Shared constraint for items of an HList

Question

Suppose we have a following definition of HList:

data HL spec where
  HLNil :: HL ()
  HLCons :: h -> HL t -> HL (h, t)

Is it possible to somehow enforce a shared constraint on its items?

As an example, following is my attempt to constrain the items to have Show instances, which fails with Couldn't match type `Char' with `Int':

class HLSpecEach spec item
instance HLSpecEach () item
instance (HLSpecEach t item, h ~ item) => HLSpecEach (h, t) item

a :: (Show item, HLSpecEach spec item) => HL spec -> Int
a = undefined

b :: HL (Int, (Char, ()))
b = undefined

c = a b

Answer 1

Easy to do if you have constraint kinds and type families. First, let me say I prefer using DataKinds for clarity

data HList ls where
  HNil :: HList '[]
  HCons :: x -> HList xs -> HList (x ': xs)

type family ConstrainAll (c :: * -> Constraint) (ls :: [*]) :: Constraint
type instance ConstrainAll c '[] = ()
type instance ConstrainAll c (x ': xs) = (c x, ConstrainAll c xs)

showAll :: ConstrainAll Show xs => HList xs -> [String]
showAll HNil = []
showAll (HCons x xs) = (show x) : showAll xs

if you don't use the new extensions it is possible, but much uglier. One option is to define custom classes for everything

class ShowAll ls where
  showAll :: HList ls -> [Show]
instance ShowAll () where
  showAll _ = []
instance (ShowAll xs, Show x) => ShowAll (x,xs)
  showAll (HCons x xs) = (show x) : (showAll xs)

which I find ugly. A more clever approach would be to fake constraint kinds

class Constrained tag aType where
  isConstained :: tag aType

data HListT tag ls where
  HNilT :: HListT tag ()
  HConsT :: x -> tag x -> HListT tag xs -> HListT tag (x,xs)

data Proxy (f :: * -> *) = Proxy 
class ConstainedAll tag ls  where
  tagThem :: Proxy tag -> HList ls -> HListT tag ls
instance ConstainedAll tag () where
  tagThem _ _ = HNilT
instance (ConstainedAll tag xs, Constrained tag x) => ConstainedAll tag (x,xs) where
  tagThem p (HCons x xs) = HConsT x isConstained (tagThem p xs)

which you can then use like

data Showable x where Showable :: Show x => Showable x
instance Show x => Constrained Showable x where isConstained = Showable

--inferred type showAll' :: HListT Showable xs -> [String]
showAll' HNilT = []
showAll' (HConsT x Showable xs) = (show x) : showAll' xs

--inferred type: showAll :: ConstainedAll Showable xs => HList xs -> [String]
showAll xs = showAll' (tagThem (Proxy :: Proxy Showable) xs)

example = showAll (HCons "hello" (HCons () HNil))

which should (havent tested) work with any GHC with GADTs, MPTC, Flexible Contexts/Instances, and Kind Signatures (you can get rid of the last one easily).

EDIT: In GHC 7.6+ you should use

type family ConstrainAll (c :: k -> Constraint) (ls :: [k]) :: Constraint

(k instead of the *) and turn on PolyKinds, but this won't work with the GHC 7.4 implementation of PolyKinds (hence the monomorphic code). In the same way, defining

data HList f ls where
  HNil :: HList f '[]
  HCons :: !(f x) -> !(HList f xs) -> HList f (x ': xs)

lets you avoid code duplication when you want things like a lazy vs strict HLists or when you want a list of dictionaries, or universal variants of higher kinded types, etc.