I've long been thinking the same thing. In many fields of mathematics the placeholder $ from the OP is often written •, i.e. partial function application is written as f(a, b, •). I've always found it weird that most functional languages, particularly heavily math-inspired ones like Haskell, deviate from that. Yes, there are isomorphisms left and right but at the end of the day you have to settle on one category and one syntax. A function f: A × B -> C is simply not the same thing as a function f: A -> B -> C. Stop treating it like it is.