haskell-lectures/VL2/content/VL2_currying6.tex

What does that mean for us? It's not just fun stuff or aesthetic. It allows us to do \textbf{partial application}. That means we do not have to give a function all arguments. If we pass an "insufficient" number of arguments it will just give us a new function! Here:
\pause
\begin{haskellcode}
addInt :: Int -> Int -> Int
addInt x y = x + y

addTwo :: Int -> Int
addTwo = addInt 2
\end{haskellcode}
You probably noticed that we did not write \hinline{addTwo x = ...}, but why would we? We gave \hinline{addInt} one argument, so the arity (we called it dimension in the gemoetrical example) is one less, but there is still one parameter left we can pass in.
\pause
The reason we can omit the \hinline{x} here is that
\begin{haskellcode}
f x y z = ...
\end{haskellcode}
is just syntax sugar for
\begin{haskellcode}
f = \x -> (\y -> (\z -> ... )) -- right-associative, ofc
\end{haskellcode}