Heterogenous collections

Techniques for implementing heterogeneous lists in Haskell.

The problem

Does some kind of collection of objects with different types in Haskell exist? Obviously, tuples are an example, but they have a fixed length. To compare tuples vs lists:

Tuples	Lists
Heterogeneous	Homogeneous
Fixed length (per tuple type)	Variable length
Always finite	May be infinite

However, what if we need a heterogeneous and non-fixed length collection? When one is used to Java, with its loose typing of collections, not having this immediately and easily available may seem strange. (Consider, for example, LinkedList<Object> from Java.)

Algebraic datatypes

If the number of types to cover is fixed, then the problem can be solved by a making a type with various data constructors, each representing a type:

data T
   = ConsInt    Int
   | ConsString String
   | ConsChar   Char

which can be used like this:

[ConsInt 42, ConsChar 'a', ConsString "foo"]

or:

data Object = IntObject Int | StringObject String

-- Note that it would be preferable to implement objectString as an instance of Show Object, this is just an example.
objectString :: Object -> String
objectString (IntObject v) = show v
objectString (StringObject v) = v

main = mapM_ (putStrLn . objectString) [(IntObject 7), (StringObject "eight")]

This is a very basic solution, and often preferable. Limitations: You will have to pattern-match all the time if you want to do anything with the data stored in the list, and it will be cumbersome to add new types, as you'll have to handle them everywhere you use said list.

A Universal type

Similar to the Object type in Java, the Dynamic type in Haskell can be used to wrap any type in the Typeable class, creating a suitable wrapper:

import Data.Dynamic
import Data.Maybe

-- 
-- A list of dynamic 
--
hlist :: [Dynamic]
hlist = [ toDyn "string"
        , toDyn (7 :: Int)
        , toDyn (pi :: Double)
        , toDyn 'x'
        , toDyn ((), Just "foo")
        ]

dyn :: Dynamic 
dyn = hlist !! 1

--
-- unwrap the dynamic value, checking the type at runtime
--
v :: Int
v = case fromDynamic dyn of
        Nothing -> error "Type mismatch"
        Just x  -> x

Existential types

Depending on needs and comfort level with fancier types, the existential approach to ADTs might solve the problem. The types aren't that scary.

This is akin to upcasting in Java to an interface that lets you print things. That way you know how to print every object (or do whatever else it is you need to do) in the list. Beware: there is no safe downcasting (that's what Typeable would be for); that would likely be more than you need.

Essentially, existential values pack up a value with operations on that value, and hide the actual value's types. Thus, objects of differing types can be used, as long as they all provide a common interface.

The most convenient way to pack a value with its methods is to use a typeclass dictionary. The typeclass declaration defines the API to be wrapped with each value. You can also pack up your own interface as an explicit field in the data type, if you want to avoid type classes.

{-# LANGUAGE ExistentialQuantification #-}
--
-- An existential type encapsulating types that can be Shown
-- The interface to the type is held in the show method dictionary
--
-- Create your own typeclass for packing up other interfaces
--
data Showable = forall a . Show a => MkShowable a

--
-- And a nice existential builder
--
pack :: Show a => a -> Showable
pack = MkShowable

--
-- A heteoregenous list of Showable values
--
hlist :: [Showable]
hlist = [ pack 3
        , pack 'x'
        , pack pi
        , pack "string"
        , pack (Just ()) ]

--
-- The only thing we can do to Showable values is show them
--
main :: IO ()
main = print $ map f hlist
    where
        f (MkShowable a) = show a

{-

*Main> main
["3","'x'","3.141592653589793","\"string\"","Just ()"]

-}

One can of course make the type Showable an instance of the type class Show itself

--
-- Make Showable itself an instance of Show
--
instance Show Showable
  where
  showsPrec p (MkShowable a) = showsPrec p a

--
-- The only thing we can do to Showable values is show them
--
main :: IO ()
main = print hlist

{-
*Main> main
[3,'x',3.14159265358979,"string",Just ()]
-}

Note how we didn't need to unwrap and show the values explicitly ourselves.

There's an alternative way of defining an existential datatype, using GADT syntax. Instead of writing

data Showable = forall a . Show a => MkShowable a

one writes

data Showable
  where
  MkShowable :: Show a => a -> Showable

i.e. giving an explicit type signature for the MkShowable data constructor. (Using explicit forall a. before the Show a => part is allowed, but not required, just as for ordinary type signatures.)

HLists, OOHaskell, type-level programming

This is the cleanest solution, but very advanced and a little restrictive. Read these two articles:

• Haskell's overlooked object system (PDF)
• Strongly typed heterogeneous collections

There is also some related material here:

• Extensible record