How to put constraints on the associated data?

Question

I would like to state that the associated data is always an instance of a certain class.

class (Context (Associated a b)) => Class a where
  data Associated a :: * -> *

instance Context (Associated a b) where
  func1 = error "func1"

However, the free variable b that is not in scope prevents me from this. One of the solutions is to copy class functions from Context, but it looks ugly.

class Class a where
  data Associated a :: * -> *
  -- duplicate all functions from class Context
  contextFunc1 :: Associated a b -> String

instance Class a => Context (Associated a b) where
  func1 = contextFunc1

Is there an idiomatic way to put constraints on associated data type which has variables not mentioned in head?

edit: I would like to keep compatibility with GHC 7.0.3

Answer 1

I don't have GHC 7.0.3 available, but I think this should work with it.

You could pass the dictionaries around manually like this (using Context = Show as an example):

{-# LANGUAGE ScopedTypeVariables, TypeFamilies, ExistentialQuantification #-}

data ShowDict a = Show a => ShowDict

class Class a where
  data Associated a :: * -> *

  getShow :: ShowDict (Associated a b)

-- Convenience function
getShowFor :: Class a => Associated a b -> ShowDict (Associated a b)
getShowFor _ = getShow

showAssociated :: Class a => Associated a b -> String
showAssociated a = 
  case getShowFor a of
    ShowDict -> -- Show (Associated a b) is made available by this pattern match 
      show a

instance Class Int where
  data Associated Int b = Foo deriving Show

  getShow = ShowDict

main = print $ showAssociated Foo

This is somewhat similar to the function copying you propose, but advantages are:

• Avoids repetition (of `Context`'s method signatures)
• Having `Show Baz` in context is somewhat more powerful than just having a function for showing a `Baz`, since it allows you to call (library) functions which require `Show Baz`, or use implied instances like `Show [Baz]`:

showAssociateds :: forall a b. Class a => [Associated a b] -> String
showAssociateds as = 
  case getShow :: ShowDict (Associated a b) of
    ShowDict ->
      show as

The main disadvantage is that using getShow always requires an explicit type signature (functions like getShowFor can mitigate this).

Answer 2

As was pointed out by @SjoerdVisscher, using forall on the left side of => in a class or instance is actually not ok, at least not yet, though my specific example does work in ghc-7.4.

---

This way it seems to work:

{-# LANGUAGE FlexibleInstances    #-}
{-# LANGUAGE TypeFamilies         #-}
{-# LANGUAGE Rank2Types           #-}
{-# LANGUAGE ConstraintKinds      #-}
{-# LANGUAGE UndecidableInstances #-}

class Context c where
  func1 :: c -> String

class (forall b. Context (Associated a b)) => Class a where
  data Associated a :: * -> *

newtype ClassTest = ClassTest { runClassTest :: String }

instance (forall b. Context (Associated ClassTest b)) => Class ClassTest where
  data Associated ClassTest b = ClassTestAssoc b (b -> ClassTest)

instance Context (Associated ClassTest b) where
  func1 (ClassTestAssoc b strFunc) = runClassTest $ strFunc b

main = putStr . func1 $ ClassTestAssoc 37 (ClassTest . show)

The extra forall b constraint in the instance seems a bit ugly and redundant, but apparently it's necessary.

$ runghc-7.4.1 tFamConstraint0.hs
37

Answer 3

One idiomatic way is to create a Context1 class. Supposing we have

class Context a where
    func :: a -> String

we might generalize as:

class Context1 f where
    func1 :: Context a => f a -> String

Then you give a single instance for all Associateds:

instance (Context1 (Associated a), Context b) => Context (Associated a b) where
    func = func1

Now it is easy to write the class you want as

instance Context1 (Associated a) => Class a where
    data Associated a :: * -> *

and you can be sure that the given Context1 (Associated a) context ensures the desired forall b. Context b => Context (Associated a b) context.

There are many examples of this pattern on Hackage, like Show1, Foldable1, and Traversable1.