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50 lines
1.1 KiB
Plaintext
50 lines
1.1 KiB
Plaintext
(* Two Way Sort
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The following program sorts an array of Boolean values, with False<True.
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E.g.
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two_way_sorted [True; False; False; True; False]
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= [False; False; False; True; True]
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- Strengthen the invariant to prove correctness.
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*)
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module TwoWaySort
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use int.Int
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use bool.Bool
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use ref.Refint
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use array.Array
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use array.ArraySwap
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use array.ArrayPermut
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predicate (<<) (x y: bool) = x = False \/ y = True
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predicate sorted (a: array bool) =
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forall i1 i2: int. 0 <= i1 <= i2 < a.length -> a[i1] << a[i2]
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let two_way_sort (a: array bool) : unit
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ensures { sorted a }
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ensures { permut_all (old a) a }
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=
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let ref i = 0 in
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let ref j = length a - 1 in
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while i < j do
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invariant { 0 <= i /\ j < length a }
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invariant { forall i1: int. 0 <= i1 < i -> a[i1] = False }
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invariant { forall i2: int. j < i2 < length a -> a[i2] = True }
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invariant { permut_all (old a) a }
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variant { j - i }
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if not a[i] then
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incr i
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else if a[j] then
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decr j
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else begin
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swap a i j;
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incr i;
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decr j
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end
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done
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end
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