renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
(* $Id$ *)
theory MuIOA
imports IOA "../../../HOL/Modelcheck/MuckeSyn"
begin
consts
Internal_of_A :: "'a => bool"
Internal_of_C :: "'a => bool"
Start_of_A :: "'a => bool"
Start_of_C :: "'a => bool"
Trans_of_A :: "'a => 'b => bool"
Trans_of_C :: "'a => 'b => bool"
IntStep_of_A :: "'a => bool"
IntStepStar_of_A :: "'a => bool"
Move_of_A :: "'a => 'b => bool"
isSimCA :: "'a => bool"
ML {*
(* 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 = [thm "asig_of_def", thm "starts_of_def", thm "trans_of_def"];
val asig_simps = [thm "asig_inputs_def", thm "asig_outputs_def",
thm "asig_internals_def", thm "actions_def"];
val comp_simps = [thm "par_def", thm "asig_comp_def"];
val restrict_simps = [thm "restrict_def", thm "restrict_asig_def"];
val hide_simps = [thm "hide_def", thm "hide_asig_def"];
val rename_simps = [thm "rename_def", thm "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" ^ (Syntax.string_of_term_global 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" ^ (Syntax.string_of_term_global 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" ^ (Syntax.string_of_term_global 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" ^ (Syntax.string_of_term_global 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" ^ (Syntax.string_of_term_global 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" ^ (Syntax.string_of_term_global sg t));
fun delete_ul [] = []
| delete_ul (x::xs) = if (is_prefix (op =) ("\^["::"["::"4"::"m"::[]) (x::xs))
then (let val (_::_::_::s) = xs in delete_ul s end)
else (if (is_prefix (op =) ("\^["::"["::"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 = [(Syntax.string_of_typ_global 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 (csubgoal, thl) =
let
val sign = Thm.theory_of_cterm csubgoal;
val subgoal = Thm.term_of csubgoal;
in
(let
val weak_case_congs = (map (#weak_case_cong o snd) o Symtab.dest o Datatype.get_all) sign;
val concl = Logic.strip_imp_concl subgoal;
val ic_str = delete_ul_string(Syntax.string_of_term_global sign (IntC sign concl));
val ia_str = delete_ul_string(Syntax.string_of_term_global sign (IntA sign concl));
val sc_str = delete_ul_string(Syntax.string_of_term_global sign (StartC sign concl));
val sa_str = delete_ul_string(Syntax.string_of_term_global sign (StartA sign concl));
val tc_str = delete_ul_string(Syntax.string_of_term_global sign (TransC sign concl));
val ta_str = delete_ul_string(Syntax.string_of_term_global sign (TransA sign concl));
val action_type_str =
Syntax.string_of_typ_global 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
(
OldGoals.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 ((global_simpset_of sign 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
(global_simpset_of sign 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();
OldGoals.pop_proof();
Thm.cterm_of sign (Logic.strip_imp_concl subgoal)
)
end)
handle malformed =>
error("No suitable match to IOA types in " ^ (Syntax.string_of_term_global sign subgoal))
end;
end
*}
end