# List of showables OOP-style in Haskell?

The HList-style solutions would work, but it is possible to reduce the complexity if you only need to work with lists of constrained existentials and you don't need the other HList machinery.

Here's how I handle this in my existentialist package:

{-# LANGUAGE ConstraintKinds, ExistentialQuantification, RankNTypes #-}

data ConstrList c = forall a. c a => a :> ConstrList c
| Nil
infixr :>

constrMap :: (forall a. c a => a -> b) -> ConstrList c -> [b]
constrMap f (x :> xs) = f x : constrMap f xs
constrMap f Nil       = []


This can then be used like this:

example :: [String]
example
= constrMap show
(( 'a'
:> True
:> ()
:> Nil) :: ConstrList Show)


It could be useful if you have a large list or possibly if you have to do lots of manipulations to a list of constrained existentials.

Using this approach, you also don't need to encode the length of the list in the type (or the original types of the elements). This could be a good thing or a bad thing depending on the situation. If you want to preserve the all of original type information, an HList is probably the way to go.

Also, if (as is the case of Show) there is only one class method, the approach I would recommend would be applying that method to each item in the list directly as in ErikR's answer or the first technique in phadej's answer.

It sounds like the actual problem is more complex than just a list of Show-able values, so it is hard to give a definite recommendation of which of these specifically is the most appropriate without more concrete information.

One of these methods would probably work out well though (unless the architecture of the code itself could be simplified so that it doesn't run into the problem in the first place).

## Generalizing to existentials contained in higher-kinded types

This can be generalized to higher kinds like this:

data AnyList c f = forall a. c a => f a :| (AnyList c f)
| Nil
infixr :|

anyMap :: (forall a. c a => f a -> b) -> AnyList c f -> [b]
anyMap g (x :| xs) = g x : anyMap g xs
anyMap g Nil       = []


Using this, we can (for example) create a list of functions that have Show-able result types.

example2 :: Int -> [String]
example2 x = anyMap (\m -> show (m x))
(( f
:| g
:| h
:| Nil) :: AnyList Show ((->) Int))
where
f :: Int -> String
f = show

g :: Int -> Bool
g = (< 3)

h :: Int -> ()
h _ = ()


We can see that this is a true generalization by defining:

type ConstrList c = AnyList c Identity

(>:) :: forall c a. c a => a -> AnyList c Identity -> AnyList c Identity
x >: xs  = Identity x :| xs
infixr >:

constrMap :: (forall a. c a => a -> b) -> AnyList c Identity -> [b]
constrMap f (Identity x :| xs) = f x : constrMap f xs
constrMap f Nil                = []


This allows the original example from the first part of this to work using this new, more general, formulation with no changes to the existing example code except changing :> to >: (even this small change might be able to be avoided with pattern synonyms. I'm not totally sure though since I haven't tried and sometimes pattern synonyms interact with existential quantification in ways that I don't fully understand).

You can create your own operator to reduce syntax noise:

infixr 5 <:

(<:) :: Show a => a -> [String] -> [String]
x <: l = show x : l


So you can do:

λ > (1 :: Int) <: True <: "abs" <: []
["1","True","\"abs\""]


This is not [1 :: Int, True, "abs"] but not much longer.

Unfortunately you cannot rebind [...] syntax with RebindableSyntax.

Another approach is to use HList and preserve all type information, i.e. no downcasts, no upcasts:

{-# LANGUAGE ConstraintKinds       #-}
{-# LANGUAGE DataKinds             #-}
{-# LANGUAGE PolyKinds             #-}
{-# LANGUAGE TypeFamilies          #-}
{-# LANGUAGE TypeOperators         #-}
{-# LANGUAGE UndecidableInstances  #-}

import GHC.Exts (Constraint)

infixr 5 :::

type family All (c :: k -> Constraint) (xs :: [k]) :: Constraint where
All c '[]       = ()
All c (x ': xs) = (c x, All c xs)

data HList as where
HNil :: HList '[]
(:::) :: a -> HList as -> HList (a ': as)

instance All Show as => Show (HList as) where
showsPrec d HNil       = showString "HNil"
showsPrec d (x ::: xs) = showParen (d > 5) (showsPrec 5 x)
. showString " ::: "
. showParen (d > 5) (showsPrec 5 xs)


And after all that:

λ *Main > (1 :: Int) ::: True ::: "foo" ::: HNil
1 ::: True ::: "foo" ::: HNil

λ *Main > :t (1 :: Int) ::: True ::: "foo" ::: HNil
(1 :: Int) ::: True ::: "foo" ::: HNil
:: HList '[Int, Bool, [Char]]


There are various ways to encode heterogenous list, in HList is one, there is also generics-sop with NP I xs. It depends on what you are trying to achieve in the larger context, if this is this preserve-all-the-types approach is what you need.

If you really, really want, you can use a heterogeneous list. This approach really isn't useful for Show, because it has a single method and all you can do is apply it, but if your class has multiple methods this could be useful.

{-# LANGUAGE PolyKinds, KindSignatures, GADTs, TypeFamilies
, TypeOperators, DataKinds, ConstraintKinds, RankNTypes, PatternSynonyms  #-}

import Data.List (intercalate)
import GHC.Prim (Constraint)

infixr 5 :&
data HList xs where
None :: HList '[]
(:&) :: a -> HList bs -> HList (a ': bs)

-- | Constraint All c xs holds if c holds for all x in xs
type family All (c :: k -> Constraint) xs :: Constraint where
All c '[] = ()
All c (x ': xs) = (c x, All c xs)

-- | The list whose element types are unknown, but known to satisfy
--   a class predicate.
data CList c where CL :: All c xs => HList xs -> CList c

cons :: c a => a -> CList c -> CList c
cons a (CL xs) = CL (a :& xs)

empty :: CList c
empty = CL None

uncons :: (forall a . c a => a -> CList c -> r) -> r -> CList c -> r
uncons _ n (CL None) = n
uncons c n (CL (x :& xs)) = c x (CL xs)

foldrC :: (forall a . c a => a -> r -> r) -> r -> CList c -> r
foldrC f z = go where go = uncons (\x -> f x . go) z

showAll :: CList Show -> String
showAll l = "[" ++ intercalate "," (foldrC (\x xs -> show x : xs) [] l) ++ "]"

test = putStrLn $showAll$ CL \$
1 :&
'a' :&
"foo" :&
[2.3, 2.5 .. 3] :&
None


Since evaluation is lazy in Haskell, how about just creating a list of the actual strings?

showables = [ show 1, show "blah", show 3.14 ]