Class system extension proposal

Allowing superclass methods to be overridden in derived classes

Motivation

The current class system in Haskell is based on the idea that you can often provide default implementations for class methods at the same time as defining the class, by using other methods of the class or its ancestors. However consider the following hierarchy, adapted from Functor hierarchy proposal and The Other Prelude:

class Functor m where
    fmap :: (a -> b) -> m a -> m b

class Functor m => Applicative m where
    return :: a -> m a

    apply :: m (a -> b) -> m a -> m b

    (>>) :: m a -> m b -> m b
    ma >> mb = (fmap (const id) ma) `apply` mb

class Applicative m => Monad m where
    (>>=) :: m a -> (a -> m b) -> m b

For all concrete instances of Monad we can define fmap, apply, and (>>) in terms of return and (>>=) as follows:

fmap f ma = ma >>= (\a -> return (f a))

apply mf ma = mf >>= \f -> ma >>= \a -> return (f a)

ma >> mb = ma >>= \_ -> mb

In other words, we'd like to be able to write:

class Applicative m => Monad m where
    (>>=) :: m a -> (a -> m b) -> m b

    fmap f ma = ma >>= (\a -> return (f a))

    apply mf ma = mf >>= \f -> ma >>= \a -> return (f a)

    ma >> mb = ma >>= \_ -> mb

and be able to define new instances of Monad just by supplying definitions for return and (>>=) by writing:

instance Monad T where
    ma >>= a_mb = ... -- some definition

    return a = ... -- some definition

However in Haskell at present we can't do this, because we are only allowed to provide default implementations for a class method in the class where the method is introduced (ie the class containing the method signature) and similarly we are only allowed to provide an implementation for a method in an instance for the class itself, not a derived class. Therefore with the above hierarchy, we would have to manually define instances of Functor and Applicative whenever we define an instance of Monad.

It is worth pointing out several reasons why we desire to be able to just define new Monad instances whithout having to explicitly define instances for Functor and Applicative:

• The idea of making Monad a subclass of Applicative was only discovered after many people had already used Monad in their programs. Therefore many existing programs already contain instance declarations for Monad as outlined above, so we would prefer not to have to change them just because the hierarchy has been refined to add extra functionality these existing programs don't use. This also applies to other hierachies in wide use at the moment, where changes have been proposed eg the Num hierarchy.
• The implementation of (>>) in terms of (>>=) for Monad is much simpler than the default implementation provided by Applicative.
• The example shows that sometimes the default implementation of a method depends on which subclass we are using, and so acts as a counterexample to the current assumption that default implementations can be provided in the class where the method is introduced.

Concrete proposal

1. Class and instance declarations would allow method implementations to be given for any methods in the class or any ancestor class.
2. Whenever an instance declaration is visible there would always be a full set of instance declarations for all ancestor classes, by supplementing the set of explicitly given instance declarations that are visible in a module by automatically generated implicit instance declarations.
3. The most specific method implementation would always be chosen (ie prefer an explicit instance method over a class method and prefer a subclass method to a superclass method)
4. Modules would only export explicit instance declarations

Clarifications

• Separate compilation is still possible because all that's happening in the proposal is that the set of explicit instance declarations in scope in the module would be supplemented by a set of compiler-generated implicit instance declarations which are only visible in the module being compiled.

Implications

One implication of this proposal would be that the resolution of an overloaded method would depend on the instances in scope in the module where the method is called. Therefore overloading would need to be resolved before modules are conceptually merged together (especially important when considering whole program optimization), and in particular overloading of the body of an inlined function would need to be resolved using the module where the function was defined not the module where it is inlined.

Another implication is that the current class system where each level in the hierarchy is independent from other levels (via separate instance declarations), solves the problem of "multiple inheritance": given (Functor m, Applicative m, Monad m) the compiler can find the definition for fmap just by looking at the instance for Functor m alone, whereas with the proposal the compiler would have to consider all the predicates in the context to determine the source of each overloaded function. This may or may not be a problem.

Explicit import/export of instances

This is needed so that large programs can be built without fear of colliding instance declarations between different packages. A possible syntax could be:

    module M
         -- exported instances 
       ( instance Monad T
       , instance Functor (F a) hiding (Functor (F Int), Functor (F Char))
       , F(..)
       ) where

    import Foo (instance Monad a hiding Monad Maybe)

    data T a
    data F a b

where the context is elided because this isn't used in instance selection (at the moment). The import directive tells the compiler to use all Monad instances exported by Foo except for the Monad Maybe instance (it doesn't matter whether or not Foo actually does export a Monad Maybe instance - all that matters here is that we don't want it if there is one).

Typeclass synonyms

This is needed for the same reason that we need type synonyms: to make complex types managable.

See http://repetae.net/john/recent/out/classalias.html.

Superclass defaults

The above propsal handles two separate issues, contexts with lots of class names, and defaults. The compatible superclass defaults propsal separates these two issues.

Extensible superclasses

This increases modularity by allowing us to add a new superclass to a class without modifying the class itself, just as at present we can always add new subclasses.

See http://taichi.ddns.comp.nus.edu.sg/taichiwiki/GPHomePage for a motivating example.

More details can be found in the paper Modular Generic Programming with Extensible Superclasses, available in ps format from http://www.comp.nus.edu.sg/~sulzmann/publications/wgp06-modulargeneric.ps or in pdf from http://users.ox.ac.uk/~wolf2335/publications/generic.pdf.

Quantified contexts

A minor annoyance is that the Monoid, MonadPlus and ArrowPlus are all essentially the same. Allowing forall in contexts gives a way to combine these classes back into one. See the proposal for details.