Difference between revisions of "Extensible datatypes"
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== Extensible datatypes == |
== Extensible datatypes == |
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− | '''Extensible datatypes''' allow a type to be defined as "open", which can later be extended by disjoint union. Here's |
+ | '''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> |
<haskell> |
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module P where |
module P where |
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+ | |||
⚫ | |||
+ | -- define open datatype |
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⚫ | |||
module Q where |
module Q where |
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import P |
import P |
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+ | -- add constructor to A |
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− | A |= MkB B |
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+ | MkB :: B -> A |
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up = MkB |
up = MkB |
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<haskell> |
<haskell> |
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− | + | open Dynamic :: * |
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class Typeable' a where |
class Typeable' a where |
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-- for each type... |
-- for each type... |
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− | + | MkBool :: Bool -> Dynamic |
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instance Typeable' Bool where |
instance Typeable' Bool where |
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<haskell> |
<haskell> |
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− | data Dynamic0 |
+ | open data Dynamic0 :: (* -> *) -> * |
− | data Dynamic1 |
+ | open data Dynamic1 :: ((* -> *) -> *) -> * |
type Dynamic = Dynamic0 Identity |
type Dynamic = Dynamic0 Identity |
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data Compose1 d0 f p = MkCompose1 (d0 (Compose f p)) |
data Compose1 d0 f p = MkCompose1 (d0 (Compose f p)) |
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− | + | MkDynamic1 :: (Dynamic1 (Compose1 Dynamic0 f)) -> Dynamic0 f |
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unDynamic1 :: Dynamic0 f -> Maybe (Dynamic1 (Compose1 Dynamic0 f)) |
unDynamic1 :: Dynamic0 f -> Maybe (Dynamic1 (Compose1 Dynamic0 f)) |
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-- for each type |
-- for each type |
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− | + | MkInt :: (f Int) -> Dynamic0 f |
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instance Typeable0 Int where |
instance Typeable0 Int where |
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fromDynamic0 _ = Nothing |
fromDynamic0 _ = Nothing |
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− | + | MkMaybe :: (g Maybe) -> Dynamic1 g |
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instance Typeable1 Maybe where |
instance Typeable1 Maybe where |
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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... |
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... |
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+ | |||
+ | == Open functions == |
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+ | |||
+ | {{stub}} |
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+ | |||
+ | == References == |
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+ | |||
+ | * Andres Löh and Ralf Hinze. [https://www.andres-loeh.de/OpenDatatypes.pdf Open Data Types and Open Functions] |
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[[Category:Proposals]] |
[[Category:Proposals]] |
Latest revision as of 11:16, 28 March 2018
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 Bs 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.
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
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...
Open functions
This article is a stub. You can help by expanding it.
References
- Andres Löh and Ralf Hinze. Open Data Types and Open Functions