## Sort an array of Boolean values

Problem 1 of the second verified software competition.

The ZIP file below contains both the source code, the Why3 proof session file and the Coq script of the proof made in Coq. The Why3 source code is then displayed, followed by a summary of the proofs.

**Authors:** Jean-Christophe Filliâtre

**Topics:** Array Data Structure

**Tools:** Why3

**References:** The 2nd Verified Software Competition

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

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(* The 2nd Verified Software Competition (VSTTE 2012) https://sites.google.com/site/vstte2012/compet Problem 1: Sorting an array of Boolean values, using swaps only *) module TwoWaySort use int.Int use bool.Bool use ref.Refint use array.Array use array.ArraySwap use array.ArrayPermut predicate le (x y: bool) = x = False \/ y = True predicate sorted (a: array bool) = forall i1 i2: int. 0 <= i1 <= i2 < a.length -> le a[i1] a[i2] let two_way_sort (a: array bool) ensures { sorted a } ensures { permut_all (old a) a } = let i = ref 0 in let j = ref (length a - 1) in while !i < !j do invariant { 0 <= !i /\ !j < length a } invariant { forall k: int. 0 <= k < !i -> a[k] = False } invariant { forall k: int. !j < k < length a -> a[k] = True } invariant { permut_all (old a) a } variant { !j - !i } if not a[!i] then incr i else if a[!j] then decr j else begin swap a !i !j; incr i; decr j end done end

# Why3 Proof Results for Project "vstte12_two_way_sort"

## Theory "vstte12_two_way_sort.TwoWaySort": fully verified

Obligations | Alt-Ergo 2.0.0 |

VC for two_way_sort | 0.09 |