story
map f [] = []
map f (x:xs) = f x : map f xs
You're supposed to infer from the short function names that f and x could be anything. The only important bit is that you can apply one argument to f (so, for example, f could take two parameters, and then map is just doing a single partial application). In that context, x and xs is actually a better convention than "first" and "rest", because they indicate the adherence to the type system. The naming here is saying that x is of the type of elements of xs, and that this is the only important information for map. This seriously helps in more complicated functions like zip, etc.