(* Title: HOL/Hoare/ExamplesAbort.thy
ID: $Id$
Author: Tobias Nipkow
Copyright 1998 TUM
Some small examples for programs that may abort.
*)
theory ExamplesAbort = HoareAbort:
lemma "VARS x y z::nat
{y = z & z \<noteq> 0} z \<noteq> 0 \<rightarrow> x := y div z {x = 1}"
by vcg_simp
lemma
"VARS a i j
{k <= length a & i < k & j < k} j < length a \<rightarrow> a[i] := a!j {True}"
apply vcg_simp
apply arith
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
apply arith
done
end