[philh]

As I said, I think that's a reasonable but nonstandard way to define the word "type" but it doesn't make much difference - type theory concerns itself with them, whatever they're called.

But to support my "nonstandard" claim:

* https://gitlab.haskell.org/ghc/ghc/-/wikis/commentary/compil... mentions "Types (possibly of higher kind); e.g. [Int], Maybe"

* https://limperg.de/ghc-extensions/#polykinds talks about "types of different kinds", using Int and Monad as examples.

* https://en.wikipedia.org/wiki/Kind_%28type_theory%29 says "the type [] (list) is a type constructor". It uses the terms "data type" and "proper type" for what I think you simply want to call "type".

It's also possible usage is just inconsistent on the subject. (Evidence for this: that second link calls constraints "type-like things", when they're just types according to me.) But my sense is that usually, people engaging seriously with type theory or advanced Haskell would call Maybe and Monad types.

(You're of course right that Maybe is a type constructor and Monad is a typeclass, but that doesn't mean they aren't also types.)