3 ms·
At this point I admit I'm way beyond my depth. This article seems to imply a correlation between the fish operator (<=<) and composition. Specifically his sect
by BoiledCabbage 10y ago
At this point I admit I'm way beyond my depth.
This article seems to imply a correlation between the fish operator (<=<) and composition. Specifically his section on Kleisli monad.
http://www.haskellforall.com/2012/08/the-category-design-pattern.html?m=1 http://www.haskellforall.com/2012/08/the-category-design-pat...
But I don't know the space well enough to know if that's answering your question.
- kmill 10y agoIt's true that the Kleisli category gives a composition law from a monad, but let's not lose sight: the point isn't whether there is a conceivable way to compose things, but whether a monad is just a monoid of functions under composition. Monads are like a monoid at the type level plus a bunch of coherence rules. For every type a, there is a "composition" m (m a) -> m a and a "unit" a -> m a. (Compare with a monoid, where there is a composition m x m -> m and a unit {1} -> m.) Also, the composition must be natural in the sense that whenever there is a map f :: a -> b then you have a bunch of "commuting squares": the composition m (m a) -> m (m b) -> m b must equal m (m a) -> m a -> m b and the composition a -> m a -> m b must equal a -> b -> m b. (Some of these maps are fmap f or fmap (fmap f).) The naturality thing is important and shows up quite a lot, and category theory was invented to understand naturality. It's sort of a higher higher order functional programming.
- BoiledCabbage 10y agoThanks this was helpful. And you're right. I was blurring the concept of composition and actual functional composition. Clearly much more to learn.