# Extensible datatypes

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:Define a type <tt>A</tt> such that for any type <tt>B</tt> you can define | :Define a type <tt>A</tt> such that for any type <tt>B</tt> you can define | ||

− | + | <haskell> | |

− | + | up :: B -> A | |

+ | down :: A -> Maybe B | ||

+ | </haskell> | ||

:such that | :such that | ||

− | + | <haskell> | |

+ | down . up = Just | ||

+ | </haskell> | ||

− | You can do this quite easily in Java or C++, mutatis mutandis | + | You can do this quite easily in Java or C++, ''mutatis mutandis''. You can't do this in Haskell (or [[O'Haskell]] either). |

− | You can do a weaker form of this with Haskell's <tt>[[Dynamic]]</tt>, where you only have to deal with | + | You can do a weaker form of this with Haskell's <tt>[[Dynamic]]</tt>, where you only have to deal with <tt>B</tt>s that are instances of <tt>Typeable</tt>. But even with that, note that <tt>Dynamic</tt>/<tt>Typeable</tt>/<tt>TypeRep</tt> are a bit messy, with instances for <tt>Typeable</tt> defined for a wide range of known types. |

An alternative approach would be to identify your <tt>B</tt> within <tt>A</tt> not per-<tt>B</tt> but per-(up,down). This would allow for instance separate (up,down) for the same <tt>B</tt> such that | An alternative approach would be to identify your <tt>B</tt> within <tt>A</tt> not per-<tt>B</tt> but per-(up,down). This would allow for instance separate (up,down) for the same <tt>B</tt> such that | ||

− | + | <haskell> | |

− | + | down1 . up2 = Nothing | |

+ | down2 . up1 = Nothing | ||

+ | </haskell> | ||

Of course this can be done with <tt>Dynamic</tt> too, by defining dummy types. But it's ugly. | Of course this can be done with <tt>Dynamic</tt> too, by defining dummy types. But it's ugly. | ||

Line 25: | Line 31: | ||

== Extensible datatypes == | == Extensible datatypes == | ||

− | + | '''Extensible datatypes''' allow a type to be defined as "open", which can later be extended by disjoint union. Here's the Löh-Hinze syntax that achieves the above OO test: | |

− | + | <haskell> | |

− | + | module P where | |

− | + | -- define open datatype | |

− | + | open data A :: * | |

− | + | module Q where | |

+ | import P | ||

− | + | -- add constructor to A | |

− | + | MkB :: B -> A | |

− | + | ||

+ | up = MkB | ||

+ | down (MkB b) = Just b | ||

+ | down _ = Nothing | ||

+ | </haskell> | ||

== Deriving Dynamic == | == Deriving Dynamic == | ||

Line 43: | Line 54: | ||

It's possible to define [[Dynamic]] using extensible datatypes. Here's a naive attempt: | It's possible to define [[Dynamic]] using extensible datatypes. Here's a naive attempt: | ||

− | + | <haskell> | |

+ | open Dynamic :: * | ||

+ | |||

+ | class Typeable' a where | ||

+ | toDyn :: a -> Dynamic | ||

+ | fromDynamic :: Dynamic -> Maybe a | ||

+ | |||

+ | -- for each type... | ||

+ | |||

+ | MkBool :: Bool -> Dynamic | ||

+ | |||

+ | instance Typeable' Bool where | ||

+ | toDyn = MkBool | ||

+ | fromDynamic (MkBool b) = Just b | ||

+ | fromDynamic _ = Nothing | ||

+ | </haskell> | ||

+ | |||

+ | |||

+ | This attempt however doesn't allow easy creation of <tt>Typeable1</tt>, <tt>Typeable2</tt> etc. A better way is to use type-constructor parameters: | ||

− | + | <haskell> | |

− | + | open data Dynamic0 :: (* -> *) -> * | |

− | + | ||

− | + | open data Dynamic1 :: ((* -> *) -> *) -> * | |

− | + | type Dynamic = Dynamic0 Identity | |

− | + | data Type a = MkType | |

− | + | ||

− | + | ||

− | + | ||

− | + | type TypeRep = Dynamic0 Type | |

− | + | class Typeable0 a where | |

+ | toDyn0 :: f a -> Dynamic0 f | ||

+ | fromDynamic0 :: Dynamic0 f -> Maybe (f a) | ||

− | + | class Typeable1 p where | |

+ | toDyn1 :: g p -> Dynamic1 g | ||

+ | fromDynamic1 :: Dynamic1 g -> Maybe (g p) | ||

− | + | data Compose p q a = MkCompose (p (q a)) | |

+ | data Compose1 d0 f p = MkCompose1 (d0 (Compose f p)) | ||

− | + | MkDynamic1 :: (Dynamic1 (Compose1 Dynamic0 f)) -> Dynamic0 f | |

− | + | unDynamic1 :: Dynamic0 f -> Maybe (Dynamic1 (Compose1 Dynamic0 f)) | |

+ | unDynamic1 (MkDynamic1 xx) = Just xx | ||

+ | unDynamic1 _ = Nothing | ||

− | + | instance (Typeable1 p,Typeable0 a) => Typeable0 (p a) | |

− | + | -- toDyn0 :: f (p a) -> Dynamic0 f | |

− | + | toDyn0 = MkDynamic1 . toDyn1 . MkCompose1 . toDyn0 . MkCompose | |

+ | -- fromDynamic0 :: Dynamic0 f -> Maybe (f (p a)) | ||

+ | fromDynamic0 dyn = do | ||

+ | dcdf <- unDynamic1 dyn | ||

+ | (MkCompose1 dcfp) <- fromDynamic1 dcdf | ||

+ | (MkCompose fpa) <- fromDynamic0 dcfp | ||

+ | return fpa | ||

− | + | -- for each type | |

− | + | ||

− | + | ||

− | + | MkInt :: (f Int) -> Dynamic0 f | |

− | + | ||

− | + | instance Typeable0 Int where | |

+ | toDyn0 = MkInt | ||

+ | fromDynamic0 (MkInt fi) = Just fi | ||

+ | fromDynamic0 _ = Nothing | ||

− | + | MkMaybe :: (g Maybe) -> Dynamic1 g | |

− | + | ||

− | + | ||

− | + | instance Typeable1 Maybe where | |

− | + | toDyn1 = MkMaybe | |

− | + | fromDynamic1 (MkMaybe gm) = Just gm | |

− | + | fromDynamic1 _ = Nothing | |

− | + | </haskell> | |

− | + | ||

− | + | ||

− | + | ||

− | + | ||

− | + | I submit that this is "hairy" rather than "ugly", but I suspect the Type-Constructors Of Unusual Kind (TCOUKs) get even hairier for <tt>Typeable2</tt>, <tt>Typeable3</tt> etc... | |

− | + | == Open functions == | |

− | + | {{stub}} | |

− | + | ||

− | + | ||

− | + | ||

− | + | == References == | |

− | + | * Andres Löh and Ralf Hinze. [http://people.cs.uu.nl/andres/OpenDatatypes.pdf Open Data Types and Open Functions] | |

− | + | ||

− | + | ||

− | + | ||

− | + | [[Category:Proposals]] |

## Latest revision as of 07:43, 16 May 2009

## Contents |

## [edit] 1 The problem

Here's a simple test for object orientation (for some reasonable definition):

- Define a type
`A`such that for any type`B`you can define

up :: B -> A down :: A -> Maybe B

- such that

`down . up = Just`

You can do this quite easily in Java or C++, *mutatis mutandis*. You can't do this in Haskell (or O'Haskell either).

You can do a weaker form of this with Haskell's `Dynamic`, where you only have to deal with `B`s that are instances of `Typeable`. But even with that, note that `Dynamic`/`Typeable`/`TypeRep` are a bit messy, with instances for `Typeable` defined for a wide range of known types.

An alternative approach would be to identify your `B` within `A` not per-`B` but per-(up,down). This would allow for instance separate (up,down) for the same `B` such that

down1 . up2 = Nothing down2 . up1 = Nothing

Of course this can be done with `Dynamic` too, by defining dummy types. But it's ugly.

## [edit] 2 Extensible datatypes

**Extensible datatypes** allow a type to be defined as "open", which can later be extended by disjoint union. Here's the Löh-Hinze syntax that achieves the above OO test:

module P where -- define open datatype open data A :: * module Q where import P -- add constructor to A MkB :: B -> A up = MkB down (MkB b) = Just b down _ = Nothing

## [edit] 3 Deriving Dynamic

It's possible to define Dynamic using extensible datatypes. Here's a naive attempt:

open Dynamic :: * class Typeable' a where toDyn :: a -> Dynamic fromDynamic :: Dynamic -> Maybe a -- for each type... MkBool :: Bool -> Dynamic instance Typeable' Bool where toDyn = MkBool fromDynamic (MkBool b) = Just b fromDynamic _ = Nothing

This attempt however doesn't allow easy creation of `Typeable1`, `Typeable2` etc. A better way is to use type-constructor parameters:

open data Dynamic0 :: (* -> *) -> * open data Dynamic1 :: ((* -> *) -> *) -> * type Dynamic = Dynamic0 Identity data Type a = MkType type TypeRep = Dynamic0 Type class Typeable0 a where toDyn0 :: f a -> Dynamic0 f fromDynamic0 :: Dynamic0 f -> Maybe (f a) class Typeable1 p where toDyn1 :: g p -> Dynamic1 g fromDynamic1 :: Dynamic1 g -> Maybe (g p) data Compose p q a = MkCompose (p (q a)) data Compose1 d0 f p = MkCompose1 (d0 (Compose f p)) MkDynamic1 :: (Dynamic1 (Compose1 Dynamic0 f)) -> Dynamic0 f unDynamic1 :: Dynamic0 f -> Maybe (Dynamic1 (Compose1 Dynamic0 f)) unDynamic1 (MkDynamic1 xx) = Just xx unDynamic1 _ = Nothing instance (Typeable1 p,Typeable0 a) => Typeable0 (p a) -- toDyn0 :: f (p a) -> Dynamic0 f toDyn0 = MkDynamic1 . toDyn1 . MkCompose1 . toDyn0 . MkCompose -- fromDynamic0 :: Dynamic0 f -> Maybe (f (p a)) fromDynamic0 dyn = do dcdf <- unDynamic1 dyn (MkCompose1 dcfp) <- fromDynamic1 dcdf (MkCompose fpa) <- fromDynamic0 dcfp return fpa -- for each type MkInt :: (f Int) -> Dynamic0 f instance Typeable0 Int where toDyn0 = MkInt fromDynamic0 (MkInt fi) = Just fi fromDynamic0 _ = Nothing MkMaybe :: (g Maybe) -> Dynamic1 g instance Typeable1 Maybe where toDyn1 = MkMaybe fromDynamic1 (MkMaybe gm) = Just gm fromDynamic1 _ = Nothing

I submit that this is "hairy" rather than "ugly", but I suspect the Type-Constructors Of Unusual Kind (TCOUKs) get even hairier for `Typeable2`, `Typeable3` etc...

## [edit] 4 Open functions

*This article is a stub. You can help by expanding it.*

## [edit] 5 References

- Andres Löh and Ralf Hinze. Open Data Types and Open Functions