## Bubble sort

Sorting an array of integers using bubble sort.

Auteurs: Claude Marché

Catégories: Array Data Structure / Sorting Algorithms

Outils: Why3

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```(* {1 Bubble sort} *)

module BubbleSort

use int.Int
use ref.Ref
use array.Array
use array.IntArraySorted
use array.ArraySwap
use array.ArrayPermut
use array.ArrayEq

let bubble_sort (a: array int)
ensures { permut_all (old a) a }
ensures { sorted a }
= for i = length a - 1 downto 1 do
invariant { permut_all (old a) a }
invariant { sorted_sub a i (length a) }
invariant { forall k1 k2: int.
0 <= k1 <= i < k2 < length a -> a[k1] <= a[k2] }
for j = 0 to i - 1 do
invariant { permut_all (old a) a }
invariant { sorted_sub a i (length a) }
invariant { forall k1 k2: int.
0 <= k1 <= i < k2 < length a -> a[k1] <= a[k2] }
invariant { forall k. 0 <= k <= j -> a[k] <= a[j] }
if a[j] > a[j+1] then swap a j (j+1);
done;
done

let test1 () =
let a = make 3 0 in
a[0] <- 7; a[1] <- 3; a[2] <- 1;
bubble_sort a;
a

let test2 () ensures { result.length = 8 } =
let a = make 8 0 in
a[0] <- 53; a[1] <- 91; a[2] <- 17; a[3] <- -5;
a[4] <- 413; a[5] <- 42; a[6] <- 69; a[7] <- 6;
bubble_sort a;
a

exception BenchFailure

let bench () raises { BenchFailure -> true } =
let a = test2 () in
if a[0] <> -5 then raise BenchFailure;
if a[1] <> 6 then raise BenchFailure;
if a[2] <> 17 then raise BenchFailure;
if a[3] <> 42 then raise BenchFailure;
if a[4] <> 53 then raise BenchFailure;
if a[5] <> 69 then raise BenchFailure;
if a[6] <> 91 then raise BenchFailure;
if a[7] <> 413 then raise BenchFailure;
a

end
```