Neither is a bifunctor if I understood that concep...

# arrow

[Jannis]

Neither is a bifunctor if I understood that concept correctly. I think its best described by looking at the type signature of bimap (haskell and arrow): (a -> b) -> (c -> d) -> p a c -> p b d and arrow fun <A, B, C, D> Kind2<F, A, B>.bimap(fl: (A) -> C, fr: (B) -> D): Kind2<F, C, D>. So the intuition is its basically a functor applied to both type arguments. Fold looks more like this (for option): (() -> b) -> (a -> B) -> Maybe a -> b fun <A, B>Option<A>.fold(none: () -> B, some: (A) -> B): B and either is similar. Fold destructures while bimap keeps structure. If you are looking for types that are bifunctors and their uses: Either has a bifunctor instance, Ior should have one and I think soon we'll have IO be parameterized to IO<E, A> and that should be a bifunctor as well

[kioba]

ahh okay so the key is to keep the structure. A very simplified explanation would be that, bimap is similar to map with the capability to give a Left?
Thank you for the arrow solution! haskell is way different and takes time to translate to kotlin, for me at lest 🙂

[Jannis]

Yes structure is key here. It is a bit more general than just Left but for either and ior that is correct. For example `Tuple2`/`Pair` and Const have a Bifunctor instance as well. (Not sure if they do in arrow, but they should!). I kind of just think of it as a functor that applies to the second typeparameter, whereas the normal functor instance prefers one. The Functor bit is important here as similar laws apply for Bifunctor. I'd suggest looking at the laws to understand what qualifies as a `Bifunctor`/`Functor` instance.

[kioba]

Yeah I actually reading the Category Theory for Programmers and thats where I found this question. Thanks for taking the time Jannis! You helped me a lot

[Jannis]

I need to read that as well 🙈 There is currently a repo that is converting the snippets to kotlin/arrow code, it is very incomplete but could help 🙂
https://github.com/arrow-kt/Category-Theory-for-Programmers.kt

[Jannis]

Welp I just noticed raul posted that below. So yeah 😄