You can use a continuation trick I describe below. First of all, I would like to work in a more general situation. So, instead of working with Set, I'd like to declare two classes:
class Returnable m a where ret :: a -> m a
and
class Bindable m a b where bind :: m a -> (a -> m b) -> m b
I'm sure you're able to define instances like "instance Ord a => Returnable Set a" by yourself. You'll need MultiParamTypeClasses and FlexibleInstances for that to work. Now, the trick:
newtype Restricted r m a = Restricted ((a -> m r) -> m r) instance Monad (Restricted r m) where return x = Restricted $ \h -> h x Restricted g >>= f = Restricted $ \h -> g $ \x -> let Restricted g' = f x in g' h
Quite simple, and doesn't mention pseudo-monadic structure of "m" at all. Now, the fun part:
embed :: Bindable m a r => m a -> Restricted r m a embed mx = Restricted (bind mx)
unembed :: Returnable m r => Restricted r m r -> m r unembed (Restricted g) = g ret
You may also want another class
class Summable m a where zero :: m a plus :: m a -> m a -> m a
and now you can have
instance Summable m r => MonadPlus (Restricted r m) where mzero = Restricted $ const zero Restricted g1 `mplus` Restricted g2 = Restricted $ \h -> g1 h `plus` g2 h
From now on, you can do something like that:
unembed $ do x <- embed $ Set.fromList [6,2,3] (do y <- return x z <- embed $ Set.fromList [1..2] guard $ y < 5 return $ y + z) `mplus` return 10
and have "fromList [3,4,5,10]", as expected On 22 Dec 2008, at 20:19, Peter Padawitz wrote:
I'd like to define a monad Set for types in the class Eq. But how can the arguments of Set be constrained when Set is defined as an instance of Monad? instance Eq a => Monad Set where ... obviously cannot work.
Is there a standard update function for fields in data types, something that OO programmers do with assignments like obj.attr := value ?
Peter
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