[Haskell-cafe] Monad instance for Data.Set, again

[Wolfgang Jeltsch]

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
-------------- next part --------------
{-# 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