Folding over a polymorphic list in Haskell

Question

I have a collection of records spread across a number of types in a large Haskell application that reference each other. All of the types involved implement a common typeclass. The typeclass contains functions that work over a variable and all of its children, very much like uniplate's para function.

This is a simplified code sample of what I'd like to build. Is it possible (and reasonable) to get generic functionality to fold over record fields that implement a given typeclass in GHC...

{-# LANGUAGE RankNTypes #-}

myPara :: forall a r . (Data a, Foo a)
       => (forall b . Foo b => b -> [r] -> r)
       -> a
       -> r

-- or as a fold
myFold :: forall a r . (Data a, Foo a)
       => (forall b . Foo b => r -> b -> r)
       -> r
       -> b
       -> r

But generic enough to work with an arbitrary typeclass?

{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE DeriveDataTypeable #-}

import Data.Data
import Data.Generics.Uniplate.Data

class Foo a where 
  fooConst :: a -> Int

data Bar = Bar {barBaz :: Baz} deriving (Typeable, Data)

instance Foo Bar where
  fooConst _ = 2

data Baz = Baz {barBar :: Bar} deriving (Typeable, Data)

instance Foo Baz where
  fooConst _ = 3

func :: Int
func = foldl (\ x y -> x + fooConst y) 0 instances where
  instances :: forall a . (Data a, Foo a) => [a]
  instances = universeBi bar
  bar = Bar{barBaz = baz}
  baz = Baz{barBar = bar}

Compiling this with GHC 7.2.1 (obviously) fails:

Repro.hs:21:42:
    Ambiguous type variable `a0' in the constraints:
      (Data a0) arising from a use of `instances' at Repro.hs:21:42-50
      (Foo a0) arising from a use of `instances' at Repro.hs:21:42-50
    Probable fix: add a type signature that fixes these type variable(s)
    In the third argument of `foldl', namely `instances'
    In the expression: foldl (\ x y -> x + fooConst y) 0 instances
    In an equation for `func':
        func
          = foldl (\ x y -> x + fooConst y) 0 instances
          where
              instances :: forall a. (Data a, Foo a) => [a]
              instances = universeBi bar
              bar = Bar {barBaz = baz}
              baz = Baz {barBar = bar}

By my reading of the uniplate documentation, the type of instances ought to be just [Baz], no? — Daniel Wagner
I'm not sure I understand what the theoretical question is. Could you make that a bit more precise in your text? (When you ask, "Is it possible to get generic functionality like this?", what does "like this" mean?) — Daniel Wagner
You are beginning to abstract over typeclasses, which Haskell is pretty bad at. Make the class concrete: eg. for Eq, use data Eq a = Eq { eq :: a -> a -> Bool }, then pass it as a parameter. Typeclasses are mainly for notational convenience, let functions do the heavy lifting. — luqui
Looks like it might be possible with ConstraintKinds in GHC 7.4 — Nathan Howell

Dmitry Dzhus Dmitry Dzhus · Accepted Answer · 2012-03-09T19:03:04

You've hit the Existential Antipattern. You shouldn't be using typeclasses for anything except cases when you need compiler to guess the type for you. List of values of type x will stay the list of values of type x no matter what typeclasses you will implement, and you can't break the type system here.

You can:

Use an ad-hoc box type as suggested above. This is just plain ugly.
Implement generic interfaces with message-passing.

data Foo = Foo { fooConst :: Int }

bar = Foo 2

baz = Foo 3

Folding over a polymorphic list in Haskell

2 Answers