## FoVeOOS'11 Competition: challenge 1, in Why3

Maximum of an array of integers, in Why3

Authors: Claude Marché

Topics: Array Data Structure

Tools: Why3

References: The COST FoVeOOS'11 Competition

see also the index (by topic, by tool, by reference, by year)

```(*
COST Verification Competition. vladimir@cost-ic0701.org

Challenge 1: Maximum in an array

Given: A non-empty integer array a.

Verify that the index returned by the method max() given below points to
an element maximal in the array.
*)

module ArrayMax

use import int.Int
use import int.MinMax
use import ref.Ref
use import array.Array

let max (a: array int) =
requires { 0 < length a }
ensures  { 0 <= result < length a /\
forall i:int. 0 <= i < a.length -> a[i] <= a[result] }
let x = ref 0 in
let y = ref (length a - 1) in
while !x <> !y do
invariant { 0 <= !x <= !y < length a /\
forall i:int.
0 <= i < !x \/ !y < i < length a ->
a[i] <= max a[!x] a[!y]
}
variant { !y - !x }
if a[!x] <= a[!y] then x := !x+1 else y := !y-1
done;
!x

end
```