Question

I’m currently trying to learn Haskell, but I’m struggling with understanding the syntax. For example, take the map function:

map :: (s -> t) -> [s] -> [t]
map f [] = []
map f (x:xs) = f x : map f xs

I understand what the function does, and that map has a function f :: s -> t as a parameter. But I read map :: (s -> t) -> [s] -> [t] as “map is a function which maps a function mapping from s to t to s and then to t”, which is obviously wrong. Could someone clear this up for me?

Answer 1

The type (s -> t) -> [s] -> [t] can be read in two ways. One way is to treat it as a function of two arguments, the first a function of type s -> t and the second a list of type [s]. The return value is of type [t].

The other way is to understand that function arrows are right-associative, so the type is equivalent to (s -> t) -> ([s] -> [t]). Under this interpretation, map is a function that takes a function from element to element s -> t and turns it into a function from list to list [s] -> [t].

Similarly, when using the function, you can think of map foo xs as applying the function map to two arguments foo and xs. Or, since function application is left-associative, you can think of it as (map foo) xs, applying map to the single argument foo to get back a new function which you then apply to xs.

Since Haskell functions are curried, these are just two ways of looking at the exact same thing.