Theory ExamplesAbort

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theory ExamplesAbort
imports HoareAbort
begin

(*  Title:      HOL/Hoare/ExamplesAbort.thy
    ID:         $Id: ExamplesAbort.thy,v 1.5 2005/07/07 10:39:32 nipkow Exp $
    Author:     Tobias Nipkow
    Copyright   1998 TUM

Some small examples for programs that may abort.
*)

theory ExamplesAbort imports HoareAbort begin

lemma "VARS x y z::nat
 {y = z & z ≠ 0} z ≠ 0 -> x := y div z {x = 1}"
by vcg_simp

lemma
 "VARS a i j
 {k <= length a & i < k & j < k} j < length a -> a[i] := a!j {True}"
apply vcg_simp
done

lemma "VARS (a::int list) i
 {True}
 i := 0;
 WHILE i < length a
 INV {i <= length a}
 DO a[i] := 7; i := i+1 OD
 {True}"
apply vcg_simp
done

end

lemma

  {y = z ∧ z ≠ 0} 
   z ≠ 0 -> x := y div z 
   {x = 1}

lemma

  {k ≤ length a ∧ i < k ∧ j < k} 
   j < length a -> i < length a -> a := a[i := a ! j] 
   {True}

lemma

  {True} 
   i := 0;
   WHILE i < length a INV {i ≤ length a} 
    DO i < length a -> a := a[i := 7]; i := i + 1 OD 
   {True}