For example, suppose we had the functions double(x) = 2 * x, square(x) = x ^ 2 and sum(x,y) = x + y. What is a function compose such as compose(compose(sum, square), double) = x^2 + 2*x? Notice that I'm asking a function that can be used for functions of any arity. For example, you could compose f(x,y,z) with g(x), h(x), i(x) into f(g(x), h(x), i(x)).
This is a common Haskell idiom, applicative functors:
composed = f <$> g1 <*> g2 <*> ... <*> gn
(A nicer introduction can be found here).
This looks very clean because of automatic partial application, and works like this:
(<*>) f g x = f x (g x)
(<$>) f g x = f (g x) -- same as (.)
For example,
f <$> g <*> h <*> i ==>
(\x -> f (g x)) <*> h <*> i ==>
(\y -> (\x -> f (g x)) y (h y)) <*> i ==>
(\y -> f (g y) (h y)) <*> i ==>
(\z -> (\y -> f (g y) (h y)) z (i z)) ==>
(\z -> f (g z) (h z) (i z)).
Applicative functors are more general, though. They are not an "algorithm", but a concept. You could also do the same on a tree, for example (if properly defined):
(+) <$> (Node (Leaf 1) (Leaf 2)) <*> (Node (Leaf 3) (Leaf 4)) ==>
Node (Leaf 4) (Leaf 6)
But I doubt that applicatives are really usable in most other languages, due to the lack of easy partial application.
来源：https://stackoverflow.com/questions/13437773/what-is-a-function-composition-algorithm-that-will-work-for-multiple-arguments