Quantified contexts

From HaskellWiki

1 The problem

The base library currently contains (essentially) the following classes:

class Monoid a where
       mempty  :: a
       mappend :: a -> a -> a
class MonadPlus m where
       mzero :: m a
       mplus :: m a -> m a -> m a
class ArrowPlus c where
       arrowZero :: c a b
       arrowPlus :: c a b -> c a b -> c a b

If you look closely 'these are all the same. The only difference is in the superclasses and in the arity of the argument. You will find that any class that is an instance of MonadPlus can be made an instance of Monoid. In fact, some types such as lists, are indeed instances of both classes.

This leads to duplication of code and of extra names for what is essentially the same thing.

class Typeable a where
       typeOf :: a -> TypeRep
class Typeable1 t where
       typeOf1 :: t a -> TypeRep
class Typeable2 t where
       typeOf2 :: t a b -> TypeRep
-- etc.

2 Chained instances

This Typeable library comes with instances

instance (Typeable2 t, Typeable a) => Typable  (t a)
instance (Typeable3 t, Typeable a) => Typable2 (t a)
-- etc.

class Monoid2 t where
       mempty2  :: t a
       mappend2 :: t a -> t a -> t a
class Monoid3 t where
       mempty3  :: t a b
       mappend3 :: t a b -> t a b -> t a b
instance Monoid2 t => Monoid (t a) where
       mempty  = mempty2
       mappend = mappend2

class (Monad m, Monoid2 m) => MonadPlus m

A big disadvantage of these instances is that it is an all or nothing aproach.

For example there is currently an instance

instance Ord k => Monoid (Map k v)

This would become imposible, because the instance would need be

instance Monoid2 Map -- we need Ord

3 Quantified contexts

An alternative would be a small extension of the Haskell language to allow quantifiers in contexts. Where we now write

function :: (Class a, Another (t a)) => Type a

We would also allow

function :: (forall b. Ctx => SomeClass b) => Type

The meaning is simple, to satisfy this context, an instance

instance Ctx => SomeClass b

is needed (or a more general one).

class (Monad m, forall a. Monoid (m a)) => MonadPlus m

or without the superflous extra class, for example

guard :: (Monad m, forall a. Monoid (m a)) => Bool -> m ()

The compiler will never infer a quantified context; the above type is not the most general type of guard. If you gave no type signature the compiler would infer

guard :: (Monad m, Monoid (m ())) => Bool -> m ()

4 Response from SimonPJ

I didn't see how Section 3 addressed the issues raised in Sections 1 and 2. For example, to avoid the cascade of `Typeable2`, `Typeable3` etc classes the solution is presumably polymorphism at the kind level. (Tim Sheard's language Omega has this.)

Still, I recognise the merit of quantification in contexts. Indeed, Ralf Hinze and I suggested it back in 2000 in Section 7 of [[http://research.microsoft.com/en-us/um/people/simonpj/papers/derive.htm Derivable type classes]]. (This section is rather independent of the rest of the paper.)

However, attractive as it is, it's quite a big step to add something akin to local instance declarations. Our ICFP'08 paper [[http://research.microsoft.com/~simonpj/papers/assoc-types/index.htm Type checking with open type functions]] relies rather crucially on not having such local instances. (We've managed to simplify the algorithm quite a bit since then, but it still relies on that assumption.)

So I'm not sure I see how to make quantified contexts compatible with type functions, and all the other stuff in Haskell. But their lack is clearly a wart, and one that may become more pressing.

Meanwhile, clarifying the proposal would be a good thing, even if it's not adopted right away.

Category: Proposals