It's not defining a function though, it's describing (by one aspect) a whole class of functions.
Take:
f: ints -> ints
If you know that, and calling it 'defining a function' is just loose English (you didn't mean completely defining) then fine, but that's what's confusing people.
It read to me like you thought it was equivalent to a function definition in code, X & Y described what would actually happen over different inputs, so I was just trying to explain, didn't mean to offend if you knew already.