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Question

So I understand you can:

> f = map (+1)
> f [1,2,3]
[2,3,4]

However, what if you do:

> g = map (+) [1,2,3]
> :t g
g :: Num a => [a -> a]

I am not sure how to use g. What are its input & output?

Answer 1

One could, for example, apply each element of the list to a specific value:

> map (\f -> f 3) g
[4,5,6]

Or you could apply each function in the list to values in the corresponding position of another list:

> zipWith (\f x -> f x) g [30,300,3000]
[31,302,3003]

Or you could pattern match on the list, or use it in a list comprehension, or index it with (!!) , or, or, or... there are endless possibilities.

Answer 2

(+) :: Num a => a -> a -> a ; it takes an number and returns a function that increases its argument.

map (+) [1, 2, 3] , then, is equivalent to [(+ 1), (+ 2), (+ 3)] . One way to use such a list of functions is with the Applicative instance of [] , which allows you to apply each function in a list to each value in another list. For example:

[(+ 1), (+ 2), (+ 3)] <*> [5] == [6, 7, 8]