Version 1 (modified by pigworker, 7 years ago) (diff)

made a start; saving before I have an accident

A matter of much consternation, here is a proposal to allow type class declarations to include default instance declarations for their superclasses. It's based on Jón Fairbairn's proposal, but it has a more explicit 'off switch' and the policy on corner-cases is rejection.

We may distinguish two uses of superclasses (not necessarily exclusive). A class can widen its superclass, extending its interface with new functionality (e.g., adding an inverse to a monoid to obtain a group -- inversion seldom provides an implementation of composition). A class can deepen its superclass (e.g., an implementation of Traversable f delivers at least enough technology to deliver Foldable f and Functor f). This proposal concerns the latter phenomenon, which is currently such a nuisance that Functor and Applicative are not superclasses of Monad. Nobody wants to be forced to write Functor and Applicative instances, just to access the Monad interface. Moreover, any proposal to refine the library by splitting a type class into depth-layers is (rightly!) greeted with howls of protest as an absence of superclass instances gives rise to breakage of the existing codebase.

Concretely, the proposal is to

  • allow class declarations to embed instance declarations for some, none, or all of their given superclass constraints, provided all such instances have distinct classes. We say that superclasses with default implementations are intrinsic superclasses. Yes to
        class Functor f => Applicative f where
          return :: x -> f x
          (<*>) :: f (s -> t) -> f s -> f t
          (>>) :: f s -> f t -> f t
          fs >> ft = return (flip const) <*> fs <*> ft
          instance Functor f where
            fmap = (<*>) . return
        class Applicative f => Monad f where
          (>>=) :: f a -> (a -> f b) -> f b
          instance Applicative f where
            ff <*> fs = ff >>= \ f -> fs >>= \ s -> return (f s)

but no to

    class (Tweedle dum, Tweedle dee) => Rum dum dee where
      instance Tweedle dum where ...
      instance Tweedle dee where ...
  • let subclass instance declarations spawn intrinsic superclass instances by default -- if we have
        class Bar t[x] => Foo x where
          instance Bar t[x] where ...
        instance C => Foo s where ...

we automatically acquire a default superclass instance

    instance C => Bar t[s] where ...
  • let subclass instance declarations provide and override the methods of their intrinsic superclasses with no extra delimitation; so we may write
        instance Monad Blah where
          return x = ...
          ba >>= bf = ...

and acquire the Monad instance, along with fully formed Applicative and Functor instances. By requiring that intrinsic superclasses be class-distinct, we ensure that the distribution of methods to spawned instances is unambiguous. Moreover, local overrides beat the default. If we write

    instance Monad Blah where
      return x = ...
      ba >>= bf = ...
      bs >> bt = ...

we override the default (>>) but keep the (<*>) in the spawned Applicative instance.