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Heterogenous collections

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('instance Show Showable',GADT existential datatype syntax,'Mk..' constructor)

Revision as of 13:22, 26 November 2006

Techniques for implementing heterogenous lists in Haskell.


1 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, the need is for heterogeneous and non-fixed length. When one is used to Java, with its loose typing of collections,not having this immediately and easily available seems strange. As an example, the need is for something like LinkedList<Object> from Java.

2 Algebraic datatypes

If the number of types to cover is fixed, then the problem can be solved by a list of data types such as

data T
   = ConsInt    Int
   | ConsString String
   | ConsChar   Char


data Object = IntObject Int | StringObject String
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 have to type-switch all the time if you want to do anything with the objects in the List, and the collections are clumsy to extend by new types.

3 A Universal type

Similar to the Object type in Java, the
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

4 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 example 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.

{-# OPTIONS -fglasgow-exts #-}
-- 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
        f (MkShowable a) = show a
*Main> main
["3","'x'","3.141592653589793","\"string\"","Just ()"]
One can of course make the type
an instance of the type class
-- Make Showable itself an instance of Show
instance Show Showable
  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
  MkShowable :: Show a => a -> Showable
i.e. giving an explicit type signature for the
data constructor. (Using explicit
forall a.
before the
Show a =>
part is allowed, but not required, just as for ordinary type signatures.)

5 HLists, OOHaskell, type-level programming

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

There is also some related material here: