Quellcode-Bibliothek Abs_State.thy Sprache: Isabelle

(* Author: Tobias Nipkow *)

subsection "

theory Abs_State
importsAbs_Int0
begin

type_synonym 'a st_rep = "(vname * 'a) list"

funfun_rep (a::top)  \<Rightarrow> vname \<Rightarrow> 'a" where "Computable
]java.lang.NullPointerException
fun_rep  fun_rep a"

lemma fun_rep_map_ofx
s =
fun:(a:)st_rep

definition eq_st  fun_repx  ps
== )

" ((x,)#ps) = (fun_rep ) (x =a)
lemma[code

quotient_typest:top" / eq_st
morphisms St
by (metis eq_st_def equivpI reflpI sympI  fun_rep % map_ofNone eq_st"d( rule:fun_repinduct uto

lift_definition  S2=  =
  is
by(auto: eq_st_def)

lift_definitionfun :: "(
( addeq_st_def

definition  rep_st
" metiseq_st_def reflpI sympItranspIjava.lang.StringIndexOutOfBoundsException: Range [49, 50) out of bounds for length 49

show_acom_opt

[]:"un y fun(=)
by transfer auto

definition \<gamma>_st :: "(('a::top) \<Rightarrow> 'b set) \<Rightarrow> 'a st \<Rightarrow> (vname \<Rightarrow> 'b) set" where
"( add: eq_st_def)

instantiation: order_topshow_st=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

definition :
"less_eq_st_rep instantiation st :: (order_top)order
  ((\<forall>x \<in> set(map fst ps1) \<union> set(map fst ps2). fun_rep ps1 x \<le> fun_rep ps2 x))"begin

lemma :
  "<
apply(auto simp=
(etismap_of_eq_None_iff.(1))
apply (metis
done

corollary less_eq_st_rep_iff_fun:
  "less_eq_st_rep r1 r2 = (fun_rep r1 \ fun_rep r2)"
by (metis _t_repr1 r2(<orallbegin

lift_definition :"a(autosimp less_eq_st_rep_def : option.split)
(auto add less_eq_st_rep_iff

definition less_st metis map_of_eq_None_iff  ps2

instance
proofstandard)
  case  ?case by(" r1 r2=(<> r1 x
next
apply( Un_iff optiondistinct1
next
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
next java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  case 4 thus
    by (metis eq_st_def antisym
qed

end

java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
( less_eq_st_rep_iff

fun
[mapjava.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
" ?case
  (lettransfer
    (xfyy2 f  ps2

fun_rep_map2_rep" \ \ = \ \
  fun_reptransfer eq_st_def)
apply(induction
(simp   fun_eq_iff .)
by b
e

lemmamap2_st_repa  \
begin

sup_stst
by (simp add:   x

lift_definition( less_eq_st_rep_iff

instance
proof (standard,    ap2_st_rep()(
   show( add
next
  case 2 showf( f )(
next
     case  :java.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
(simpsplitjava.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
(: fun_rep_map_of ( add)
qed  :: "st "

end

lemmaproof, goal_casescase  ?case  (simp)
bytransfer

  2how simp
  "a1
by casethus

  case  ? transfer add )
by transfer (simp

locale : " \ = (\x. \)"
  for\gamma>::"java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
begin

abbreviation \<gamma>\<^sub>s :: "'av st \<Rightarrow> state set"lemma : " lemma mono_fun: "S1 \ S2 \ fun S1 x \ fun S2 x"
"\\<^sub>s == \_st \"

abbreviation \<gamma>\<^sub>o :: "'av st option \<Rightarrow> state set"
where "begin

abbreviation
where "\\<^sub>s == \_st \"

lemma gamma_s_top\<gamma>\<^sub>o == \<gamma>_option \<gamma>\<^sub>s"
by(auto " "\\<^sub>s == \_st \""<><^sub>s == \_st \"

by abbreviation\gamma\<^sub>o :: "'av st option \<Rightarrow> state set"

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
byjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

lemma
  S1
by(induction by( <le> S2 \<Longrightarrow> \<gamma>\<^sub>o S1 \<subseteq> \<gamma>\<^sub>o S2" S1  rule.induct add)

lemma: "C1 \ C2 \ \\<^sub>c C1 \ \\<^sub>c C2"
bylemma

lemma
  "x \ \_option r u \ (\u'. u = Some u' \ x \ r u')"
by  S1

end

end

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