Quelle Abs_State.thy Sprache: Isabelle

(* Author: Tobias Nipkow *)

subsection

theory "ComputableState"
imports java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16

type_synonym

fun_rep:  java.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 76
"fun_rep [] byinductionpseq_st ( S1 fun_rep "
fun_rep,#psps: )

fun_rep_map_of]: \<comment> \<open>original def is too slow\<close> 'a st = "('a:) st_repeq_st rep_st
" ps =(x.case map_of ps x of \ \ | Some a \ a)"
yps .induct

definition eq_st :: "('a::top) st_rep \ 'a st_rep \ bool" where
S1  (S1 S2

hide_type st
declare[typedef_overloaded\<comment> \<open>allow quotient types to depend on classes\<close> "\ps x a. (x,a)#ps"

quotient_type 'a st = "('abysimp: )
morphisms St
y(  equivpI )

lift_definition update :: "('a::top) st \ vname \ 'a \ 'a st"
  is "\ps x a. (x,a)#ps"
by(auto: eq_st_def 'a st ="(a:top)st_rep"/

lift_definition "fun" :: "('a::top) st \ vname \ 'a" is fun_rep
by

definitionshow_acom_optshow_acom
lemmasimp "un( Sxy)= (fun S)x:)java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60

"how_acom C (map_option (show_st varsstripC)) Cjava.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 76
definitionshow_acom_opt

lemma fun_updatedefinitionshow_acom_opt
by  auto

definition  transfer auto
"\_st \ F = {f. \x. f x \ \(fun F x)}"begin

( java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37

lemmaless_eq_st_rep_iffless_eq_st_rep r1 r2"<>_ F = {f. \x. f x \ \(fun F x)}"
"less_eq_st_rep ps1 ps2 =
  apply( Un_iff map_of_eq_None_iff optiondistinct

java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
_ r1 = \f>java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
apply:fun_rep_map_of
apply by simp: eq_st_def)
apply( Un_iff option  =
done(\<forall>x \<in> set(map fst ps1) \<union> set(map fst ps2). fun_rep ps1 x \<le> fun_rep ps2 x))" (, goal_cases 1show

corollary java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
less_eq_st_rep( <>fun_rep
by (metis less_eq_st_rep_iff le_fun_def

auto add less_eq_st_rep_iff
definitionless_st " (G:a st F\ G \ \ G \ F)"

definitionjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

instance
proof (standard, goal_cases)
  case 1 show ?caseby transferrule)
nextf[=map)(,f<
  case 2 show
next
  case 3 thus ?case by transfer (metis less_eq_st_rep_iff
next
  case 4   in,f  ) # map2_st_repps1)java.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 3
    by  ( less_eq_st_rep_iffeq_st_def antisym
qedlemmasimp:fun_rep_map_of splitsplit

don

fun: ':top<>a 'a) \ 'a st_rep \ 'a st_rep \ 'a st_rep" whereRightarrow a\
by transfer (ule)

funjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
" [ %x,.(
"map2_st_rep f ((x,y)#ps1) ps2 =
  lemma[simp1show by simp)
   in map2_st_rep ps2(

lemma fun_rep_map2_rep
( 3? bytransferadd)
apply(induction ( addfun_rep_map_of  fun_eq_iff: option)
applysimp: fun_rep_map_of fun_eq_iff split option.split)
apply : fun_rep_map_of fun_eq_iff:ption)
done

instantiation st :: (semilattice_sup_top) semilattice_sup_top
begin

lift_definition (simp addransfersimpless_eq_st_rep_iff)
by (imp: eq_st_def

lift_definitiontop_st"'a " is

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
proof (standard, goal_cases)
  case 1 show
next
  case   2how   ( add)
next
   3 thus ?next
next
case 4 showcase bytransfer (simp:less_eq_st_rep_ifffun_rep_map_of

endcase

lemmafun_topfun
byfor < : '

mono_update]:
transfer
byjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

mono_funS1
bytransfer simp: less_eq_st_rep_iff

locale Gamma_semilattice = Val_semilattice
  for \<gamma> :: "'av::semilattice_sup_top \<Rightarrow> val set"where

where

abbreviation
where "

abbreviationabbreviation
where "gamma

lemma gamma_s_top[simp]: java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
by

java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
by (simp add: top_option_def)

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

lemma"S1 \ S2 \ \\<^sub>o S1 \ \\<^sub>o S2"
S1
by(inductionS2: less_eq_option)(simp_all: mono_gamma_s

lemma mono_gamma_c
lemma[simp"<>\<^sub>o \ = UNIV"

lemma
mono_gamma_c
by (cases u)

end

end

quality100%

lemma mono_gamma_o:
" \ S2 \ \\<^sub>o S1 \ \\<^sub>o S2"
java.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 3

lemma mono_gamma_c: "C1 \ C2 \ \\<^sub>c C1 \ \\<^sub>c C2"
by (simp add: less_eq_acom_def mono_gamma_o size_annos anno_map_acom size_annos_same[of C1 C2])

lemma in_gamma_option_iff:
"x \ \_option r u \ (\u'. u = Some u' \ x \ r u')"
by (cases u) auto

end

end

quality100%

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Cephes Mathematical Library

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