Theory ExamplesAbort

theory ExamplesAbort
imports Hoare_Logic_Abort
(*  Title:      HOL/Hoare/ExamplesAbort.thy
Author: Tobias Nipkow
Copyright 1998 TUM

Some small examples for programs that may abort.
*)


theory ExamplesAbort imports Hoare_Logic_Abort 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}"

by vcg_simp

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}"

by vcg_simp

end