module SelectionSort
    use int.Int
    use array.Array
    use array.IntArraySorted
    use array.ArraySwap
    use array.ArrayPermut

    let selection_sort (xs: array int)
      ensures { sorted xs }
      ensures { permut_all (old xs) xs } = 

    let ref min = 0 in 
    for i = 0 to length xs - 1 do
      invariant { sorted_sub xs 0 i }
      invariant { permut_all (old xs) xs }
      invariant { forall k1 k2: int. 0 <= k1 < i <= k2 < length xs -> xs[k1] <= xs[k2] }
        
      min <- i;
      for j = i + 1 to length xs - 1 do
        invariant { i <= min < j }
        invariant { forall k:int . i <= k < j -> xs[min] <= xs[k] }
        
        if xs[j] < xs[min] then min <- j
      done;
      swap xs min i;
    done
end