I've heard that there are some problems with Haskell's "broken" constraint system, as of GHC 7.6 and below. What's "wrong" with it? Is there a comparable existing system that overcomes those flaws?
For example, both edwardk and tekmo have run into trouble (e.g. this comment from tekmo).
Ok, I had several discussions with other people before posting here because I wanted to get this right. They all showed me that all the problems I described boil down to the lack of polymorphic constraints.
The simplest example of this problem is the MonadPlus class, defined as:
class MonadPlus m where
mzero :: m a
mplus :: m a -> m a -> m a
... with the following laws:
mzero `mplus` m = m
m `mplus` mzero = m
(m1 `mplus` m2) `mplus` m3 = m1 `mplus` (m2 `mplus` m3)
Notice that these are the Monoid laws, where the Monoid class is given by:
class Monoid a where
mempty :: a
mappend :: a -> a -> a
mempty `mplus` a = a
a `mplus` mempty = a
(a1 `mplus` a2) `mplus` a3 = a1 `mplus` (a2 `mplus` a3)
So why do we even have the MonadPlus class? The reason is because Haskell forbids us from writing constraints of the form:
(forall a . Monoid (m a)) => ...
So Haskell programmers must work around this flaw of the type system by defining a separate class to handle this particular polymorphic case.
However, this isn't always a viable solution. For example, in my own work on the pipes library, I frequently encountered the need to pose constraints of the form:
(forall a' a b' b . Monad (p a a' b' b m)) => ...
Unlike the MonadPlus solution, I cannot afford to switch the Monad type class to a different type class to get around the polymorphic constraint problem because then users of my library would lose do notation, which is a high price to pay.
This also comes up when composing transformers, both monad transformers and the proxy transformers I include in my library. We'd like to write something like:
data Compose t1 t2 m r = C (t1 (t2 m) r)
instance (MonadTrans t1, MonadTrans t2) => MonadTrans (Compose t1 t2) where
lift = C . lift . lift
This first attempt doesn't work because lift does not constrain its result to be a Monad. We'd actually need:
class (forall m . Monad m => Monad (t m)) => MonadTrans t where
lift :: (Monad m) => m r -> t m r
... but Haskell's constraint system does not permit that.
This problem will grow more and more pronounced as Haskell users move on to type constructors of higher kinds. You will typically have a type class of the form:
class SomeClass someHigherKindedTypeConstructor where
...
... but you will want to constrain some lower-kinded derived type constructor:
class (SomeConstraint (someHigherKindedTypeConstructor a b c))
=> SomeClass someHigherKindedTypeConstructor where
...
However, without polymorphic constraints, that constraint is not legal. I've been the one complaining about this problem the most recently because my pipes library uses types of very high kinds, so I run into this problem constantly.
There are workarounds using data types that several people have proposed to me, but I haven't (yet) had the time to evaluate them to understand which extensions they require or which one solves my problem correctly. Somebody more familiar with this issue could perhaps provide a separate answer detailing the solution to this and why it works.
[a follow-up to Gabriel Gonzalez answer]
The right notation for constraints and quantifications in Haskell is the following:
<functions-definition> ::= <functions> :: <quantified-type-expression>
<quantified-type-expression> ::= forall <type-variables-with-kinds> . (<constraints>) => <type-expression>
<type-expression> ::= <type-expression> -> <quantified-type-expression>
| ...
...
Kinds can be omitted, as well as foralls for rank-1 types:
<simply-quantified-type-expression> ::= (<constraints-that-uses-rank-1-type-variables>) => <type-expression>
For example:
{-# LANGUAGE Rank2Types #-}
msum :: forall m a. Monoid (m a) => [m a] -> m a
msum = mconcat
mfilter :: forall m a. (Monad m, Monoid (m a)) => (a -> Bool) -> m a -> m a
mfilter p ma = do { a <- ma; if p a then return a else mempty }
guard :: forall m. (Monad m, Monoid (m ())) => Bool -> m ()
guard True = return ()
guard False = mempty
or without Rank2Types (since we only have rank-1 types here), and using CPP (j4f):
{-# LANGUAGE CPP #-}
#define MonadPlus(m, a) (Monad m, Monoid (m a))
msum :: MonadPlus(m, a) => [m a] -> m a
msum = mconcat
mfilter :: MonadPlus(m, a) => (a -> Bool) -> m a -> m a
mfilter p ma = do { a <- ma; if p a then return a else mempty }
guard :: MonadPlus(m, ()) => Bool -> m ()
guard True = return ()
guard False = mempty
The "problem" is that we can't write
class (Monad m, Monoid (m a)) => MonadPlus m where
...
or
class forall m a. (Monad m, Monoid (m a)) => MonadPlus m where
...
That is, forall m a. (Monad m, Monoid (m a)) can be used as a standalone constraint, but can't be aliased with a new one-parametric typeclass for *->* types.
This is because the typeclass defintion mechanism works like this:
class (constraints[a, b, c, d, e, ...]) => ClassName (a b c) (d e) ...
i.e. the rhs side introduce type variables, not the lhs or forall at the lhs.
Instead, we need to write 2-parametric typeclass:
{-# LANGUAGE MultiParamTypeClasses, FlexibleContexts, FlexibleInstances #-}
class (Monad m, Monoid (m a)) => MonadPlus m a where
mzero :: m a
mzero = mempty
mplus :: m a -> m a -> m a
mplus = mappend
instance MonadPlus [] a
instance Monoid a => MonadPlus Maybe a
msum :: MonadPlus m a => [m a] -> m a
msum = mconcat
mfilter :: MonadPlus m a => (a -> Bool) -> m a -> m a
mfilter p ma = do { a <- ma; if p a then return a else mzero }
guard :: MonadPlus m () => Bool -> m ()
guard True = return ()
guard False = mzero
Cons: we need to specify second parameter every time we use MonadPlus.
Question: how
instance Monoid a => MonadPlus Maybe a
can be written if MonadPlus is one-parametric typeclass? MonadPlus Maybe from base:
instance MonadPlus Maybe where
mzero = Nothing
Nothing `mplus` ys = ys
xs `mplus` _ys = xs
works not like Monoid Maybe:
instance Monoid a => Monoid (Maybe a) where
mempty = Nothing
Nothing `mappend` m = m
m `mappend` Nothing = m
Just m1 `mappend` Just m2 = Just (m1 `mappend` m2) -- < here
:
(Just [1,2] `mplus` Just [3,4]) `mplus` Just [5,6] => Just [1,2]
(Just [1,2] `mappend` Just [3,4]) `mappend` Just [5,6] => Just [1,2,3,4,5,6]
Analogically, forall m a b n c d e. (Foo (m a b), Bar (n c d) e) gives rise for (7 - 2 * 2)-parametric typeclass if we want * types, (7 - 2 * 1)-parametric typeclass for * -> * types, and (7 - 2 * 0) for * -> * -> * types.
