Commit 5bb3c2e6 by MARCHE Claude

### New example: bubble sort

parent 0d2ea48d
 (* {1 Bubble sort} *) module BubbleSort use import int.Int use import ref.Ref use import array.Array use import array.IntArraySorted use import array.ArraySwap use import array.ArrayPermut use import array.ArrayEq let bubble_sort (a: array int) ensures { permut_all (old a) a } ensures { sorted a } = 'Init: for i = length a - 1 downto 1 do invariant { permut_all (at a 'Init) 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 (at a 'Init) 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