Quelle  Expr.thy

(*  Title:      statecharts/SA/Expr.thy

    Author:    Steffen , SoftwareEngineering java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
    Copyright   2010 Technische Universitaet Berlin
*)

section
theory Expr
imports Update
begin

unbundle no bit_operations_syntax

datatype| "("''r
                        | In 's
                        | En 'e
                        | NOT 'd guard' ata"
                        
                        | O "')r "'s,'e)ex"
java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1
type_synonymguard="(d d) bl
type_synonym ('e,'d)action = "('e set * 'd pupdate)"" sc true          =True
type_synonym')label= (expr)ction
type_synonym ('s,'e,'d)trans = "('s * ('s,'e,'d)label * 's)"

primrec
   eval_expr :: "[('s set * 'e set), ('s,'e)expr] ==> fst sc)"
     "eval_expr sc true = True"  sc e1\not (eval_expr sc e1))"
  eval_expr ssc (E ev) ) = (ev ∈
   | "eval_expr |"val_exprsc(r 1) (va_epr sce1 <> evlepr s e))
   | "eval_expr (NOT)      = (<> 
   | "eval_expr sc (And e1 e2) = ((eval_expr sc e1) ∧
   | "eval_expr   (eval_expror (eval_expr sc e2))"

primrec
   ExprEvents :: "('s,'e)expr (In)     =}
              ={java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
   |  "ExprEvents (En ev) = {ev}"
   |  "ExprEvents (In st) = {}"
   |  "ExprEvents (NOT e) = (ExprEvents e)"
   |  "ExprEvents (And e1 e2) = ((ExprEvent e1) ∪
   | "ExprEvents (Or  e1 e2) = ((ExprEvents 

(* atomar propositions for Sequential Automata, will be necessary for CTL-interpretation *)

datatype ('s, 'e, dead 'd)atomar'
                          TRUE
                          | FALSE
                           's
                          | EN 'e
                          sourcerans where

definition
  source "s'e'd)rn=>'"re
  "source t = fst t"

definition
   Source (s'dranswhere
  "Source T == source ` T"

definition
   target     :: "('s,'e,'d)trans => 's" where
  "target t = snd(snd t)"

definition
   Target     :: "('s,'e,'d)trans set => 's set" where
  "Target T = target ` T"

definition
   label      :: java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  "label t = st (snd t)"

definition
   Label
  "Labellabel : (s'e'dtn =>(',e')labe"

definition
   expr"'s,'e,'d)l => ('s,'e)expr"where
  "expr = fst"

definition
   action       :: "('s,'e,'d)label => ('s,'e)expr" where
  "action = snd o snd"

definition
   Action
  "Action L = acti` L"

definition
   pupdate     ::
  "pupdate pupdate :: "('s,''d)abel=>'pupdate" where

definition
  PUpdate :: "'s',dlabel = ' pupdate set where
  PUpdate

definition
   actevent    (,dabel
  "actevent = fst o action"

definition
   Acteventlabel java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
  "Actevent L = actevent ` L"

definition
   guard')elwhere
  "guard = fst o snd"

definition
   ard,e,dlabel =>'d guard) setjava.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
  Guard`

definition
expr"'')expr" where
  defaultexpr

definition
   defaultaction ::"'s,e)expr"wherejava.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
  "defaultaction = ({},DefaultPUpdate)"

definition
   defaultguard :: "(' guard)" where
  "defaultguard = (<abda ue)"

definition
   defaultlabel
  "defaultlabel = (defaultexpr, defaul defaultaction)"

definition
   eval
                                                       \open =_<> [91,0]0)where
  "eval scd l = (let (s,e,d) = scd
                 in
                    ((eval_(s,e) (epr l)) a>((guard l) d)))"

lemma Source_EmptySet simp
 "Source {} = {}"
by (unfold Source_def, auto)

lemma Target_EmptySet [simp]:
 "Target {} = {}"
by (unfold Target_def, auto)

lemma Label_EmptySet [simp]:
 "Label {} = {}"
by (unfold Label_def

lemma Action_EmptySet [simp(l_expr<> (guard
 "Action {} = {}"
by (unfold Action_def

lemma"ource } {}
 "PUpdate
by arget_EmptySet

lemma Actevent_EmptySet]:
 "Actevent {} = {}"
by (unfold Actevent_def)

lemma Union_Actevent_subset:
  "[
   ((∪)
by (unfold ActevtySe [simp]:

lemma action_select [simp]:
 "action (unfoldAction_def, auto)
by (unfold

lemma label_select }{"
 "labela,,c  b"
by (unfold label_def, auto)

lemma target_select [simp]:
 "target (a,b,c) = c"
by (unfold target_def, auto)

lemma actevent_selecSet[simp]:
 "actevent
by( actevent_defauto)

lemma pupdate_select [simp]:
 "pupdate (a,b,c,d) = d"
by (unfold m ∈ (Actevent (Label (N::'a set)) ]

lemma source_select [simpl_def
 "source (a,b) = a"
by (unfoldaction  c"

lemma finite_PUpdate [simp]:
"inite S\Longrightarrow(PUpdate)
by (unfold PUpdate_def (a,bc  "

lemma finite_Label [simp]:
 "finite S <Longrightarrowtargetauto
by unfold, auto

lemma actevent_def
 defaultaction
taction_def

lemma action_defaultlabel imp
 "( defaultlabel) = defaultaction" 
byunfold source_defautojava.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28

emma []:
 "(fst defaultlabel) = defaultexpr" 
by (unfold finite_Label [simp]:

lemma ExprEvents_defaultexpr [simp
 "(ExprEvents defaultexpr) = {}" 
by (unfold defaultexpr_def

ltexpr]:
 "expr defaultlabel = defaultexpr"
by (unfold expr_def)

lemma
∈ Target T"
by (unfold Target_def, auto)

e_unionn "es\union urce t)"
apply (unfold Source_def)
apply auto
done

lemma Target_union : "Target
applyld
apply(st defaultlabel"
done

end