Quelle  Ex.thy

java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
  imports by standard finite_surj ". _ Abs_label])
begin

(* Query specific part START *)
abbreviation state :: finite begin
abbreviation labelN :: nat where b (st rule finite_surj[of ".}" Abs_state]
abbreviation sta:: nat where "\"
typedef  " .< intro!: exI[of _ 0)
typedef label = "{0 ..< labelN}" by (auto intro!: exI[of _ 0])
typedef state = "{0 ..< stateN}" by (auto intro!: exI[of _ 0])
setup_lifting type_definition_ctr_loc
setup_lifting type_definition_label
setup_lifting type_definition_state

lift_definition p1 :: ctr_loc is 0 by auto
lift_definition p2 :: ctr_loc is 1 by auto
lift_definition p3 :: ctr_loc is 2 by auto
lift_definition x :: label is 0 by auto
lift_definition y :: label is 1 by auto
lift_definition q1 :: state is 0 by auto
lift_definition q2 :: state is 1 by auto
lift_definition qf :: state is 2 by auto

(* Define rules of PDS, and the two P-automata *)
definition pds_rules :: "(ctr_loc, label) rule set" where
  " ctr_loc:enum begin"enum_ctr_loc = ctr_loc_"
  ((p1, y), (definition P list_exlist
  (p1 (p2, y)),
  ((p2, x), (p3 image_iff inj_on_def
  p3p2 x))}"
definition initial_automaton :: "((ctr_loc, state, label.pred_mapist_ex_iff__ases
  "initial_automaton
  stantiation ::: linorder egin
  (Int p2, y,Noniinit qf)),
  ((Init p2, x, Init p2)),
  ((Init p3, x, Noninit q _eq_ctr_loc : "r_loc ctr_loc ==>
definition final_automaton_,beltransition
  "final_automaton = {

   ctr_loc : equal begin
  ((Noninit q1, y, Noninit q2))}"

definition final_ctr_loc(tandard;) auto
definition
definition
definition initial_ctr_loc_st initial_ctr_loc_st
(* Query specific part END *)

instantiation ctr_loc "enum_ex_label P =list_ex P label_list"
instance (standard,rule[of{< __Abs_ctr_loc)
  (simp, metis Rep_ctr_loc image_iff inj_on_def
end
instantiation label ::listpred_map.pred_set) (metis)+
instance by
  (simp :: begin
end
instantiation state less_eq_label"\<> 
instance standard, rule finite_surj[of "0 . stateNbs_state
  ( (tandard
end

lift_definition
instantiation equal_statestate Rightarrow state ==>
definitionenum_ctr_loc =ctr_loc_list
definition "enum_all_ctr_loc P = list_all P ctr_loc_li
definition "enum_ex_ctr_loc_t"
instance by (standard, auto simp: enum_ctr_loc_def enum_all_ctr_loc_def enum_ex_ctr_loc_def
       ctr_loc_list_def image_iff distinct_map inj_on_def Abs_c
       
end

instantiationctr_locnorrbegin
lift_definition less_ctr_loc :: "ctr_loc
lift_definition less_eq_ctr_loc :: "ctr_loc ==>
instance by (standard; transfer) auto
end

instantiation ctr_loc :: equal begin
lift_definition equal_ctr_loc :: "ctr_loc ==> ctr_loc ==> bool" is "(=)" .
instance by (standard; transfer) auto
end

lift_definition (code_dt) label_list :: "label list" is "[0 ..< labelN]" by (auto simp: list.pred_set)
instantiation label :: enum begin
definition "enum_label = label_list"
definition "enum_all_label P = list_all P label_list"
definition "enum_ex_label P = list_ex P label_list"
instance by (standard, auto simp: enum_label_def enum_all_label_def enum_ex_label_def
       label_list_def image_iff distinct_map inj_on_def Abs_label_inject
       list.pred_map list.pred_set list_ex_iff) (metis Abs_label_cases)+
end

instantiation label :: linorder begin
lift_definition less_label :: "label ==> label ==> bool" is "(<)" .
lift_definition less_eq_label :: "label ==> label ==> bool" is "(≤)" .
instance by (standard; transfer) auto
end

instantiation label :: equal begin
lift_definition equal_label :: "label ==> label ==> bool" is "(=)" .
instance by (standard; transfer) auto
end

instantiation state :: equal begin
lift_definition equal_state :: "state ==> state ==> bool" is "(=)" .
instance by (standard; transfer) auto
end

(* The check function agrees with the encoded answer (Some True) 
   and therefore the proof succeeds as expected. *)
lemma
  "check pds_rules initial_automaton initial_ctr_loc initial_ctr_loc_st
                   final_automaton   final_ctr_loc   final_ctr_loc_st   = Some True"
  by eval

end