"Could not deduce (MArray (STUArray s) Int (ST s)) from context ()" when applying runST

Question

I'm in the process of learning haskell and came across this problem:

Using Glasgow Haskell Compiler, Version 6.10.4, for Haskell 98, stage 2 booted by GHC version 6.10.1

Common beginning of the file

{-# LANGUAGE FlexibleContexts #-}

module UPSO where

import Control.Monad(forM,forM_)
import Control.Monad.ST.Lazy (ST,runST)
import Data.Array.MArray (MArray, Ix, getBounds, newArray, readArray, writeArray)
import Data.Array.ST (STArray,STUArray)

minmax xs@(x:_) = foldr (\x (l,u) -> (min x l,max x u)) (x,x) xs

modify a i f = do
    x <- readArray a i
    writeArray a i (f x)

increment a i = modify a i (+1)
decrement a i = modify a i (\x -> x - 1)

uniquePermutationsM t 0 = return $! [[]]
uniquePermutationsM t pos = do
    (l,u) <- getBounds t
    perms <- forM [l..u] (\d -> do
         count <- readArray t d -- t[d]
        if count == 0
            then return $! []
            else do
                decrement t d
                pss <- uniquePermutationsM t (pos-1)
                increment t d
                return $! (map (d:) pss)
        )
    return $! (concat perms)

Using STArray (works)

mkArray :: (Int,Int) -> (ST s) (STArray s Int Int)    
mkArray bounds = newArray bounds 0 

uniquePermutationsST ::  [Int] -> ST s [[Int]]
uniquePermutationsST xs = do
    let bounds@(l,u) = (minmax xs) 
    t <- mkArray  bounds
    forM_ xs (increment t)
    pos <- sum `fmap` mapM (readArray t) [l..u]
    uniquePermutationsM t pos

uniquePermutations xs = runST (uniquePermutationsST xs)

Using STUArray (doesn't work)

But when I try to switch to unboxed arrays, I get an error message.

mkArray :: (Int,Int) -> (ST s) (STUArray s Int Int)    
mkArray bounds = newArray bounds 0 

uniquePermutationsST ::  [Int] -> ST s [[Int]]
uniquePermutationsST xs = do
    let bounds@(l,u) = (minmax xs) 
    t <- mkArray  bounds
    forM_ xs (increment t)
    pos <- sum `fmap` mapM (readArray t) [l..u]
    uniquePermutationsM t pos

uniquePermutations xs = runST (uniquePermutationsST xs)

Error messages

Could not deduce (MArray (STUArray s) Int (ST s))
  from the context ()
  arising from a use of 'newArray' at UPSO.hs:35:17-33
Possible fix:
  add (MArray (STUArray s) Int (ST s)) to the context of
    the type signature for 'mkArray'
  or add an instance declaration for (MArray (STUArray s) Int (ST s))
In the expression: newArray bounds 0
In the definition of 'mkArray': mkArray bounds = newArray bounds 0

and also:

Could not deduce (MArray (STUArray s) Int (ST s))
  from the context ()
  arising from a use of 'increment' at UPSO.hs:41:14-24

After almost two hours of fiddling with the type annotations I hope someone can point me in the right direction. What on earth is going wrong?

Thank you for your time.

Answer 1

I've posted the same question on the haskell mailing list and got this answer:

This works if I [use the strict] Control.Monad.ST instead of Control.Monad.ST.Lazy.

The problem is that the MArray instances are declared for the strict ST monad; there appear to be no corresponding instances for the lazy ST monad.
-- by Dave Menendez (http://www.eyrie.org/~zednenem/)

Didn't think of that. But makes kind of sense not to define these instances, since unboxed values cannot have their computation delayed.

Peter Gammie pointed out that one can apply the function strictToLazyST of the Control.Monad.ST.Lazy module to use unboxed mutable arrays in a lazy state thread. Keep in mind though that the array still is strict in its contents.

http://www.haskell.org/ghc/docs/latest/html/libraries/base/Control-Monad-ST-Lazy.html#v%3AstrictToLazyST