unlimitedpower.md

App

(>>=) :: m a -> (a -> m b) -> m b
(<$>) :: (a -> b) -> f a -> f b

Very hard to understand that both functions are similar in their essence.

(=<<) :: (a -> m b) -> m a -> m b
(<$>) :: (a ->   b) -> f a -> f b
($)   :: (a ->   b) ->   a ->   b

We naturally find that the only difference between thoses functions is the extra effect. Removing the effects would obviously lead to (=<<) = (<$>) = ($)

This property mean that I could replace all (=<<) and (<$>) with ($) if I remove the extra effects from the involved functions, with my code still typechecking.

Comp

(<=<) :: (b -> m c) -> (a -> m b) -> a -> m c
.     :: (b ->   c) -> (a ->   b) -> a ->   c

The same pattern arise with kleisli composition. The only difference being again the extra effect.