Curried Functions

Functions in Haskell are also free to return functions as their results. This brings us to curried functions which take in one argument at a time and return a function that takes in additional arguments. Actually, all functions in Haskell with multiple arguments are applied this way (unless explicitly stated otherwise) – the function is first applied to the first argument and returns another function that is then applied to the second argument and so on. Let's explore this with an example `multiply` function that takes in three numbers and multiplies them:

ghci> multiply x y z = x * y * z
ghci> :t multiply
multiply :: Num a => a -> a -> a -> a

-- a -> a -> a -> a actually means:
Num a => a -> (a -> (a -> a))

That is, multiply takes the argument x of type a and returns another function that takes in the argument y (also of type a) and returns another function that takes in the argument z (also of type a) that then returns the final result (also of type a). To avoid unnecessary parentheses, the function arrow -> associates to the right by convention, while the function application associates to the left:

multiply x y z
-- is actually:
((multiply x) y) z