[Haskell-cafe] Type constraints and classes
Thomas van Noort
thomas at cs.ru.nl
Sun Apr 26 09:23:17 EDT 2009
This is a recurring problem[1] and I'm still looking for a really
satisfying solution. The only working and non-verbose solution I found
is the one Miguel suggests. Although I'm not too fond of splitting up
the monadic functions into separate type classes. A similar solution is
described elsewhere[2]. It also desribes how you can use Template
Haskell to regain the power of the do-notation with your own restricted
monad type class.
Kind regards,
Thomas
[1]
http://www.nabble.com/Monad-instance-for-Data.Set%2C-again-td16259448.html
[2]
http://www.randomhacks.net/articles/2007/03/15/data-set-monad-haskell-macros
Miguel Mitrofanov wrote:
> {-# LANGUAGE MultiParamTypeClasses #-}
> class Returnable m a where ret :: a -> m a
> class Bindable m a b where bind :: m a -> (a -> m b) -> m b
> newtype MOAMonad r m a = MOAMonad ((a -> m r) -> m r)
> instance Monad (MOAMonad r m) where
> return x = MOAMonad $ ($ x)
> MOAMonad h >>= f = MOAMonad $ \p -> h $ \x -> let MOAMonad h' = f x
> in h' p
> fromMOAMonad :: Returnable m r => MOAMonad r m r -> m r
> fromMOAMonad (MOAMonad h) = h ret
> toMOAMonad :: Bindable m a r => m a -> MOAMonad r m a
> toMOAMonad mx = MOAMonad $ \p -> bind mx p
> class FMappable f a b where fmp :: (a -> b) -> f a -> f b
> newtype MOAFunctor r f a = MOAFunctor ((a -> r) -> f r)
> instance Functor (MOAFunctor r f) where
> fmap f (MOAFunctor h) = MOAFunctor $ \p -> h $ p . f
> fromMOAFunctor :: MOAFunctor r f r -> f r
> fromMOAFunctor (MOAFunctor h) = h id
> toMOAFunctor :: FMappable f a r => f a -> MOAFunctor r f a
> toMOAFunctor fx = MOAFunctor $ \p -> fmp p fx
>
> -- MOA stands for "Mother Of All"
>
> On 26 Apr 2009, at 15:21, Neil Brown wrote:
>
>> Hi,
>>
>> I have a Haskell problem that keeps cropping up and I wondered if
>> there was any solution/work-around/dirty-hack that could help. I keep
>> wanting to define class instances for things like Functor or Monad,
>> but with restrictions on the inner type. I'll explain with an
>> example, because I find explaining this in words a bit difficult.
>> Let's say I want to create a Monad instance for Set akin to that for
>> lists:
>>
>> ==
>> import Data.Set
>> import Prelude hiding (map)
>>
>> instance Monad Set where
>> return = singleton
>> m >>= f = fold union empty (map f m)
>>
>> -- Error: Could not deduce (Ord a, Ord b) from the context (Monad Set)
>> ==
>>
>> Everything fits (I think) -- except the type-class constraints.
>> Obviously my Monad instance won't work if you have things inside the
>> set that aren't Ord, but I can't work out how to define a restricted
>> instance that only exists for types that have Ord instances. I can't
>> express the constraint on the instance because the a and b types of
>> return and >>= aren't visible in the class header. Shifting the
>> constraint to be present in the type doesn't seem to help either (e.g.
>> newtype Ord a => MySet a = MySet (Set a)...).
>>
>> Is there any way to get such instances as the one for Set working? I
>> cannot carry around a compare function myself in a data type that
>> wraps Set, because return cannot create such functions without the
>> original type-class instance. I don't actually need a Monad for Set,
>> but it neatly demonstrates my problem of wanting constraints on the
>> type inside a Monad (or a Functor, or an Applicative, etc).
>>
>> I worked around a similar problem with Functor by opting for a new
>> Functor-like type-class with the constraints, but doing that with
>> Monad rules out using all the monad helper functions (liftM, mapM,
>> etc), and the do notation, which would be a step too far. All
>> suggestions are welcome, no matter how hacky, or how many GHC
>> extensions are required :-) (provided they don't break all the other
>> monads, e.g. redefining the signature of Monad).
>>
>> Thanks,
>>
>> Neil.
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>
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