Function returning result of any constructor of a GADT

Question

I'm currently having a fight with the typechecker when I try to create a function returning Thing a (where Thing is a GADT). A minimal contrived example:

{-#LANGUAGE GADTs, EmptyDataDecls #-}
module Main where

-- Define a contrived GADT
data TFoo
data TBar
data Thing a where
  Foo :: Int -> Thing TFoo
  Bar :: String -> Thing TBar

combine :: [Thing a]
combine = [Foo 1, Bar "abc"]

main :: IO ()
main = undefined

The typechecker gets unhappy that a doesn't match TBar . Presumably this is because it has already inferred that a is TFoo . But, this is surprising, because with regular sum types you can do:

data Thing = Foo Int | Bar String

combine :: [Thing]
combine = [Foo 1, Bar "abc"]

Is there anyway to return a type parametric over the GADT parameter?

Outside of the context of the contrived examples, I need GADTs so I can type certain functions to only take a Foo , but before that I need to also be able to just return a list of Thing s.

Answer 1

You've got your quantifiers mixed up.

combine :: [Thing a]

means (the forall is implicit in the syntax)

combine :: forall a. [Thing a]

Essentially, combine needs to be a [Thing a] no matter what a is, because a is chosen by the code that calls combine . Or, in another sense,

-- psuedo-Haskell
combine :: (a :: *) -> [Thing a]

combine is a function that takes a type as argument and promises to construct a list of Things of that type. The only possible definition of combine with this type signature is combine = [] , plus a bunch of dumb ones like [undefined] , etc. Eg combine = [Foo 1] would not work either, because a is not being inferred, because it's not combine that sets a ; it's the user.

You want

-- psuedo-Haskell
combine :: [exists a. Thing a]

which means " combine is a list of things, and each thing is a Thing of some unknown type" (and every Thing can be of a different type). The exists quantifier is the flipside of forall . It means the definition of combine can set whatever type it wants and the user will have to deal with it. Haskell doesn't support exists out-of-the-box, so you need to define an intermediate data type:

data SomeThing = forall a. SomeThing (Thing a)

The syntax is a bit backwards for using the universal quantifier to create existential quantification, but the idea is that you get

SomeThing :: forall a. Thing a -> SomeThing

which essentially erases the knowledge of what a is.

You can then have

combine :: [SomeThing]
combine = [SomeThing $ Foo 1, SomeThing $ Bar "abc"]