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57 lines
1.5 KiB
Plaintext
57 lines
1.5 KiB
Plaintext
/*
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* Copyright (c) 2013-2016 Galois, Inc.
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* Distributed under the terms of the BSD3 license (see LICENSE file)
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*/
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/* To see this in action, try:
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:sat nQueens : (Solution n)
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where n is the board-size
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You may find that cvc4 takes a long time for solutions bigger than 5.
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For those sizes, we have had good luck with both Yices and Z3.
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To do that,
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:set prover=Z3
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or
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:set prover=yices
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*/
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all : {n, a} (fin n) => (a -> Bit, [n]a) -> Bit
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all (f, xs) = [ f x | x <- xs ] == ~zero
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contains xs e = [ x == e | x <- xs ] != zero
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distinct : {n,a} (fin n, Cmp a) => [n]a -> Bit
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distinct xs =
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[ if n1 < n2 then x != y else True
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| (x,n1) <- numXs , (y,n2) <- numXs
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] == ~zero
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where
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numXs = [ (x,n) | x <- xs | n <- [ (0:[width n]) ... ] ]
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type Position n = [width (n - 1)]
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type Board n = [n](Position n)
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type Solution n = Board n -> Bit
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checkDiag : {n} (fin n, n >= 1) => Board n -> (Position n, Position n) -> Bit
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checkDiag qs (i, j) = (i >= j) || (diffR != diffC)
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where qi = qs @ i
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qj = qs @ j
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diffR = if qi >= qj then qi-qj else qj-qi
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diffC = j - i // we know i < j
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nQueens : {n} (fin n, n >= 1) => Solution n
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nQueens qs = all (inRange qs, qs) /\ all (checkDiag qs, ijs `{n}) /\ distinct qs
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ijs : {n}(fin n, n>= 1)=> [_](Position n, Position n)
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ijs = [ (i, j) | i <- [0 .. (n-1)], j <- [0 .. (n-1)]]
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inRange : {n} (fin n, n >= 1) => Board n -> Position n -> Bit
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inRange qs x = x <= `(n - 1)
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property nQueensProve x = (nQueens x) == False
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