While musing what more useful standard class to suggest to this one
class Coordinate c where
createCoordinate :: x -> y -> c x y
getFirst :: c x y -> x
getSecond :: c x y -> y
addCoordinates :: (Num x, Num y) => c x y -> c x y -> c x y
it occured me that instead of something VectorSpace
-y or R2
, a rather more general beast might lurk here: a Type -> Type -> Type
whose two contained types can both be extracted. Hm, perhaps they can be extract
ed?
Turns out neither the comonad
nor bifunctors
package contains something called Bicomonad
. Question is, would such a class even make sense, category-theoretically? Unlike Bimonad
(which also isn't defined, and I couldn't really see how might look), a naïve definition seems plausible:
class Bifunctor c => Bicomonad c where
fst :: c x y -> x
snd :: c x y -> y
bidup :: c x y -> c (c x y) (c x y)
probably with the laws
fst . bidup ≡ id
snd . bidup ≡ id
bimap fst snd . bidup ≡ id
bimap bidup bidup . bidup ≡ bidup . bidup
but I find it disquieting that both fields of the result of bidup
contain the same type, and there are quite a number of other, perhaps “better” conceivable signatures.
Any thoughts?
This is not an answer, but for Bimonad
, how about this?
class Biapplicative p => Bimonad p where
(>>==) :: p a b -> (a -> b -> p c d) -> p c d
biap :: Bimonad p => p (a -> b) (c -> d) -> p a c -> p b d
biap p q = p >>== \ab cd -> q >>== \a c -> bipure (ab a) (cd c)
instance Bimonad (,) where
(a,b) >>== f = f a b
I don't know if this is categorically right/interesting, or even remotely useful, but it smells right from a Haskell perspective. Does it match your Bicomonad
or something similar?
来源:https://stackoverflow.com/questions/40835094/what-would-be-the-methods-of-a-bi-comonad