[Haskell-cafe] Type constraints and classes
nccb2 at kent.ac.uk
Sun Apr 26 07:21:21 EDT 2009
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 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).
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