Quelle Imperative_Reverse.thy Sprache: Isabelle

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

theory "/mperative_HOL"
imports "../Imperative_HOL"
begindo

swapjava.lang.NullPointerException
  "swap Arrayupdiyajava.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
<.
     y \<leftarrow> Array.nth a j;
     .upd
     Array  swap.simps
      elim
( simp)

fun rev :: " "wap dox\<leftarrow> Array.nth a i;
  "rev a i j Array.upd i y a;
swap

   }
  ()"

declare.simpsrev del rev. ha!- ) is  'java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63

lemma swap_pointwise: assumes " case a(i+)j-java.lang.StringIndexOutOfBoundsException: Range [26, 27) out of bounds for length 26
    True
      else if
else!)
using assms unfolding swap.simps 'where
elim
(auto       and r =  .t a!i

lemmaassumesrevjava.lang.StringIndexOutOfBoundsException: Range [57, 56) out of bounds for length 56
shows (< Array
      else if
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
   induct induct
  case (1   ".geth . a"
thus ?case
   ( "i "
    case True caseslength  simp:Array
    with rev[ j=0] elim)
    obtain sym Listh ) simp
definition=Array
      and
exampleSML ? OCaml_imp? Scala
    from rev
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

    have "k < i \ i = k \ (i < k \ k < j) \ j = k \ j < k" by arith
    with True show ?thesis
      by (elim disjE) (auto simp: eq swap_pointwise[OF swp])
  next
    case False
    with 1[unfolded rev.simps[of a i j]]
    show ?thesis
      by (cases "k = j") (auto elim: effect_elims)
  qed
qed

lemma rev_length:
  assumes "effect (rev a i j) h h' r"
  shows "Array.length h a = Array.length h' a"
using assms
proof (induct a i j arbitrary: h h' rule: rev.induct)
  case (1 a i j h h'')
  thus ?case
  proof (cases "i < j")
    case True
    with 1[unfolded rev.simps[of a i j]]
    obtain h' where
      swp: "effect (swap a i j) h h' ()"
      and rev: "effect (rev a (i + 1) (j - 1)) h' h'' ()"
      by (auto elim: effect_elims)
    from swp rev 1 True show ?thesis
      unfolding swap.simps
      by (elim effect_elims) fastforce
  next
    case False
    with 1[unfolded rev.simps[of a i j]]
    show ?thesis
      by (auto elim: effect_elims)
  qed
qed

lemma rev2_rev': assumes "effect (rev a i j) h h' u"
  assumes "j < Array.length h a"
  shows "subarray i (j + 1) a h' = List.rev (subarray i (j + 1) a h)"
proof -
  {
    fix k
    assume "k < Suc j - i"
    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: length_nths' rev_nth min_def nth_nths' intro!: nth_equalityI)
qed

lemma rev2_rev:
  assumes "effect (rev a 0 (Array.length h a - 1)) h h' u"
  shows "Array.get h' a = List.rev (Array.get h a)"
  using rev2_rev'[OF assms] rev_length[OF assms] assms
    by (cases "Array.length h a = 0", auto simp add: Array.length_def
      subarray_def rev.simps[where j=0] elim!: effect_elims)
  (drule sym[of "List.length (Array.get h a)"], simp)

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

export_code example checking SML SML_imp OCaml? OCaml_imp? Haskell? Scala Scala_imp

end

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