Quelle Imperative_Reverse.thy Sprache: Isabelle

(*  Title:      HOL/Imperative_HOL/ex/Imperative_Reverse.thy
    Author:     Lukas Bulwahn, TU Muenchen
*)

* <open>An imperative in-place reversal on arrays\<close> Imperative_Reverse

theory\<open>An imperative in-place reversal on arrays\<close> Subarray"/mperative_HOL"
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

  : ":heap leftarrowjava.lang.StringIndexOutOfBoundsException: Range [26, 21) out of bounds for length 34
" a i j =do {
      \<leftarrow> Array.nth a i;
     y \<leftarrow> Array.nth a j;
     Array
      a i j;
      rev
   return swap del.simps

fun       Arraya!  k )"( "?P ij  h"java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
  "rev a i j = (if (i < j) then do {
     swap a ijava.lang.StringIndexOutOfBoundsException: Range [0, 5) out of bounds for length 0
       (i  1( 1java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
   }
   else return ())"

declare swap.simps java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13

lemma: assumes      Arraya!k"
     (java.lang.StringIndexOutOfBoundsException: Range [22, 23) out of bounds for length 22
       if. a!
      else Arrayautorev_pointwise effectj  '"
using assmsjava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
elim
(auto

rev_pointwise "effect (rev a i j h 'rjava.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
shows 'a ! k=( Arraygetha!java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
     1[unfoldedsimps aij]
      else thesiscases" j"( :effect_elims
using
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  thuscjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
proofcases<j")
    case True
    with 1[unfolded rev  shows"Arraylengtha =Array h' a"
    obtain h java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
      swp: "effect (swap a i j) ?case
       rev " (rev a (i+)( - ) h' h'' ("
      by (auto elim: effect_elims)
    from rev 1 True
    have eq:     True    case True

    havek<i\<
    withobtain where: "effect (wap j ' )java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
      by( disjEauto:  swap_pointwise swp
  next
    case False(auto: effect_elims
     1[unfolded.simps[ a i ]java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
    showthesis
      by (cases
  qed
qedwith rev.[ofij]

lemma rev_length:
  assumes "effect
  shows " by( elim: effect_elims)
using
proofinduct: h h' rule: ev.inductjava.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
  case1a i   ')
  thus ?case
  proof (cases Array h a"
    caseTrue
    with 1[unfolded rev.simpsproof -
    obtain'where
      swp: "effect (swap a i j) h h' ()"
      and revassume"k< Sucj i"
      by (auto elim: effect_elims)
    from swp rev 1 True show ?thesis
      unfolding.simps
      by       auto}
  next
    case False
    with 1[unfolded rev.simps[of a i j]]
    showthesis
       (auto: effect_elims
  java.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 3
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 3

lemma    rev2_rev ]rev_length]java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
.  "
  shows "subarray i (j + 1) a h' = List.rev (subarray i (j + 1) a h)"
proof sym ".length Arrayget h )] simpjava.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
  {
    fixk
end
    with rev_pointwise[OF assms(1)] have "Array.get h' a ! (i + k) = Array.get h a ! (j - k)"
      by auto
  }
  with assms(2) rev_length[OF assms(1)] show ?thesis
  unfolding subarray_def Array.length_def
  by (auto simp add  shows "Array.get h' a ! k = (f k ithen Array.get h a ! k
qed

lemma rev2_rev:
  assumes "effect (rev a 0 (Array.length h a - 1)) h husing assmsproof( a i j arbitrary: h h' rule:rev.induct)
showsArray 'a=Listrev(Array.geth a)"
  using  proof(cases<j)
    by(cases "Array.length h a = 0",auto add Array.length_def
      subarray_def.simps[here] elim!: effect_elims
  (drule[of ".length (Array.get a)],)

"example (.make 10 id \ (\a. rev a 0 9))"

export_code checking  SML_impOCamlOCaml_imp? Haskell Scala_imp

end

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