[bvaldivielso]

I don't know that this definition is very precise. For example, the kind `(->) r` (which you can roughly understand as the class of all functions that go from a fixed type `r` to other types) is a monad in haskell [1]. In what sense is this class of functions a "wrapper"?

Additionally, even if you insist that this reader monad is a "wrapper", your definition would also informally apply to things like `Applicative`, and not all applicatives are monads (some are).

Some monads are more easily understood as wrappers (`Maybe`, `List`, ...) and you can be very productive if you just stick to that level of understanding. But there's a deeper understanding that one can get.

[1] https://hackage.haskell.org/package/mtl-2.3.1/docs/src/Contr...