[dandlift]

My take, with no pretension of being accurate:

Say we have a function with signature

    f :: Int -> Int -> Int -> Int

Let's say this just add those Ints together.

Now let's create another function by partially applying the initial function: f1 = f 42

f1 signature will be

    f1 :: Int -> Int -> Int

Kind of "consuming" the signature. Repeat this until using up all the parameters. You end up with a function with no parameters, which map to a single Int.

You could say that f3 -> Int (note, not a valid notation for the sake of example). No need for a different symbol.