Am Montag, 24. März 2008 20:47 schrieb Henning Thielemann: > […] > Here is another approach that looks tempting, but unfortunately does not > work, and I wonder whether this can be made working. > > module RestrictedMonad where > > import Data.Set(Set) > import qualified Data.Set as Set > > class AssociatedMonad m a where > > class RestrictedMonad m where > return :: AssociatedMonad m a => a -> m a > (>>=) :: (AssociatedMonad m a, AssociatedMonad m b) => > m a -> (a -> m b) -> m b > > instance (Ord a) => AssociatedMonad Set a where > > instance RestrictedMonad Set where > return = Set.singleton > x >>= f = Set.unions (map f (Set.toList x))
> […] The problem is that while an expression of type (AssociatedMonad Set a, AssociatedMonad Set b) => Set a -> (a -> Set b) -> Set b has type (Ord a, Ord b) => Set a -> (a -> Set b) -> Set b, the opposite doesn’t hold. Your AssociatedMonad class doesn’t provide you any Ord dictionary which you need in order to use the Set functions. The instance declaration instance (Ord a) => AssociatedMonad Set a says how to construct an AssociatedMonad dictionary from an Ord dictionary but not the other way round. But it is possible to give a construction of an Ord dictionary from an AssociatedMonad dictionary. See the attached code. It works like a charm. :-) Best wishes, Wolfgang
{-# LANGUAGE ExistentialQuantification, MultiParamTypeClasses, FlexibleInstances, TypeFamilies #-} import Data.Set (Set) import qualified Data.Set as Set class Suitable monad val where data Constraints monad val :: * constraints :: monad val -> Constraints monad val class NewMonad monad where newReturn :: (Suitable monad val) => val -> monad val newBind :: (Suitable monad val, Suitable monad val') => monad val -> (val -> monad val') -> monad val' instance (Ord val) => Suitable Set val where data Constraints Set val = Ord val => SetConstraints constraints _ = SetConstraints instance NewMonad Set where newReturn = Set.singleton newBind set1 set2Gen = let set2Constraints = constraints result result = case set2Constraints of SetConstraints -> Set.unions $ map set2Gen $ Set.toList set1 in result
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