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2013-03-13T14:20:56.493
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<p>Given the legendary helpfulness of the Haskell community, the lack of an answer at this point is a strong indication that there's no good solution in the current type system.</p> <p>I've already outlined the flawed solutions in the question, so I'll just post a complete version of my example. This is basically what I used to solve most alignment problems on Rosalind:</p> <pre><code>{-# LANGUAGE FlexibleContexts, RankNTypes, ScopedTypeVariables #-} import Control.Applicative import Control.Monad import Control.Monad.ST import Data.Maybe import Data.Array.ST import Data.Array.Unboxed class IArray UArray e => Unboxable e where newSTUArray_ :: forall s i. Ix i => (i, i) -> ST s (STUArray s i e) readSTUArray :: forall s i. Ix i => STUArray s i e -> i -> ST s e writeSTUArray :: forall s i. Ix i => STUArray s i e -> i -> e -> ST s () instance Unboxable Bool where newSTUArray_ = newArray_ readSTUArray = readArray writeSTUArray = writeArray instance Unboxable Double where newSTUArray_ = newArray_ readSTUArray = readArray writeSTUArray = writeArray {- Same for Char, Float, (Int|Word)(|8|16|32|64)... -} {-# INLINE dynamicProgramming2DSTU #-} dynamicProgramming2DSTU :: forall e i j . ( Unboxable e, Ix i, Ix j, Enum i, Enum j ) => (forall m . (Monad m, Applicative m) => (i -> j -> m e) -> (i -> j -> m e)) -> (i -> j -> Maybe e) -> (i, i) -> (j, j) -> (i -> j -> e) dynamicProgramming2DSTU program boundaryConditions (xl, xh) (yl, yh) = arrayLookup where arrayLookup :: i -> j -> e arrayLookup xi yj = fromMaybe (resultArray ! (xi, yj)) $ boundaryConditions xi yj arrB :: ((i, j), (i, j)) arrB = ((xl, yl), (xh, yh)) resultArray :: UArray (i, j) e resultArray = runSTUArray resultArrayST resultArrayST :: forall s. ST s (STUArray s (i, j) e) resultArrayST = do arr <- newSTUArray_ arrB let acc xi yj = maybe (readSTUArray arr (xi, yj)) return $ boundaryConditions xi yj forM_ [xl..xh] $ \xi -> do forM_ [yl..yh] $ \yj -> do result <- program acc xi yj writeSTUArray arr (xi, yj) result return arr </code></pre>
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