**diff options**

author | AndreiBarbu <> | 2013-08-14 08:53:46 (GMT) |
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committer | hdiff <hdiff@hdiff.luite.com> | 2013-08-14 08:53:46 (GMT) |

commit | a6267d1b1b823fb571614323cd160991e29af86d (patch) | |

tree | c227aa2810b629b9c9ff8a7897e8d788810c6a9f |

version 1.01.0

-rw-r--r-- | Control/Monad/CSP.hs | 246 | ||||

-rw-r--r-- | LICENSE | 165 | ||||

-rw-r--r-- | README.md | 41 | ||||

-rw-r--r-- | Setup.lhs | 4 | ||||

-rw-r--r-- | csp.cabal | 23 |

5 files changed, 479 insertions, 0 deletions

diff --git a/Control/Monad/CSP.hs b/Control/Monad/CSP.hs new file mode 100644 index 0000000..e611287 --- /dev/null +++ b/Control/Monad/CSP.hs @@ -0,0 +1,246 @@ +{-# LANGUAGE TypeFamilies #-} + +module Control.Monad.CSP + ( + -- * Overview + -- $overview + + -- * Building CSPs + mkDV, + constraint1, + constraint2, + constraint, + -- * Solving CSPs + oneCSPSolution, + allCSPSolutions, + solveCSP, + CSPResult(..), + -- * Low-level internal + csp, + domain, + demons, + isBound, + domainSize, + localWriteIORef, + binding, + addConstraint, + restrictDomain, + -- * Types + DV(..), + DVContainer(..), + Constraint, + CSP(..), + ) where +import Control.Monad.Amb +import Control.Monad +import Control.Monad.State.Strict +import Data.IORef +import System.IO.Unsafe + +-- $overview +-- +-- This constructs a discrete constraint satisfaction problem (CSP) +-- and then solves it. A discrete CSP consists of a number of +-- variables each having a discrete domain along with a number of +-- constraints between those variables. Solving a CSP searches for +-- assignments to the variables which satisfy those constraints. At +-- the moment the only constraint propagation technique available is +-- arc consistency. +-- +-- Here is a simple example which solves Sudoku +-- puzzles, project Euler problem 96. +-- +-- @ +--import Data.List +--import Control.Monad.CSP +-- +--solveSudoku :: (Enum a, Eq a, Num a) => [[a]] -> [[a]] +--solveSudoku puzzle = oneCSPSolution $ do +-- dvs \<- mapM (mapM (\\a -> mkDV $ if a == 0 then [1 .. 9] else [a])) puzzle +-- mapM_ assertRowConstraints dvs +-- mapM_ assertRowConstraints $ transpose dvs +-- sequence_ [assertSquareConstraints dvs x y | x <- [0,3,6], y <- [0,3,6]] +-- return dvs +-- where assertRowConstraints = mapAllPairsM_ (constraint2 (/=)) +-- assertSquareConstraints dvs i j = +-- mapAllPairsM_ (constraint2 (/=)) [(dvs !! x) !! y | x <- [i..i+2], y <- [j..j+2]] +-- +-- mapAllPairsM_ :: Monad m => (a -> a -> m b) -> [a] -> m () +-- mapAllPairsM_ f [] = return () +-- mapAllPairsM_ f (_:[]) = return () +-- mapAllPairsM_ f (a:l) = mapM_ (f a) l >> mapAllPairsM_ f l +-- +--sudoku3 = [[0,0,0,0,0,0,9,0,7], +-- [0,0,0,4,2,0,1,8,0], +-- [0,0,0,7,0,5,0,2,6], +-- [1,0,0,9,0,4,0,0,0], +-- [0,5,0,0,0,0,0,4,0], +-- [0,0,0,5,0,7,0,0,9], +-- [9,2,0,1,0,8,0,0,0], +-- [0,3,4,0,5,9,0,0,0], +-- [5,0,7,0,0,0,0,0,0]] +-- @ +-- +-- >>> solveSudoku sudoku3 +-- [[4,6,2,8,3,1,9,5,7],[7,9,5,4,2,6,1,8,3],[3,8,1,7,9,5,4,2,6],[1,7,3,9,8,4,2,6,5],[6,5,9,3,1,2,7,4,8],[2,4,8,5,6,7,3,1,9],[9,2,6,1,7,8,5,3,4],[8,3,4,2,5,9,6,7,1],[5,1,7,6,4,3,8,9,2]] + + +data DV r a = DV { dvDomain :: IORef [a], dvConstraints :: IORef [Constraint r] } +type Constraint r = AmbT r IO () + +data DVContainer r = DVContainer { dvcIsBound :: AmbT r IO Bool, + dvcConstraints :: AmbT r IO (), + dvcABinding :: AmbT r IO () } + +data CSP r x = CSP { unCSP :: IORef [DVContainer r] -> IO x } + +-- | Lift an IO computation into the CSP monad. CSPs are only in IO +-- temporarily. +csp :: IO x -> CSP r x +csp x = CSP (\_ -> x) + +instance Monad (CSP r) where + CSP x >>= y = CSP (\s -> x s >>= (\(CSP z) -> z s) . y) + return a = CSP (\_ -> return a) + +-- | Extract the current domain of a variable. +domain :: DV t t1 -> IO [t1] +domain (DV d _) = readIORef d + +-- | Extract the current constraints of a variable. +demons :: DV r a -> IO [Constraint r] +demons dv = readIORef (dvConstraints dv) + +-- | Is the variable currently bound? +isBound :: DV t t1 -> IO Bool +isBound dv = domain dv >>= return . (== 1) . length + +-- | Compute the size of the current domain of variable. +domainSize :: DV t t1 -> IO Int +domainSize dv = domain dv >>= return . length + +-- | Create a variable with the given domain +mkDV :: [a] -> CSP r (DV r a) +mkDV xs = do + d <- csp $ newIORef xs + c <- csp $ newIORef [] + let dv = DV d c + CSP (\x -> modifyIORef x $ ((DVContainer (lift $ isBound dv) + (lift (demons dv) >>= sequence_) + (do + d' <- lift $ readIORef d + e <- aMemberOf d' + restrictDomain dv (\_ -> return [e]))) + :)) + return dv + +-- | This performs a side-effect, writing to the given IORef but +-- records this in the nondeterministic computation so that it can be +-- undone when backtracking. +localWriteIORef :: IORef a -> a -> AmbT r IO () +localWriteIORef ref new = do + previous <- lift $ readIORef ref + uponFailure (lift $ writeIORef ref previous) + lift $ writeIORef ref new + +-- | The low-level function out of which constraints are +-- constructed. It modifies the domain of a variable. +restrictDomain :: DV r a -> ([a] -> IO [a]) -> AmbT r IO () +restrictDomain dv f = do + l' <- lift (domain dv >>= f) + when (null l') fail' + size <- lift $ domainSize dv + when (length l' < size) $ do + localWriteIORef (dvDomain dv) l' + constraints <- lift $ demons dv + sequence_ constraints + +-- | Add a constraint to the given variable. +addConstraint :: DV r1 a -> Constraint r1 -> CSP r () +addConstraint dv c = csp $ modifyIORef (dvConstraints dv) (c :) + +-- | Assert a unary constraint. +constraint1 :: (a -> Bool) -> DV r1 a -> CSP r () +constraint1 f dv = addConstraint dv $ restrictDomain dv $ (return . filter f) + +-- | Assert a binary constraint with arc consistency. +constraint2 :: (a -> t1 -> Bool) -> DV t a -> DV t t1 -> CSP r () +constraint2 f x y = do + addConstraint x $ + restrictDomain y + (\yd -> do + xd <- (domain x) + return $ filter (\ye -> any (\xe -> f xe ye) xd) yd) + addConstraint y $ + restrictDomain x + (\xd -> do + yd <- (domain y) + return $ filter (\xe -> any (\ye -> f xe ye) yd) xd) + +-- | Assert an n-ary constraint with arc consistency. One day this +-- will allow for a heterogeneous list of variables, but at the moment +-- they must all be of the same type. +constraint :: ([a] -> Bool) -> [DV r1 a] -> CSP r () +constraint f dvl = + mapM_ (\(dv1, k) -> + addConstraint dv1 $ + (mapM_ (\(dv2, i) -> do + unless (i == k) $ + restrictDomain dv2 + (\d2 -> do + ddvl <- mapM domain dvl + return $ filter (\d2e -> + let loop [] es _ = f (reverse es) + loop (d:ds) es j | i == j = loop ds (d2e:es) (j + 1) + | otherwise = any (\e -> loop ds (e : es) (j + 1)) d + in loop ddvl [] 0) d2)) + $ zip dvl ([1..] :: [Int]))) + $ zip dvl ([1..] :: [Int]) + +-- | Retrieve the current binding of a variable. +binding :: DV t b -> IO b +binding d = domain d >>= return . head + +-- | This extracts results from a CSP. +class CSPResult a where + type Result a + result :: a -> IO (Result a) +instance CSPResult (DV r a) where + type Result (DV r a) = a + result = binding +instance (CSPResult a, CSPResult b) => CSPResult (a,b) where + type Result (a,b) = (Result a, Result b) + result (a,b) = do + a' <- result a + b' <- result b + return (a', b') +instance (CSPResult a) => CSPResult [a] where + type Result [a] = [Result a] + result = mapM result + +-- | Solve the given CSP. The CSP solver is a nondeterministic +-- function in IO and this is the generic interface which specifies +-- how the nondeterministic computation should be carried out. +solveCSP :: CSPResult a1 => (AmbT r IO (Result a1) -> IO a) -> CSP r a1 -> a +solveCSP runAmb (CSP f) = + (unsafePerformIO $ runAmb $ do + dvcs <- lift $ newIORef [] + r <- lift $ f dvcs + dvcs' <- lift $ readIORef dvcs + -- One round of applying all constraints + mapM_ dvcConstraints dvcs' + let loop [] = return () + loop (d:ds) = do + dvcABinding d + filterM (liftM not . dvcIsBound) ds >>= loop + in filterM (liftM not . dvcIsBound) dvcs' >>= loop + lift $ result r >>= return) + +-- | Return a single solution to the CSP. 'solveCSP' running with 'oneValueT' +oneCSPSolution :: CSPResult a1 => CSP (Result a1) a1 -> Result a1 +oneCSPSolution = solveCSP oneValueT + +-- | Return all solutions to the CSP. 'solveCSP' running with +-- 'allValuesT' +allCSPSolutions :: CSPResult a1 => CSP (Result a1) a1 -> [Result a1] +allCSPSolutions = solveCSP allValuesT @@ -0,0 +1,165 @@ + GNU LESSER GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/> + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + + This version of the GNU Lesser General Public License incorporates +the terms and conditions of version 3 of the GNU General Public +License, supplemented by the additional permissions listed below. + + 0. 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Such new +versions will be similar in spirit to the present version, but may +differ in detail to address new problems or concerns. + + Each version is given a distinguishing version number. If the +Library as you received it specifies that a certain numbered version +of the GNU Lesser General Public License "or any later version" +applies to it, you have the option of following the terms and +conditions either of that published version or of any later version +published by the Free Software Foundation. If the Library as you +received it does not specify a version number of the GNU Lesser +General Public License, you may choose any version of the GNU Lesser +General Public License ever published by the Free Software Foundation. + + If the Library as you received it specifies that a proxy can decide +whether future versions of the GNU Lesser General Public License shall +apply, that proxy's public statement of acceptance of any version is +permanent authorization for you to choose that version for the +Library. diff --git a/README.md b/README.md new file mode 100644 index 0000000..6866268 --- /dev/null +++ b/README.md @@ -0,0 +1,41 @@ +# CSP + +A simple example which solves Sudoku puzzles, project Euler problem 96. + + solveSudoku :: (Enum a, Eq a, Num a) => [[a]] -> [[a]] + solveSudoku puzzle = oneCSPSolution $ do + dvs <- mapM (mapM (\a -> mkDV $ if a == 0 then [1 .. 9] else [a])) puzzle + mapM_ assertRowConstraints dvs + mapM_ assertRowConstraints $ transpose dvs + sequence_ [assertSquareConstraints dvs x y | x <- [0,3,6], y <- [0,3,6]] + return dvs + where assertRowConstraints = mapAllPairsM_ (constraint2 (/=)) + assertSquareConstraints dvs i j = + mapAllPairsM_ (constraint2 (/=)) [(dvs !! x) !! y | x <- [i..i+2], y <- [j..j+2]] + + sudoku3 = [[0,0,0,0,0,0,9,0,7], + [0,0,0,4,2,0,1,8,0], + [0,0,0,7,0,5,0,2,6], + [1,0,0,9,0,4,0,0,0], + [0,5,0,0,0,0,0,4,0], + [0,0,0,5,0,7,0,0,9], + [9,2,0,1,0,8,0,0,0], + [0,3,4,0,5,9,0,0,0], + [5,0,7,0,0,0,0,0,0]] + + mapAllPairsM_ :: Monad m => (a -> a -> m b) -> [a] -> m () + mapAllPairsM_ f [] = return () + mapAllPairsM_ f (_:[]) = return () + mapAllPairsM_ f (a:l) = mapM_ (f a) l >> mapAllPairsM_ f l + + solveSudoku sudoku3 + +## Future + + - Docs! + - Allow a randomized execution order for CSPs + - CSPs don't need use IO internally. ST is enough. + - Constraint synthesis. Already facilitated by the fact that + constraints are internally nondeterministic + - Other constraint types for CSPs, right now only AC is implemented + - n-ary heterogeneous constraints diff --git a/Setup.lhs b/Setup.lhs new file mode 100644 index 0000000..6b32049 --- /dev/null +++ b/Setup.lhs @@ -0,0 +1,4 @@ +#! /usr/bin/env runhaskell + +> import Distribution.Simple +> main = defaultMain diff --git a/csp.cabal b/csp.cabal new file mode 100644 index 0000000..97592d5 --- /dev/null +++ b/csp.cabal @@ -0,0 +1,23 @@ +Name: csp +Version: 1.0 +Description: Constraint satisfaction problem (CSP) solvers +License: LGPL +License-file: LICENSE +Author: Andrei Barbu <andrei@0xab.com> +Maintainer: Andrei Barbu <andrei@0xab.com> +Category: Control, AI, Constraints, Failure, Monads +Build-Type: Simple +cabal-version: >= 1.6 +synopsis: + Discrete constraint satisfaction problem (CSP) solvers. +extra-source-files: README.md + +source-repository head + type: git + location: git://github.com/abarbu/csp-haskell.git + +Library + Build-Depends: base >= 3 && < 5, mtl >= 2, containers, nondeterminism + Exposed-modules: + Control.Monad.CSP + ghc-options: -Wall |