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 tog

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.