(* MuIOA.ML declares function mk_sim_oracle used by oracle "Sim" (see MuIOAOracle.thy). There, implementation relations for I/O automatons are proved using the model checker mucke (invoking cal_mucke_tac defined in MCSyn.ML). *) exception SimFailureExn of string; val ioa_simps = [asig_of_def,starts_of_def,trans_of_def]; val asig_simps = [asig_inputs_def,asig_outputs_def,asig_internals_def,actions_def]; val comp_simps = [par_def,asig_comp_def]; val restrict_simps = [restrict_def,restrict_asig_def]; val hide_simps = [hide_def,hide_asig_def]; val rename_simps = [rename_def,rename_set_def]; local exception malformed; fun fst_type (Type("*",[a,_])) = a | fst_type _ = raise malformed; fun snd_type (Type("*",[_,a])) = a | snd_type _ = raise malformed; fun element_type (Type("set",[a])) = a | element_type t = raise malformed; fun IntC sg (Const("Trueprop",_) $ ((Const("op <=",_) $ (_ $ concreteIOA)) $ _)) = let val aut_typ = #T(rep_cterm(cterm_of sg concreteIOA)); val sig_typ = fst_type aut_typ; val int_typ = fst_type sig_typ in Const("Asig.internals",Type("fun",[sig_typ,int_typ])) $ (Const("Automata.asig_of",Type("fun",[aut_typ,sig_typ])) $ concreteIOA) end | IntC sg t = error("malformed automaton def for IntC:\n" ^ (Sign.string_of_term sg t)); fun StartC sg (Const("Trueprop",_) $ ((Const("op <=",_) $ (_ $ concreteIOA)) $ _)) = let val aut_typ = #T(rep_cterm(cterm_of sg concreteIOA)); val st_typ = fst_type(snd_type aut_typ) in Const("Automata.starts_of",Type("fun",[aut_typ,st_typ])) $ concreteIOA end | StartC sg t = error("malformed automaton def for StartC:\n" ^ (Sign.string_of_term sg t)); fun TransC sg (Const("Trueprop",_) $ ((Const("op <=",_) $ (_ $ concreteIOA)) $ _)) = let val aut_typ = #T(rep_cterm(cterm_of sg concreteIOA)); val tr_typ = fst_type(snd_type(snd_type aut_typ)) in Const("Automata.trans_of",Type("fun",[aut_typ,tr_typ])) $ concreteIOA end | TransC sg t = error("malformed automaton def for TransC:\n" ^ (Sign.string_of_term sg t)); fun IntA sg (Const("Trueprop",_) $ ((Const("op <=",_) $ _) $ (_ $ abstractIOA))) = let val aut_typ = #T(rep_cterm(cterm_of sg abstractIOA)); val sig_typ = fst_type aut_typ; val int_typ = fst_type sig_typ in Const("Asig.internals",Type("fun",[sig_typ,int_typ])) $ (Const("Automata.asig_of",Type("fun",[aut_typ,sig_typ])) $ abstractIOA) end | IntA sg t = error("malformed automaton def for IntA:\n" ^ (Sign.string_of_term sg t)); fun StartA sg (Const("Trueprop",_) $ ((Const("op <=",_) $ _) $ (_ $ abstractIOA))) = let val aut_typ = #T(rep_cterm(cterm_of sg abstractIOA)); val st_typ = fst_type(snd_type aut_typ) in Const("Automata.starts_of",Type("fun",[aut_typ,st_typ])) $ abstractIOA end | StartA sg t = error("malformed automaton def for StartA:\n" ^ (Sign.string_of_term sg t)); fun TransA sg (Const("Trueprop",_) $ ((Const("op <=",_) $ _) $ (_ $ abstractIOA))) = let val aut_typ = #T(rep_cterm(cterm_of sg abstractIOA)); val tr_typ = fst_type(snd_type(snd_type aut_typ)) in Const("Automata.trans_of",Type("fun",[aut_typ,tr_typ])) $ abstractIOA end | TransA sg t = error("malformed automaton def for TransA:\n" ^ (Sign.string_of_term sg t)); fun is_prefix [] s = true | is_prefix (p::ps) [] = false | is_prefix (p::ps) (x::xs) = (p=x) andalso (is_prefix ps xs); fun delete_ul [] = [] | delete_ul (x::xs) = if (is_prefix ("\^["::"["::"4"::"m"::[]) (x::xs)) then (let val (_::_::_::s) = xs in delete_ul s end) else (if (is_prefix ("\^["::"["::"0"::"m"::[]) (x::xs)) then (let val (_::_::_::s) = xs in delete_ul s end) else (x::delete_ul xs)); fun delete_ul_string s = implode(delete_ul (explode s)); fun type_list_of sign (Type("*",a::b::_)) = (type_list_of sign a) @ (type_list_of sign b) | type_list_of sign a = [(Sign.string_of_typ sign a)]; fun structured_tuple l (Type("*",s::t::_)) = let val (r,str) = structured_tuple l s; in (fst(structured_tuple r t),"(" ^ str ^ "),(" ^ (snd(structured_tuple r t)) ^ ")") end | structured_tuple (a::r) t = (r,a) | structured_tuple [] _ = raise malformed; fun varlist_of _ _ [] = [] | varlist_of n s (a::r) = (s ^ (Int.toString(n))) :: (varlist_of (n+1) s r); fun string_of [] = "" | string_of (a::r) = a ^ " " ^ (string_of r); fun tupel_typed_of _ _ _ [] = "" | tupel_typed_of sign s n [a] = s ^ (Int.toString(n)) ^ "::" ^ a | tupel_typed_of sign s n (a::r) = s ^ (Int.toString(n)) ^ "::" ^ a ^ "," ^ (tupel_typed_of sign s (n+1) r); fun double_tupel_typed_of _ _ _ _ [] = "" | double_tupel_typed_of sign s t n [a] = s ^ (Int.toString(n)) ^ "::" ^ a ^ "," ^ t ^ (Int.toString(n)) ^ "::" ^ a | double_tupel_typed_of sign s t n (a::r) = s ^ (Int.toString(n)) ^ "::" ^ a ^ "," ^ t ^ (Int.toString(n)) ^ "::" ^ a ^ "," ^ (double_tupel_typed_of sign s t (n+1) r); fun tupel_of _ _ _ [] = "" | tupel_of sign s n [a] = s ^ (Int.toString(n)) | tupel_of sign s n (a::r) = s ^ (Int.toString(n)) ^ "," ^ (tupel_of sign s (n+1) r); fun double_tupel_of _ _ _ _ [] = "" | double_tupel_of sign s t n [a] = s ^ (Int.toString(n)) ^ "," ^ t ^ (Int.toString(n)) | double_tupel_of sign s t n (a::r) = s ^ (Int.toString(n)) ^ "," ^ t ^ (Int.toString(n)) ^ "," ^ (double_tupel_of sign s t (n+1) r); fun eq_string _ _ _ [] = "" | eq_string s t n [a] = s ^ (Int.toString(n)) ^ " = " ^ t ^ (Int.toString(n)) | eq_string s t n (a::r) = s ^ (Int.toString(n)) ^ " = " ^ t ^ (Int.toString(n)) ^ " & " ^ (eq_string s t (n+1) r); fun merge_var_and_type [] [] = "" | merge_var_and_type (a::r) (b::s) = "(" ^ a ^ " ::" ^ b ^ ") " ^ (merge_var_and_type r s) | merge_var_and_type _ _ = raise malformed; in fun mk_sim_oracle sign (subgoal,thl) = (let val weak_case_congs = DatatypePackage.weak_case_congs_of sign; val concl = (Logic.strip_imp_concl subgoal); val ic_str = delete_ul_string(Sign.string_of_term sign (IntC sign concl)); val ia_str = delete_ul_string(Sign.string_of_term sign (IntA sign concl)); val sc_str = delete_ul_string(Sign.string_of_term sign (StartC sign concl)); val sa_str = delete_ul_string(Sign.string_of_term sign (StartA sign concl)); val tc_str = delete_ul_string(Sign.string_of_term sign (TransC sign concl)); val ta_str = delete_ul_string(Sign.string_of_term sign (TransA sign concl)); val action_type_str = Sign.string_of_typ sign (element_type(#T (rep_cterm(cterm_of sign (IntA sign concl))))); val abs_state_type_list = type_list_of sign (element_type(#T (rep_cterm(cterm_of sign (StartA sign concl))))); val con_state_type_list = type_list_of sign (element_type(#T (rep_cterm(cterm_of sign (StartC sign concl))))); val tupel_eq = eq_string "s" "t" 0 abs_state_type_list; val abs_pre_tupel_typed = tupel_typed_of sign "s" 0 abs_state_type_list; val abs_s_t_tupel_typed = double_tupel_typed_of sign "s" "t" 0 abs_state_type_list; val con_pre_tupel_typed = tupel_typed_of sign "cs" 0 con_state_type_list; val con_s_t_tupel_typed = double_tupel_typed_of sign "cs" "ct" 0 con_state_type_list; val abs_pre_tupel = tupel_of sign "s" 0 abs_state_type_list; val abs_post_tupel = tupel_of sign "t" 0 abs_state_type_list; val abs_s_t_tupel = double_tupel_of sign "s" "t" 0 abs_state_type_list; val abs_s_u_tupel = double_tupel_of sign "s" "u" 0 abs_state_type_list; val abs_u_t_tupel = double_tupel_of sign "u" "t" 0 abs_state_type_list; val abs_u_v_tupel = double_tupel_of sign "u" "v" 0 abs_state_type_list; val abs_v_t_tupel = double_tupel_of sign "v" "t" 0 abs_state_type_list; val con_pre_tupel = tupel_of sign "cs" 0 con_state_type_list; val con_post_tupel = tupel_of sign "ct" 0 con_state_type_list; val con_s_t_tupel = double_tupel_of sign "cs" "ct" 0 con_state_type_list; val abs_pre_varlist = varlist_of 0 "s" abs_state_type_list; val abs_post_varlist = varlist_of 0 "t" abs_state_type_list; val abs_u_varlist = varlist_of 0 "u" abs_state_type_list; val abs_v_varlist = varlist_of 0 "v" abs_state_type_list; val con_pre_varlist = varlist_of 0 "cs" con_state_type_list; val con_post_varlist = varlist_of 0 "ct" con_state_type_list; val abs_post_str = string_of abs_post_varlist; val abs_u_str = string_of abs_u_varlist; val con_post_str = string_of con_post_varlist; val abs_pre_str_typed = merge_var_and_type abs_pre_varlist abs_state_type_list; val abs_u_str_typed = merge_var_and_type abs_u_varlist abs_state_type_list; val abs_v_str_typed = merge_var_and_type abs_v_varlist abs_state_type_list; val con_pre_str_typed = merge_var_and_type con_pre_varlist con_state_type_list; val abs_pre_tupel_struct = snd( structured_tuple abs_pre_varlist (element_type(#T(rep_cterm(cterm_of sign (StartA sign concl)))))); val abs_post_tupel_struct = snd( structured_tuple abs_post_varlist (element_type(#T(rep_cterm(cterm_of sign (StartA sign concl)))))); val con_pre_tupel_struct = snd( structured_tuple con_pre_varlist (element_type(#T(rep_cterm(cterm_of sign (StartC sign concl)))))); val con_post_tupel_struct = snd( structured_tuple con_post_varlist (element_type(#T(rep_cterm(cterm_of sign (StartC sign concl)))))); in ( push_proof(); Goal ( "(Internal_of_A = (% a::(" ^ action_type_str ^ "). a:(" ^ ia_str^ "))) --> (Internal_of_C = (% a::(" ^ action_type_str ^ "). a:(" ^ ic_str ^ "))) --> (Start_of_A = (% (" ^ abs_pre_tupel_typed ^ "). (" ^ abs_pre_tupel_struct ^ "):(" ^ sa_str ^ "))) --> (Start_of_C = (% (" ^ con_pre_tupel_typed ^ "). (" ^ con_pre_tupel_struct ^ "):(" ^ sc_str ^ "))) --> (Trans_of_A = (% (" ^ abs_s_t_tupel_typed ^ ") (a::(" ^ action_type_str ^ ")). ((" ^ abs_pre_tupel_struct ^ "),a,(" ^ abs_post_tupel_struct ^ ")):(" ^ ta_str ^ "))) --> (Trans_of_C = (% (" ^ con_s_t_tupel_typed ^ ") (a::(" ^ action_type_str ^ ")). ((" ^ con_pre_tupel_struct ^ "),a,(" ^ con_post_tupel_struct ^ ")):(" ^ tc_str ^ "))) --> (IntStep_of_A = (% (" ^ abs_s_t_tupel_typed ^ "). ? (a::(" ^ action_type_str ^ ")). Internal_of_A a & Trans_of_A (" ^ abs_s_t_tupel ^ ") a" ^ ")) --> (IntStepStar_of_A = mu (% P (" ^ abs_s_t_tupel_typed ^ "). (" ^ tupel_eq ^ ") | (? " ^ abs_u_str ^ ". IntStep_of_A (" ^ abs_s_u_tupel ^ ") & P(" ^ abs_u_t_tupel ^ ")))" ^ ") --> (Move_of_A = (% (" ^ abs_s_t_tupel_typed ^ ") (a::(" ^ action_type_str ^ ")). (Internal_of_C a & IntStepStar_of_A(" ^ abs_s_t_tupel ^ ")) | (? " ^ abs_u_str_typed ^ ". ? " ^ abs_v_str_typed ^ ". IntStepStar_of_A(" ^ abs_s_u_tupel ^ ") & " ^ "Trans_of_A (" ^ abs_u_v_tupel ^ ") a & IntStepStar_of_A(" ^ abs_v_t_tupel ^ "))" ^ ")) --> (isSimCA = nu (% P (" ^ con_pre_tupel_typed ^ "," ^ abs_pre_tupel_typed ^ "). (! (a::(" ^ action_type_str ^ ")) " ^ con_post_str ^ ". Trans_of_C (" ^ con_s_t_tupel ^ ") a -->" ^ " (? " ^ abs_post_str ^ ". Move_of_A (" ^ abs_s_t_tupel ^ ") a & P(" ^ con_post_tupel ^ "," ^ abs_post_tupel ^ "))))" ^ ") --> (! " ^ con_pre_str_typed ^ ". ! " ^ abs_pre_str_typed ^ ". (Start_of_C (" ^ con_pre_tupel ^ ") & Start_of_A (" ^ abs_pre_tupel ^ ")) --> isSimCA(" ^ con_pre_tupel ^ "," ^ abs_pre_tupel ^ "))"); by (REPEAT (rtac impI 1)); by (REPEAT (dtac eq_reflection 1)); (* Bis hierher wird im Kapitel 4 erl"autert, ab hier im Kapitel 5 *) by (full_simp_tac ((simpset() delcongs (if_weak_cong :: weak_case_congs) delsimps [not_iff,split_part]) addsimps (thl @ comp_simps @ restrict_simps @ hide_simps @ rename_simps @ ioa_simps @ asig_simps)) 1); by (full_simp_tac (Mucke_ss delcongs (if_weak_cong :: weak_case_congs) delsimps [not_iff,split_part]) 1); by (REPEAT (if_full_simp_tac (simpset() delcongs (if_weak_cong :: weak_case_congs) delsimps [not_iff,split_part]) 1)); by (call_mucke_tac 1); (* Bis hierher wird im Kapitel 5 erl"autert, ab hier wieder im Kapitel 4 *) by (atac 1); result(); pop_proof(); Logic.strip_imp_concl subgoal ) end) handle malformed => error("No suitable match to IOA types in " ^ (Sign.string_of_term sign subgoal)); end