functors

The problem is that the category-theory view of functors and monads and monoids completely dominates the literature.

For OCaml: - row polymorphism (in particular polymorphic variants) - higher-order and applicative functors (not the Haskell thing).

Note that functors in different languages mean different things.

Yes, applicative code is a relatively new development in Haskell: applicative functors were discovered only in 2008.

I think the issue is whether the usage of applicative functors was necessary or just for the sake of being clever for no added benefit.

Today it is if-theory, yesterday it was categories and functors, and the day before, group representations.

I am guessing there are commonly accepted idioms and libraries around the use of functors, monads, applicatives, etc..

The pictures/diagrams in it helped me really make sense of applicatives, functors, and monads.

They aren't the same thing, but are very similar): alertDialog.setMessage(...).setPositiveButtonText(...).setNegativeButtonText(...).setPositiveButtonOnClickListener(...).setNegativeButtonOnClickListener(...).build().show() Functors (in OCaml) can be viewed as Java's abstract-generic-classes with dependency injection [0].

Want to know more about Functors and Monads (maybe even applicatives O_o)?

The author appears to be an experienced Haskeller, so I'm sure they're aware of applicative functors.

As it turns out, for Haskell and most datatype-like functors there is exactly one law abiding implementation of fmap implicit in the structure of the type.

So ML has functors (not Haskell functors, certainly certainly certainly not C++ functors) which are "parameterized modules that actually work".

This helps conceptualizing the mechanism, in a way that "binding of flattened functors returning null or non-null monads" doesn't.

You might wonder, "well why don't functors have a generic constructor", and (among other answers to that) the reason is that it doesn't serve any purpose in the functor laws.

So this is going to sound snarky and/or stupid at first, but: Monads are functors with a 'join' ("flatten") operation.

Check out Functors, Applicatives, And Monads In Pictures[3].