How is the list monad a "computation builder"? Sounds to me like "programmable semicolons" and other nonsense: Monad is a typeclass that means very different things depending on what type you're using. It's the shape that has meaning: this level of abstraction is just going to be hard to grasp correctly no matter what you call it.

Likewise with "Mappable": in most other languages, `map` is only an operation on lists or list-like things. `ask` in `Reader` is implementable with Functor only: by what tortured metaphor does `Mappable` help you understand that? Also it sounds like Java. Yuck :)

Names are a bikeshed. Monad, Applicative and Functor have the advantage of at least being rigorous, I can't see any other name being better.