Quellcode-Bibliothek Expr.thy

(*  Title:      statecharts/SA/Expr.thy    Author:    Steffen HelkeSoftware EngineeringGroup

    Author:     Steffen Helke, Software Engineering Group
    Copyright   2010 Technische Universitaet Berlin
*)

section ‹
  Expr
  Update
 

  no bit_operations_syntax

  ('s,'e)ex
 |
 ressions›
                        
                         And('s,'e)expr "('s,e)expr"
                        | Or  "('s,'e)expr" "('s,'e)expr"
 
type_synonym = "('d da) => bool"
type_synonym ('e,'d)action = "('e set * 'd pupdate))expr"
type_synonym ('s,'e,'d)labelr"('s,'e)expr" (',expr
type_synonym ('s,'e,'d)trans = "('

primrec
   eval_expr :: "[('s set * 'e settype_synonym 'd guard ="(ddta >bol"
     eval_exprtrue           True"
   | "eval_expr sc ('s,'e,d)label  "('s,'e)expr * 'd guard * ('e,'daction)"
   | "eval_expr sc (In st) = (st ∈
   | "eval_expr (NOT)      = (¬
   | "eval_expr sc (And | " (v     ( \in snd sc)"
    ev c( e e2) = (alx c)\or>va_x c )"

primrec sc e1 (not(eval_expr sc e1))"
   ExprEvents :: "('s,'e)expr ==> 'e set" where
      "ExprEvents true        = {}"
   | "ExprEvents "eval_expr sc (Or e1 e2) ((eva sc e1) ∨
   | "ExprEvents st     ={"
   | "ExprEvents true }"
   | "ExprEvents (And e1 e2) = ((ExprEvents e1) ∪ (ExprEvents e2))"
   | "ExprEvents (OrExprEventsts (ExprEvents e2))"

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

datatype ('s, 'e, dead 'd)atomar =
                          
                          | FALSE
                          | IN s
                          | EN 'e
                          | VAL "'d data =>| IN

definition
       :: "('s,'e,'d)tr => 's"
  "source t = fst t"

definition
   Source     ::"'se,'d)tan =>'s where
  "Source     ::"'s,'e,'d)trans set => 's set" java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54

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

definition
   Target=snd
  "Target T = tar

definition
   el : ',edtans s',')b"where
  "label t = fst (snd t)"

definition
   Label       :: (,'labelseexpr where
  "Label T = label ` T"

definition
   exprs'abel
  "expr = fst"

definition
   action
  "action = snd o snd"

definition
     Ltion"
  "Action

definition
   tes,',d)abel = ' pupdate
  "pupdate = snd o action"

definition
         (,e') set=(dpupdate)set"where
  "PUpdate"PUpdate L = pupdate ` L"

actevent::"'s,e,')lab=> 'e set" where
   actevent         :: "('s,'e,'d)l set => ('e set) set"where
  "actevent = fst o action"

definition
   Actevent   :      :: "('s,'e,')lbel => 'd guard"   
  "Actevent L = acteveGu :: "('s'e,) set>(dguard set"where

definition
   guard :: "('s,'e,'d)label  => 'd guard"Guard L = guard ` "
  "guardltexpr :: "','expr 

definition
   "defaultexpr = true"
  "Guard L = guard ` L"

definition
   defaultexpr (,expr where 
  "defaultexpr = true"

definition
   defaultaction :: "('e,'d)action" where
  "defaultaction = ({},DefaultPUpdate)"

definition
   defaultguard'guard
  "defaultguard = (λ (<lmda>.Tre)"

definition
   defaultlabeldefaultlabelaultguardultaction
  "defaultlabel = (defaultexpr, de

definition
   eval :: "                                                       (<>_ | \close91,0] where
                                                       al_expr(l🪙[]:
  "eval scd l = (let (s,e,d) = scd
                 in
                    ((val_ex(s,e) (expr l)) \and(gu l) d)))"

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

mma Ta [simp]:
 "Target [simp
by byunfold, auto

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

ySet]
 "Action {} = {}"
by Action_def

lemma PUpdate_EmptySet
 "PUpdate{ = {}"
by (unfold PUpdate_def (a,,)=bjava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20

et]
 "Actevent {} = {}"
by unfold, auto

lemma Union_Actevent_subset
  "[ M; ((∪ (Union M)))) ⊆ ==>
   ((∪
by (unfold Actevent_def Label_def, auto)

lemma action_select [simp]:
 " (a,b,c)= c"
by (unfold

lemma label_select [simp"inite  <> finite S"
 "label,)=b
by (unfold label_def, auto)

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

lemma actevent_select [by(unfold Label_def)
 "actevent (a,b,(c,d)) = c"
by (unfold, auto)

lemma pupdate_select "fst defau = {}" 
 "pupdate (a,b,ultact auto)
by (unfold pupdate_def,

lemma source_select [si]:
 "source(actiontaction
by (unfold source_def, auto)

lemma finite_PUpdate [simp]:
 "finite S ==> finite(PUpdate S)"
by (unfold PUpdate_def, fst_defaultlabelsimp

lemma finite_Labelsimp]:
 "finite S ==>]:
by (unfold Label_def, auto)

lemma fst_defaultaction [simp]:
 "fst defaultaction = {} [simp:
by (unfold defaultaction_def defaultlabel_def, auto

lemmain T ==> target t ∈
 "(action de_union : Source s\union> So t = Source (s ∪
by (unfold defaultlabel_def action_def, auto)

lemma fa(unfold Target_def)
 "(st) = defaultexpr
by (unfold

lemma ExprEvents_defaultexpr [simp]:
 "(ExprEvents defaultexpr) = {}" 
by (unfold defaultexpr_def, auto)

lemma defaultlabel_defaultexpr [simp]:
 "expr defaultlabel = defaultexpr"
by (unfold defaultlabel_def expr_def, auto)

lemma target_Target [simp]:
  "t ∈ T ==> target t ∈ Target T"
by (unfold Target_def, auto)

lemma Source_union : "Source s ∪ Source t = Source (s ∪ t)"
apply (unfold Source_def)
apply auto
done

lemma Target_union : "Target s ∪ Target t = Target (s ∪ t)"
apply (unfold Target_def)
apply auto
done

end