Understanding Haskell function signature

Question

I m new in haskell's world and I m having some troubles with function signatures :

What does it mean in simple worlds :

add:: Integer -> Integer -> Integer

Does it mean that the two first parameters are Integer and the returned value is Integer too ?

Can you explain me, the aim of using arrows to determine a type of parameter or at least give me a brief explanation about this function signature ?

Answer 1

Colloquially we may indeed refer to add as a function that takes two Integers and produces an Integer. However to understand the notation, you need to understand that technically there's no such thing as a function that takes two arguments in Haskell.

Rather every function takes exactly one argument and the type of a function is written a -> r where a is the type of the argument and r is the type of the result. The function arrow is right-associative, which means that the type a -> (b -> c) can be written without parentheses as a -> b -> c.

So Integer -> Integer -> Integer is the same as Integer -> (Integer -> Integer), which tells us that add is a function that takes an Integer and produces another function of type Integer -> Integer. This is known as currying and is the usual way to "encode" multi-argument functions in Haskell.

To call such a curried function, we can write add 1 2, which, because function application is left associative, is the same as (add 1) 2, first calling add 1 to get a function of type Integer -> Integer and then applying that function to the argument 2.

Answer 2

As a simple mental model - yes, the thing after the last arrow is a return type, and everything else are parameters.

Signatures for 2-and-more-ary functions look this way because they are actually unary functions returning another 1-and-more-ary function.

In your case

add :: Integer -> (Integer -> Integer)

Passing add an argument gives

add 3 :: (Integer -> Integer)

And add 3 4, therefore is just Integer type.