wiki:DefaultSuperclassInstances

Default superclass instances

Note a new version of this proposal, IntrinsicSuperclasses, with a revised notation is beginning to appear.

A matter of much consternation, here is a proposal to allow type class declarations to include default instance declarations for their superclasses. Moreover, subclass instance declarations should be able to override the method definitions in their default superclass instances. It's based on Jón Fairbairn's proposal, but it has a more explicit 'off switch' and the policy on corner-cases is rejection. Credit is due also to the superclass defaults proposal, class system extension proposal and its ancestors, in particular, John Meacham's class alias proposal.

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). The subclass methods provide extra functionality, but do not induce a standard implementation of the superclass. Num provides arithmetic operations, widening Eq, but does not induce an implementation of (==).
  • A class can deepen its superclass, providing methods at least as expressive, admitting a default implementation of superclass functionality (e.g., the compare function from an Ord instance can be used to give an Eq instance; traverse from Traversable f can be instantiated to foldMapDefault for Foldable f and fmapDefault for Functor f).

(SLPJ I don't understand this distinction clearly.)

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.

Default superclass instances are implemented in the Strathclyde Haskell Enhancement. The crucial property which drives the feature is that method names uniquely identify the classes to which they belong, so that methods defined in a subclass instance can be distributed to the appropriate generated superclass instance. They should enable some tidying of the library, with relatively few tears. Moreover, they should allow us to deepen type class hierarchies as we learn. Retaining backward compatibility in relative silence is the motivation for an opt-in default.

Design goals

The major design goal is this:

Design goal 1: a class C can be re-factored into a class C with a superclass S, without disturbing any clients

The difficulty is that if you start with

class C a where
   f :: ...
   g :: ...

and lots of clients write instances of C and functions that use it:

instance C ClientType
  f = ...blah...
  g = ...blah...

foo :: C a => ...
foo = ...

Now you want to refactor C thus:

class S a where
  f :: ...
class S a => C a where
  g :: ...

Design goal 1 is that this change should not force clients to change their code. Haskell 98 does not satisfy this goal. In Haskell 98 the client function foo is fine unmodified, but the instance declaration would have to be split into two.

Design goal 2: write implementations of sub-classes that imply their superclass implementations

  • Example 1: once you say
    instance Ord (T a) where
      compare = ...
    
    then the implementation of (==) in Eq is obvious. So, in the class decl for Ord we'd like to say (modulo syntax, see below)
    class Eq a => Ord a where
      ...
      instance Eq a where
        (==) a b = case compare a b of { EQ -> True; _ -> False }
    
  • Example 2: once you say instance Monad M, the instances for Functor M and Applicative M can be derivived from the definitions of (>>=) and return. And similarly if you say instance Applicative M, the Functor M instance is derivable.
  • Example 3: once you say instance Traversable T you can derive Foldable and Functor. Obvious question: if something is both Foldable and Applicative, which Functor instance do you get? Answer: the programmer must be able to control this (see "the opt-out mechanism" below).

Goal 2 is closely linked to Goal 1. Suppose the library originally had

class C a where
  f :: ...
  g :: ...
  f = ...g...   -- Default method for f, defined using g

Now the client relies on the default method:

instance C ClientType where
  g = ....

Now the library author wants to split C as before:

class S a where
  f :: ...
  f = ...g...   -- Uh oh!  Can't do this

class S a => C a where
  g :: ...

So we want to specify a default method for f in superclass S, which works when we have a C too:

class S a => C a where
  g :: ...
  instance S a where
     f = ...g...   -- default method for f

The proposal

Concretely, the proposal is as follows.

Default superclass instances

First, we allow a class declaration to include a default superclass instance declaration for some, none, or all of its superclass constraints (transitively). We say that superclasses (transitively) with default implementations are intrinsic superclasses. Example:

    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

Note the instance declaration nested inside the class declaration. This is the default superclass instance declaration, and Functor thereby becomes an intrinsic superclass of Applicative. Moreover, note that the definition of fmap uses the <*> operation of Applicative; that is the whole point!

Here is another example:

    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)

Here, Applicative is an intrinsic superclass of Monad.

We might also want to give a different implementation of fmap for monads than the one generated by the Applicative class declaration:

    class Applicative f => Monad f where
      (>>=) :: f a -> (a -> f b) -> f b
      instance Applicative f where
        hiding instance Functor
        ff <*> fs = ff >>= \ f -> fs >>= \ s -> return (f s)
      instance Functor f where
        fmap f x = x >>= \y -> return (f y)

(In fact this fmap would, after optimisation of a particular instance and if enough inlining too place, generate the same code, but that might not always be the case.)

Instance declarations

A default superclass instance in a class declaration for class C has an effect on the instance declarations for C.

Specifically:

  • An instance declaration
    instance Q => C ty where ...defs...
    
    for class C generates an extra instance declaration
    instance Q => Si ty where ....
    
    for each intrinsic superclass Si of C
  • The method definitions in ...defs... are distributed to the appropriate instance declaration, according to which class the method belongs to.
  • Any methods that are not specified explicitly are "filled in" from the default definition given in the default superclass instance. (If there is no default definition, then a warning is produced, and a definition that calls error is used instead.)

For example, assume the class declaration for Monad above. Then this instance declaration:

  instance Monad m where
    (>>=) = ...blah...
    (<*)  = ...bleh...

would generate an extra instance declaration for the instrinsic superclass Applicative, with the methods distributed appropriately:

  instance Monad m where
    (>>=) = ...blah...

  instance Applicative m where
    (<*) = ...bleh...  -- Programmer specified

    ff <*> fs = ff >>= \ f -> fs >>= \ s -> return (f s)
                       -- From the default superclass instance

We call these extra instance declarations an intrinsic instance declaration. (The term "derived instance" is already taken!)

This process is recursive. Since Functor is an intrinsic superclass of Applicative, the intrinsic instance for Applicative recursively generates an intrinsic instance for Functor:

  instance Functor m where
    fmap = (<*>) . return	-- From default superclass instance

The opt-out mechanism

Just because you can make default instances, they are not always the instances you want. A key example is

    instance Monad m => Monad (ReaderT r m) where ...

which would give us by default the intrinsic instance

    instance Monad m => Applicative (ReaderT r m) where ...

thus preventing us adding the more general

    instance Applicative m => Applicative (ReaderT r m) where ...

To inhibit the generation of an intrinsic instance declaration, one can use a hiding clause in the instance declaration:

    instance Sub x where
      ...
      hiding instance Super

which acts to prevent the generation of instances for Super and all of Super's intrinsic superclasses in turn. For example: write

    instance Monad m => Monad (ReaderT r m) where ...
      return x = ...
      ba >>= bf = ...
      hiding instance Applicative

The hiding clause applies to all the intrinsic instances generated from an instance declaration. For example, we might write

    instance Monad T where
      return x = ...
      ba >>= bf = ...
      hiding instance Functor

Note that Functor is only an indirect intrinsic superclass of Monad, via Applicative. So the above instance would generate an intrinsic instance for Applicative but not for Functor.

See below for more about the opt-out mechanism.

Details

Each default superclass instance declaration in a class declaration must be for a distinct class. So one of these is OK and the other is not:

    -- This is ILLEGAL
    class (Tweedle dum, Tweedle dee) => Rum dum dee where
      instance Tweedle dum where ...
      instance Tweedle dee where ...

    -- But this is OK 
    class (Tweedle dum, Tweedle dee) => Rum dum dee where
      instance Tweedle dee where ...

By requiring that intrinsic superclasses be class-distinct, we ensure that the distribution of methods to spawned instances is unambiguous.

Flags

The declaration of a class with a default superclass instance would require a language extension flag; but the instances of such a class would not. Again Design Goal 1 means that we want to impact client code as little as possible.


Possible variations

The design of the opt-out mechanism

Jón's proposal had a more subtle opt-out policy, namely that an intrinsic superclass can be silently pre-empted by an instance for the superclass from a prior or the present module. For example, instead of

  instance Functor T where ...

  instance Monad T where
    return x = ...
    ba >>= bf = ...
    hiding instance Functor

you would simply say

  instance Functor T where ...

  instance Monad T where
    return x = ...
    ba >>= bf = ...

Of course, the instance of Functor T might be in a different module entirely. Note that to declare an instance of the subclass, one must produce an instance of the superclass by the same module at the latest.

This quiet exclusion policy is not enough to handle the case of multiple candidate intrinsic instances arising from multiple intrinsic superclasses (e.g., Traversable and Monad giving competing Functor instances), so some explicit hiding form is required even under the "silent pre-emption" plan.

The question for us, then, is what should happen if an intrinsic superclass not explicitly hidden were to clash with an explicit instance from the same or a prior module. We could

  1. Reject this as a duplicate instance declaration, which indeed it is. We acknowledge that it creates an issue with legacy code --- that is, it contradicts Design Goal 1 --- precisely because there are plenty of places where we have written the full stack of instances, often just doing the obvious default thing.
  1. Allow the explicit to supersede the intrinsic default, but issue a warning suggesting to either remove the explicit instance or add an explicit opt-out.
  1. Allow the explicit to supersede the intrinsic default silently. This fits with Design Goal 1, but risks perplexity: if I make use of some cool package which introduces some Foo :: * -> *, I might notice that Foo is a monad and add a Monad Foo instance in my own code, expecting the Applicative Foo instance to be generated in concert; to my horror, I find my code has subtle bugs because the package introduced a different, non-monadic, Applicative Foo instance which I'm accidentally using instead.

There is considerable support in the email discussion thread for Option 2 or 3, on the grounds that Option 1 contradicts Design Goal 1.

Perhaps Option 2 is the pragmatic choice.

Opting in rather than out

The [ http://www.haskell.org/haskellwiki/Superclass_defaults superclass default proposal] deals with the question of opt-outs by intead requiring you to opt in. A Monad instance would look like

  instance (Functor T, Applicative T, Monad T) where
    (>>=) = ...blah...
    return = ...bleh...

where we explicitly ask the compiler to generate an instance of Applicative T and Functor T. The disadvantage is that you have to know to do so, which contradicts Design Goal 1.

Multi-headed instance declarations

While we're about it, to allow multi-headed instance declarations for class-disjoint conjunctions, with the same semantics for constraint duplication and method distribution as for the defaults, so

    instance S => (C x, C' x) where
      methodOfC  = ...
      methodOfC' = ...

is short for

    instance S => C x where
      methodOfC  = ...
    instance S => C' x where
      methodOfC' = ...

This proposal fits handily with the kind Fact proposal, which allows multiple constraints to be abbreviated by ordinary type synonyms. So we might write

  type Stringy x = (Read x, Show s)
  instance Stringy Int where
    read = ...
    show = ...

The common factor is that one instance declaration is expanded into several with the method definitions distributed appropriately among them.

Feature interactions

What about interaction with other features?

  • deriving. If you say deriving(Ord) do you get the Eq by default? What if you want to specify a manual instance for Eq? Ditto standalone deriving. (pigworker We use the same logic as if the derived instances were written by hand in the same module as the datatype (or standalone declaration). If you say deriving(Ord), you get the default. If you say deriving(Ord, Eq) under option 2, the derived Eq preempts the default one. But we do then need to be able to say deriving (Ord hiding Eq) to allow explicit opt-out if another default superclass offers an Eq which we prefer.)
  • Generic default methods. (pigworker Default methods in default superclass instances override class default methods and are overridden by specific implementations in subclass instances. So I can define Applicative to have a default class method <*> which fails with a specific message; I can make class Monad give a default implementation (<*>) = ap; I can give a specific instance Monad which overrides <*>, perhaps for improved efficiency.)
  • Associated types, and default type synonyms. Presumably they obey the same rules as for default methods. (pigworker Yes. You can put any declaration into a default superclass instance, and the same sorts of definitions as you can with default methods in class declarations. Notably, data instances are forbidden, because they could result in multiple declarations of the same constructor. (Must get around to an 'overloaded constructors' proposal.))

Migration issues

Adopting this proposal raises the question of which default superclass instances should be added to the existing library and hence how much damage we might do. We do not have to look too far to find issues to consider.

Splitting a class by adding a new superclass

Had this proposal been in force at the time, Applicative would have been introduced as an intrinsic superclass of Monad. The return method would have been moved to Applicative, pure would not exist, and <*> for Monads would be ap by default. Bold claim: no code would have broken, but some Applicative instances would have been generated with overly tight constraints (requiring Monad where Applicative would do). With no prior Applicative instances to conflict with the default ones, we should simply have had a different interpretation of the existing Monad instances.

Giving a superclass a default instance in one or more of its existing subclasses

Currently, Applicative is a subclass of Functor. We can (and probably should) give a default implementation of Functor with fmap = (<*>) . pure. As it is currently forbidden to give an Applicative instance in the absence of a Functor instance, we should expect (given Option 2) to be sprayed with warnings that default Functor instances are being pre-empted, but (bold claim) we should find that all code still compiles, with no default superclass instances being generated. By the same token, if we also give a default Functor instance for Traversable, we shall similarly find all such instance generations pre-empted. Correspondingly, wherever some functor is both Applicative and Traversable, there will be no need to make an explicit hiding declaration.

Making an existing class a new but intrinsic superclass of another existing class

Currently, Applicative is not a superclass of Monad, but it should be (in the manner described above). What will happen to existing code (under Option 2)? Only some instances of Applicative will be duplicates, and those will all be orphans. When a Monad instance is declared, any existing Applicative will pre-empt the default, but certainly an Applicative instance will be in scope, generated or not. If, in a module further downstream, an Applicative instance (necessarily orphan) is added, there must have been no prior Applicative instance, so the Monad instance will now generate one which the orphan Applicative duplicates. There is no perfect solution to this problem. We could reduce the damage but increase the potential perplexity by allowing default generated instances in earlier modules to pre-empt explicit instances in later modules, accompanied by a noisy warning. Even then, some code would fail to compile if the pre-empting default instance were to be more tightly constrained than the pre-empted one (quite apart from the fact that it might do something completely different).

Is this only a legacy issue? This proposal makes ought-to-be-a-superclass relationships cheap, so we might hope that, in future, we would have to be slow on the uptake to be creating classes which could have a useful super/sub-class relationship but somehow do not. The danger of code damage we identify here might thus be better tackled by a localized and transitional strategy.


Applications

If you want superclass instances, add yourself below with a quick sketch of what your application is

For years, I have been pretending that Monads are not Functors. When applicative functors showed up, I could accept them as functors, but my internal contradictions prevented me to accept them as monads. This is a cry for help!

-- Haskell 98

SHE currently provides these default superclass instances. To save you a click, that's this little lot:

class Functor f => Applicative f where
  instance Functor f where
    fmap = (<*>) . pure
  ...

class Applicative f => Monad f where
  instance Applicative f where
    pure = return
    ff <*> sf = ff >>= \ f -> sf >>= \ s -> return (f s)
  ...

class Traversable f where
  instance Foldable f where
    foldMap = foldMapDefault
  instance Functor f where
    fmap = fmapDefault
  ...

class MonadPlus f where
  instance Alternative f where
    empty = mzero
    (<|>) = mplus
  ...

We should, of course, also add

class Eq x => Ord x where
  instance Eq x where
    x == y = EQ == compare x y

What else are good candidates for default instances in the existing setup?

Last modified 8 months ago Last modified on Jul 16, 2014 9:05:00 AM