Personal tools

Heterogenous collections

From HaskellWiki

(Difference between revisions)
Jump to: navigation, search
(Editting and formatting)
(Existential types: Modernized the source code)
(8 intermediate revisions by 4 users not shown)
Line 1: Line 1:
This page is a very hasty and ad-hoc summary of a common discussion on
+
Techniques for implementing heterogenous lists in Haskell.
the haskell-cafe list. If you find it hard to read, please complain
 
there and somebody hopefully will come to help.
 
   
  +
== The problem ==
   
=== 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.
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:
+
To compare tuples vs lists:
   
 
{| border="1" cellpadding="2" align="center"
 
{| border="1" cellpadding="2" align="center"
 
|-
 
|-
 
!Tuples!!Lists
 
!Tuples!!Lists
|+
+
|-
 
|Heterogeneous||Homogeneous
 
|Heterogeneous||Homogeneous
|+
+
|-
 
|Fixed length (per tuple type)||Variable length
 
|Fixed length (per tuple type)||Variable length
|+
+
|-
|Always finite||May be unending
+
|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
+
However, the need is for heterogeneous and non-fixed length. When one is
easily available seems strange. As an example, the need is for something like LinkedList<Object> from java.
+
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.
   
  +
== Algebraic datatypes ==
   
=== Algebraic datatypes ===
+
If the number of [[type]]s to cover is fixed, then the problem can be
+
solved by a list of data types such as
If the number of [[type]]s to cover is fixed, then the problem can be solved by a list of data types such as
 
   
 
<haskell>
 
<haskell>
data T =
+
data T
ConsInt Int
+
= ConsInt Int
 
| ConsString String
 
| ConsString String
 
| ConsChar Char
 
| ConsChar Char
  +
</haskell>
  +
  +
which can be used like this:
  +
  +
<haskell>
  +
[ConsInt 42, ConsChar 'a', ConsString "foo"]
 
</haskell>
 
</haskell>
   
Line 43: Line 51:
 
</haskell>
 
</haskell>
   
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.
+
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.
   
  +
== A Universal type ==
   
  +
Similar to the Object type in Java, the <hask>Dynamic</hask> type in
  +
Haskell can be used to wrap any type in the Typeable class, creating a
  +
suitable wrapper:
   
=== HLists, OOHaskell, type-level programming ===
+
<haskell>
  +
import Data.Dynamic
  +
import Data.Maybe
   
This is the cleanest solution, but very advanced and a little restrictive. Read these two articles:
+
--
  +
-- A list of dynamic
  +
--
  +
hlist :: [Dynamic]
  +
hlist = [ toDyn "string"
  +
, toDyn (7 :: Int)
  +
, toDyn (pi :: Double)
  +
, toDyn 'x'
  +
, toDyn ((), Just "foo")
  +
]
   
* http://homepages.cwi.nl/~ralf/HList/
+
dyn :: Dynamic
* http://homepages.cwi.nl/~ralf/OOHaskell/
+
dyn = hlist !! 1
   
There is also some related material here:
+
--
  +
-- unwrap the dynamic value, checking the type at runtime
  +
--
  +
v :: Int
  +
v = case fromDynamic dyn of
  +
Nothing -> error "Type mismatch"
  +
Just x -> x
  +
</haskell>
   
* [[Extensible record]]
+
== [[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.
   
=== [[Existential types]] ===
+
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.
   
Depending on needs and comfort level with fancier types, the existential approach to ADTs might solve the problem. The following code is a demonstration you can cut-and-paste-and-run.
+
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.
   
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.
+
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
There are other ways to do this with existentials (e.g. bounded existentials), but this is what came out of my head when I read your post. Existentials seems to be the "Haskellish" way to reduce a heterogenous list to a collection of objects with common operations. [[HList]] would be the Haskellish way for more static and flexible assurances.
+
value. You can also pack up your own interface as an explicit field in the data
  +
type, if you want to avoid type classes.
   
 
<haskell>
 
<haskell>
{-# OPTIONS -fglasgow-exts #-}
+
{-# 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
   
module Test where
+
--
  +
-- And a nice existential builder
  +
--
  +
pack :: Show a => a -> Showable
  +
pack = MkShowable
   
data PrintPackage = forall a . PrintPackage a (a -> String)
+
--
  +
-- A heteoregenous list of Showable values
  +
--
  +
hlist :: [Showable]
  +
hlist = [ pack 3
  +
, pack 'x'
  +
, pack pi
  +
, pack "string"
  +
, pack (Just ()) ]
   
instance Show PrintPackage where
+
--
show (PrintPackage val showMethod) = showMethod val
+
-- 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
   
list = [ PrintPackage 3 show
+
{-
, PrintPackage "string" show
 
, PrintPackage 3.4 show
 
]
 
   
main = print list
+
*Main> main
  +
["3","'x'","3.141592653589793","\"string\"","Just ()"]
  +
  +
-}
 
</haskell>
 
</haskell>
  +
  +
One can of course make the type <hask>Showable</hask> an instance of the type class <hask>Show</hask> itself
  +
<haskell>
  +
--
  +
-- 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 ()]
  +
-}
  +
</haskell>
  +
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 [[Generalised algebraic datatype | GADT]] syntax. Instead of writing
  +
<haskell>
  +
data Showable = forall a . Show a => MkShowable a
  +
</haskell>
  +
one writes
  +
<haskell>
  +
data Showable
  +
where
  +
MkShowable :: Show a => a -> Showable
  +
</haskell>
  +
i.e. giving an explicit type signature for the <hask>MkShowable</hask> data constructor.
  +
(Using explicit <hask>forall a.</hask> before the <hask>Show a =></hask> 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:
  +
  +
* http://homepages.cwi.nl/~ralf/HList/
  +
* http://homepages.cwi.nl/~ralf/OOHaskell/
  +
  +
There is also some related material here:
  +
  +
* [[Extensible record]]
  +
  +
  +
  +
[[Category:FAQ]]
  +
[[Category:Idioms]]
  +
[[Category:Glossary]]

Revision as of 15:14, 29 March 2011

Techniques for implementing heterogenous lists in Haskell.

Contents

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

which can be used like this:

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

or:

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
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

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.

{-# 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.)

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: