Missing Apply law

[eschnett]

The Composition Applicative laws is really an Apply law:

pure (.) <*> u <*> v <*> w ≡ u <*> (v <*> w)

You can rewrite the first term pure (.) <*> u as fmap (.) u, and then it does not depend on pure any more, making it a law for the Apply typeclass. This law is just Apply's associativity in disguise.

[chessai]

alright, i've just adding this. running builds locally.

do you think Associativity is a good name with which to refer to this law?

[chessai]

We should also test the following, but I'm not sure what to name these at all. I'd appreciate your input @eschnett.

x <.> (f <$> y) = (. f) <$> x <.> y
f <$> (x <.> y) = (f .) <$> x <.> y
(mf <$> m) .> (nf <$> n) = nf <$> (m .> n)
(mf <$> m) <. (nf <$> n) = mf <$> (m <. n)

[eschnett]

It's called "Composition Law" when written with pure. I'd still call it "Composition".