) = \
-\ (s(n)=None | (? a. s(n)=Some(a) & a ~: externals(asig_of(A)))) \
-\ & \
-\ (mk_trace 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 (!simpset setloop (split_tac [expand_if]))));
- by (Fast_tac 1);
-qed "mk_trace_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 1);
- by (asm_simp_tac (!simpset 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 (!simpset delsimps bex_simps) 1);
- by (safe_tac (!claset));
- by (res_inst_tac [("x","(%i.if i<n then fst ex i \
-\ else (if i=n then Some a else None), \
-\ %i.if i<Suc n then snd ex i else t)")] bexI 1);
- by (res_inst_tac [("x","Suc(n)")] exI 1);
- by (Simp_tac 1);
- by (Asm_simp_tac 1);
- by (REPEAT(rtac allI 1));
- by (res_inst_tac [("m","na"),("n","n")] (make_elim less_linear) 1);
- by (etac disjE 1);
- by (asm_simp_tac (!simpset addsimps [less_Suc_eq]) 1);
- by (etac disjE 1);
- by (Asm_simp_tac 1);
- by (forward_tac [less_not_sym] 1);
- by (asm_simp_tac (!simpset addsimps [less_not_refl2,less_Suc_eq]) 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 (!claset));
- by (res_inst_tac [("Q","reachable A (snd ex n)")] conjunct1 1);
- by (nat_ind_tac "n" 1);
- by (fast_tac (!claset addIs [p1,reachable_0]) 1);
- by (eres_inst_tac[("x","n")]allE 1);
- by (eres_inst_tac[("P","%x.!a.?Q x a"), ("opt","fst ex n")] optionE 1);
- by (Asm_simp_tac 1);
- by (safe_tac (!claset));
- by (etac (p2 RS mp) 1);
- by (ALLGOALS(fast_tac(!claset 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 (!claset addSIs [invariantI] addSDs [p1,p2]) 1);
-qed "invariantI1";
-
-val [p1,p2] = goalw IOA.thy [invariant_def]
-"[| invariant A P; reachable A s |] ==> P(s)";
- by (rtac (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 (!simpset addsimps
- ([actions_def,asig_comp_def]@asig_projections)) 1);
- by (Fast_tac 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 (!simpset 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 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)) then (fst(s),a,fst(t)):trans_of(A) \
-\ else fst t=fst s) & \
-\ (if a:actions(asig_of(B)) then (fst(snd(s)),a,fst(snd(t))):trans_of(B) \
-\ else fst(snd(t))=fst(snd(s))) & \
-\ (if a:actions(asig_of(C)) then \
-\ (fst(snd(snd(s))),a,fst(snd(snd(t)))):trans_of(C) \
-\ else fst(snd(snd(t)))=fst(snd(snd(s)))) & \
-\ (if a:actions(asig_of(D)) then \
-\ (snd(snd(snd(s))),a,snd(snd(snd(t)))):trans_of(D) \
-\ else snd(snd(snd(t)))=snd(snd(snd(s)))))";
- by (simp_tac (!simpset 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 (!simpset 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 (!simpset addsimps (par_def::ioa_projections)) 1);
-qed "asig_of_par";
-
-
-goal IOA.thy "externals(asig_of(A1||A2)) = \
-\ (externals(asig_of(A1)) Un externals(asig_of(A2)))";
-by (asm_full_simp_tac (!simpset addsimps [externals_def,asig_of_par,asig_comp_def,asig_inputs_def,asig_outputs_def,Un_def,set_diff_def]) 1);
-by (rtac set_ext 1);
-by (Fast_tac 1);
-qed"externals_of_par";
-
-goalw IOA.thy [externals_def,actions_def,compat_ioas_def,compat_asigs_def]
- "!! a. [| compat_ioas A1 A2; a:externals(asig_of(A1))|] ==> a~:internals(asig_of(A2))";
-by (Asm_full_simp_tac 1);
-by (best_tac (!claset addEs [equalityCE]) 1);
-qed"ext1_is_not_int2";
-
-goalw IOA.thy [externals_def,actions_def,compat_ioas_def,compat_asigs_def]
- "!! a. [| compat_ioas A2 A1 ; a:externals(asig_of(A1))|] ==> a~:internals(asig_of(A2))";
-by (Asm_full_simp_tac 1);
-by (best_tac (!claset addEs [equalityCE]) 1);
-qed"ext2_is_not_int1";
-
-val ext1_ext2_is_not_act2 = ext1_is_not_int2 RS int_and_ext_is_act;
-val ext1_ext2_is_not_act1 = ext2_is_not_int1 RS int_and_ext_is_act;
-
--- a/src/HOL/IOA/meta_theory/IOA.thy Wed Apr 30 11:53:30 1997 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,196 +0,0 @@
-(* Title: HOL/IOA/meta_theory/IOA.thy
- ID: $Id$
- Author: Tobias Nipkow & Konrad Slind
- Copyright 1994 TU Muenchen
-
-The I/O automata of Lynch and Tuttle.
-*)
-
-IOA = Asig + Option +
-
-types
- 'a seq = "nat => 'a"
- 'a oseq = "nat => 'a option"
- ('a,'b)execution = "'a oseq * 'b seq"
- ('a,'s)transition = "('s * 'a * 's)"
- ('a,'s)ioa = "'a signature * 's set * ('a,'s)transition set"
-
-consts
-
- (* IO automata *)
- state_trans::"['action signature, ('action,'state)transition set] => bool"
- asig_of ::"('action,'state)ioa => 'action signature"
- starts_of ::"('action,'state)ioa => 'state set"
- trans_of ::"('action,'state)ioa => ('action,'state)transition set"
- IOA ::"('action,'state)ioa => bool"
-
- (* Executions, schedules, and traces *)
-
- is_execution_fragment,
- has_execution ::"[('action,'state)ioa, ('action,'state)execution] => bool"
- executions :: "('action,'state)ioa => ('action,'state)execution set"
- mk_trace :: "[('action,'state)ioa, 'action oseq] => 'action oseq"
- reachable :: "[('action,'state)ioa, 'state] => bool"
- invariant :: "[('action,'state)ioa, 'state=>bool] => bool"
- has_trace :: "[('action,'state)ioa, 'action oseq] => bool"
- traces :: "('action,'state)ioa => 'action oseq set"
- NF :: "'a oseq => 'a oseq"
-
- (* Composition of action signatures and automata *)
- compatible_asigs ::"('a => 'action signature) => bool"
- asig_composition ::"('a => 'action signature) => 'action signature"
- compatible_ioas ::"('a => ('action,'state)ioa) => bool"
- ioa_composition ::"('a => ('action, 'state)ioa) =>('action,'a => 'state)ioa"
-
- (* binary composition of action signatures and automata *)
- compat_asigs ::"['action signature, 'action signature] => bool"
- asig_comp ::"['action signature, 'action signature] => 'action signature"
- compat_ioas ::"[('action,'s)ioa, ('action,'t)ioa] => bool"
- "||" ::"[('a,'s)ioa, ('a,'t)ioa] => ('a,'s*'t)ioa" (infixr 10)
-
- (* Filtering and hiding *)
- filter_oseq :: "('a => bool) => 'a oseq => 'a oseq"
-
- restrict_asig :: "['a signature, 'a set] => 'a signature"
- restrict :: "[('a,'s)ioa, 'a set] => ('a,'s)ioa"
-
- (* Notions of correctness *)
- ioa_implements :: "[('action,'state1)ioa, ('action,'state2)ioa] => bool"
-
- (* Instantiation of abstract IOA by concrete actions *)
- rename:: "('a, 'b)ioa => ('c => 'a option) => ('c,'b)ioa"
-
-defs
-
-state_trans_def
- "state_trans asig R ==
- (!triple. triple:R --> fst(snd(triple)):actions(asig)) &
- (!a. (a:inputs(asig)) --> (!s1. ? s2. (s1,a,s2):R))"
-
-
-asig_of_def "asig_of == fst"
-starts_of_def "starts_of == (fst o snd)"
-trans_of_def "trans_of == (snd o snd)"
-
-ioa_def
- "IOA(ioa) == (is_asig(asig_of(ioa)) &
- (~ starts_of(ioa) = {}) &
- state_trans (asig_of ioa) (trans_of ioa))"
-
-
-(* An execution fragment is modelled with a pair of sequences:
- * the first is the action options, the second the state sequence.
- * Finite executions have None actions from some point on.
- *******)
-is_execution_fragment_def
- "is_execution_fragment A ex ==
- let act = fst(ex); state = snd(ex)
- in !n a. (act(n)=None --> state(Suc(n)) = state(n)) &
- (act(n)=Some(a) --> (state(n),a,state(Suc(n))):trans_of(A))"
-
-
-executions_def
- "executions(ioa) == {e. snd e 0:starts_of(ioa) &
- is_execution_fragment ioa e}"
-
-
-reachable_def
- "reachable ioa s == (? ex:executions(ioa). ? n. (snd ex n) = s)"
-
-
-invariant_def "invariant A P == (!s. reachable A s --> P(s))"
-
-
-(* Restrict the trace to those members of the set s *)
-filter_oseq_def
- "filter_oseq p s ==
- (%i.case s(i)
- of None => None
- | Some(x) => if p x then Some x else None)"
-
-
-mk_trace_def
- "mk_trace(ioa) == filter_oseq(%a.a:externals(asig_of(ioa)))"
-
-
-(* Does an ioa have an execution with the given trace *)
-has_trace_def
- "has_trace ioa b ==
- (? ex:executions(ioa). b = mk_trace ioa (fst ex))"
-
-normal_form_def
- "NF(tr) == @nf. ? f. mono(f) & (!i. nf(i)=tr(f(i))) &
- (!j. j ~: range(f) --> nf(j)= None) &
- (!i. nf(i)=None --> (nf (Suc i)) = None) "
-
-(* All the traces of an ioa *)
-
- traces_def
- "traces(ioa) == {trace. ? tr. trace=NF(tr) & has_trace ioa tr}"
-
-(*
- traces_def
- "traces(ioa) == {tr. has_trace ioa tr}"
-*)
-
-compat_asigs_def
- "compat_asigs a1 a2 ==
- (((outputs(a1) Int outputs(a2)) = {}) &
- ((internals(a1) Int actions(a2)) = {}) &
- ((internals(a2) Int actions(a1)) = {}))"
-
-
-compat_ioas_def
- "compat_ioas ioa1 ioa2 == compat_asigs (asig_of(ioa1)) (asig_of(ioa2))"
-
-
-asig_comp_def
- "asig_comp a1 a2 ==
- (((inputs(a1) Un inputs(a2)) - (outputs(a1) Un outputs(a2)),
- (outputs(a1) Un outputs(a2)),
- (internals(a1) Un internals(a2))))"
-
-
-par_def
- "(ioa1 || ioa2) ==
- (asig_comp (asig_of ioa1) (asig_of ioa2),
- {pr. fst(pr):starts_of(ioa1) & snd(pr):starts_of(ioa2)},
- {tr. let s = fst(tr); a = fst(snd(tr)); t = snd(snd(tr))
- in (a:actions(asig_of(ioa1)) | a:actions(asig_of(ioa2))) &
- (if a:actions(asig_of(ioa1)) then
- (fst(s),a,fst(t)):trans_of(ioa1)
- else fst(t) = fst(s))
- &
- (if a:actions(asig_of(ioa2)) then
- (snd(s),a,snd(t)):trans_of(ioa2)
- else snd(t) = snd(s))})"
-
-
-restrict_asig_def
- "restrict_asig asig actns ==
- (inputs(asig) Int actns, outputs(asig) Int actns,
- internals(asig) Un (externals(asig) - actns))"
-
-
-restrict_def
- "restrict ioa actns ==
- (restrict_asig (asig_of ioa) actns, starts_of(ioa), trans_of(ioa))"
-
-
-ioa_implements_def
- "ioa_implements ioa1 ioa2 ==
- ((inputs(asig_of(ioa1)) = inputs(asig_of(ioa2))) &
- (outputs(asig_of(ioa1)) = outputs(asig_of(ioa2))) &
- traces(ioa1) <= traces(ioa2))"
-
-rename_def
-"rename ioa ren ==
- (({b. ? x. Some(x)= ren(b) & x : inputs(asig_of(ioa))},
- {b. ? x. Some(x)= ren(b) & x : outputs(asig_of(ioa))},
- {b. ? x. Some(x)= ren(b) & x : internals(asig_of(ioa))}),
- starts_of(ioa) ,
- {tr. let s = fst(tr); a = fst(snd(tr)); t = snd(snd(tr))
- in
- ? x. Some(x) = ren(a) & (s,x,t):trans_of(ioa)})"
-
-end
--- a/src/HOL/IOA/meta_theory/Solve.ML Wed Apr 30 11:53:30 1997 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,209 +0,0 @@
-(* Title: HOL/IOA/meta_theory/Solve.ML
- ID: $Id$
- Author: Tobias Nipkow & Konrad Slind
- Copyright 1994 TU Muenchen
-
-Weak possibilities mapping (abstraction)
-*)
-
-open Solve;
-
-Addsimps [mk_trace_thm,trans_in_actions];
-
-goalw Solve.thy [is_weak_pmap_def,traces_def]
- "!!f. [| IOA(C); IOA(A); externals(asig_of(C)) = externals(asig_of(A)); \
-\ is_weak_pmap f C A |] ==> traces(C) <= traces(A)";
-
- by (simp_tac(!simpset addsimps [has_trace_def])1);
- by (safe_tac (!claset));
-
- (* choose same trace, therefore same NF *)
- by (res_inst_tac[("x","mk_trace C (fst ex)")] exI 1);
- by (Asm_full_simp_tac 1);
-
- (* give execution of abstract automata *)
- by (res_inst_tac[("x","(mk_trace A (fst ex),%i.f(snd ex i))")] bexI 1);
-
- (* Traces coincide *)
- by (asm_simp_tac (!simpset addsimps [mk_trace_def,filter_oseq_idemp])1);
-
- (* Use lemma *)
- by (forward_tac [states_of_exec_reachable] 1);
-
- (* Now show that it's an execution *)
- by (asm_full_simp_tac(!simpset addsimps [executions_def]) 1);
- by (safe_tac (!claset));
-
- (* Start states map to start states *)
- by (dtac bspec 1);
- by (atac 1);
-
- (* Show that it's an execution fragment *)
- by (asm_full_simp_tac (!simpset addsimps [is_execution_fragment_def])1);
- by (safe_tac (!claset));
-
- by (eres_inst_tac [("x","snd ex n")] allE 1);
- by (eres_inst_tac [("x","snd ex (Suc n)")] allE 1);
- by (eres_inst_tac [("x","a")] allE 1);
- by (Asm_full_simp_tac 1);
-qed "trace_inclusion";
-
-(* Lemmata *)
-
-val prems = goal HOL.thy "(P ==> Q-->R) ==> P&Q --> R";
- by(fast_tac (!claset addDs prems) 1);
-val imp_conj_lemma = result();
-
-
-(* fist_order_tautology of externals_of_par *)
-goal IOA.thy "a:externals(asig_of(A1||A2)) = \
-\ (a:externals(asig_of(A1)) & a:externals(asig_of(A2)) | \
-\ a:externals(asig_of(A1)) & a~:externals(asig_of(A2)) | \
-\ a~:externals(asig_of(A1)) & a:externals(asig_of(A2)))";
-by (asm_full_simp_tac (!simpset addsimps [externals_def,asig_of_par,asig_comp_def,asig_inputs_def,asig_outputs_def]) 1);
- by (Fast_tac 1);
-val externals_of_par_extra = result();
-
-goal Solve.thy "!!s.[| reachable (C1||C2) s |] ==> reachable C1 (fst s)";
-by (asm_full_simp_tac (!simpset addsimps [reachable_def]) 1);
-by (etac bexE 1);
-by (res_inst_tac [("x",
- "(filter_oseq (%a.a:actions(asig_of(C1))) \
-\ (fst ex), \
-\ %i.fst (snd ex i))")] bexI 1);
-(* fst(s) is in projected execution *)
- by (Simp_tac 1);
- by (Fast_tac 1);
-(* projected execution is indeed an execution *)
-by (asm_full_simp_tac
- (!simpset addsimps [executions_def,is_execution_fragment_def,
- par_def,starts_of_def,trans_of_def,filter_oseq_def]
- setloop (split_tac[expand_if,expand_option_case])) 1);
-qed"comp1_reachable";
-
-
-(* Exact copy of proof of comp1_reachable for the second
- component of a parallel composition. *)
-goal Solve.thy "!!s.[| reachable (C1||C2) s|] ==> reachable C2 (snd s)";
-by (asm_full_simp_tac (!simpset addsimps [reachable_def]) 1);
-by (etac bexE 1);
-by (res_inst_tac [("x",
- "(filter_oseq (%a.a:actions(asig_of(C2)))\
-\ (fst ex), \
-\ %i.snd (snd ex i))")] bexI 1);
-(* fst(s) is in projected execution *)
- by (Simp_tac 1);
- by (Fast_tac 1);
-(* projected execution is indeed an execution *)
-by (asm_full_simp_tac
- (!simpset addsimps [executions_def,is_execution_fragment_def,
- par_def,starts_of_def,trans_of_def,filter_oseq_def]
- setloop (split_tac[expand_if,expand_option_case])) 1);
-qed"comp2_reachable";
-
-
-(* Composition of possibility-mappings *)
-
-goalw Solve.thy [is_weak_pmap_def] "!!f g.[| is_weak_pmap f C1 A1 & \
-\ externals(asig_of(A1))=externals(asig_of(C1)) &\
-\ is_weak_pmap g C2 A2 & \
-\ externals(asig_of(A2))=externals(asig_of(C2)) & \
-\ compat_ioas C1 C2 & compat_ioas A1 A2 |] \
-\ ==> is_weak_pmap (%p.(f(fst(p)),g(snd(p)))) (C1||C2) (A1||A2)";
- by (rtac conjI 1);
-(* start_states *)
- by (asm_full_simp_tac (!simpset addsimps [par_def, starts_of_def]) 1);
-(* transitions *)
-by (REPEAT (rtac allI 1));
-by (rtac imp_conj_lemma 1);
-by (REPEAT(etac conjE 1));
-by (simp_tac (!simpset addsimps [externals_of_par_extra]) 1);
-by (simp_tac (!simpset addsimps [par_def]) 1);
-by (asm_full_simp_tac (!simpset addsimps [trans_of_def]) 1);
-by (rtac (expand_if RS ssubst) 1);
-by (rtac conjI 1);
-by (rtac impI 1);
-by (etac disjE 1);
-(* case 1 a:e(A1) | a:e(A2) *)
-by (asm_full_simp_tac (!simpset addsimps [comp1_reachable,comp2_reachable,
- ext_is_act]) 1);
-by (etac disjE 1);
-(* case 2 a:e(A1) | a~:e(A2) *)
-by (asm_full_simp_tac (!simpset addsimps [comp1_reachable,comp2_reachable,
- ext_is_act,ext1_ext2_is_not_act2]) 1);
-(* case 3 a:~e(A1) | a:e(A2) *)
-by (asm_full_simp_tac (!simpset addsimps [comp1_reachable,comp2_reachable,
- ext_is_act,ext1_ext2_is_not_act1]) 1);
-(* case 4 a:~e(A1) | a~:e(A2) *)
-by (rtac impI 1);
-by (subgoal_tac "a~:externals(asig_of(A1)) & a~:externals(asig_of(A2))" 1);
-(* delete auxiliary subgoal *)
-by (Asm_full_simp_tac 2);
-by (Fast_tac 2);
-by (simp_tac (!simpset addsimps [conj_disj_distribR] addcongs [conj_cong]
- setloop (split_tac [expand_if])) 1);
-by(REPEAT((resolve_tac [conjI,impI] 1 ORELSE etac conjE 1) THEN
- asm_full_simp_tac(!simpset addsimps[comp1_reachable,
- comp2_reachable])1));
-qed"fxg_is_weak_pmap_of_product_IOA";
-
-
-goal Solve.thy "!!s.[| reachable (rename C g) s |] ==> reachable C s";
-by (asm_full_simp_tac (!simpset addsimps [reachable_def]) 1);
-by (etac bexE 1);
-by (res_inst_tac [("x",
- "((%i. case (fst ex i) \
-\ of None => None\
-\ | Some(x) => g x) ,snd ex)")] bexI 1);
-by (Simp_tac 1);
-(* execution is indeed an execution of C *)
-by (asm_full_simp_tac
- (!simpset addsimps [executions_def,is_execution_fragment_def,
- par_def,starts_of_def,trans_of_def,rename_def]
- setloop (split_tac[expand_option_case])) 1);
-by (best_tac (!claset addSDs [spec] addDs [sym] addss (!simpset)) 1);
-qed"reachable_rename_ioa";
-
-
-goal Solve.thy "!!f.[| is_weak_pmap f C A |]\
-\ ==> (is_weak_pmap f (rename C g) (rename A g))";
-by (asm_full_simp_tac (!simpset addsimps [is_weak_pmap_def]) 1);
-by (rtac conjI 1);
-by (asm_full_simp_tac (!simpset addsimps [rename_def,starts_of_def]) 1);
-by (REPEAT (rtac allI 1));
-by (rtac imp_conj_lemma 1);
-by (simp_tac (!simpset addsimps [rename_def]) 1);
-by (asm_full_simp_tac (!simpset addsimps [externals_def,asig_inputs_def,asig_outputs_def,asig_of_def,trans_of_def]) 1);
-by (safe_tac (!claset));
-by (rtac (expand_if RS ssubst) 1);
- by (rtac conjI 1);
- by (rtac impI 1);
- by (etac disjE 1);
- by (etac exE 1);
-by (etac conjE 1);
-(* x is input *)
- by (dtac sym 1);
- by (dtac sym 1);
-by (Asm_full_simp_tac 1);
-by (REPEAT (hyp_subst_tac 1));
-by (cut_inst_tac [("C","C"),("g","g"),("s","s")] reachable_rename_ioa 1);
-by (assume_tac 1);
-by (Asm_full_simp_tac 1);
-(* x is output *)
- by (etac exE 1);
-by (etac conjE 1);
- by (dtac sym 1);
- by (dtac sym 1);
-by (Asm_full_simp_tac 1);
-by (REPEAT (hyp_subst_tac 1));
-by (cut_inst_tac [("C","C"),("g","g"),("s","s")] reachable_rename_ioa 1);
-by (assume_tac 1);
-by (Asm_full_simp_tac 1);
-(* x is internal *)
-by (simp_tac (!simpset addsimps [de_Morgan_disj, de_Morgan_conj, not_ex]
- addcongs [conj_cong]) 1);
-by (rtac impI 1);
-by (etac conjE 1);
-by (cut_inst_tac [("C","C"),("g","g"),("s","s")] reachable_rename_ioa 1);
-by (Auto_tac());
-qed"rename_through_pmap";
--- a/src/HOL/IOA/meta_theory/Solve.thy Wed Apr 30 11:53:30 1997 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,22 +0,0 @@
-(* Title: HOL/IOA/meta_theory/Solve.thy
- ID: $Id$
- Author: Tobias Nipkow & Konrad Slind
- Copyright 1994 TU Muenchen
-
-Weak possibilities mapping (abstraction)
-*)
-
-Solve = IOA +
-
-constdefs
-
- is_weak_pmap :: "['c => 'a, ('action,'c)ioa,('action,'a)ioa] => bool"
- "is_weak_pmap f C A ==
- (!s:starts_of(C). f(s):starts_of(A)) &
- (!s t a. reachable C s &
- (s,a,t):trans_of(C)
- --> (if a:externals(asig_of(C)) then
- (f(s),a,f(t)):trans_of(A)
- else f(s)=f(t)))"
-
-end