The class you're looking for is Applicative. The (<*>) operator handles application of "effectful" things to "effectful" things, whereas (<$>) handles the application of non-"effectful" things to "effectful" things. This situation is interesting because it highlights the fact that there is a distinction between the meaning of whitespace between function and argument vs the meaning of whitespace between argument and argument.

`Applicative` is not enough for monads.
`Applicative` is like functor only for functions
with many arguments. It's good for patterns:

(a -> b -> c -> d) -> (m a -> m b -> m c -> m d)

Monads are good for patterns

(a -> b -> c -> m d) -> (m a -> m b -> m c -> m d)

So I can not express it with `Applicative`. My
analogy really breaks down on functions with
several arguments, since as you have pointed out there are
two white spaces. But I like the idea of using
one sign for normal and monadic and maybe applicative
applications.

Anton