On Jan 26, 2010, at 8:11 AM, Xingzhi Pan wrote:
I'm a little confused with the type of step here. Can it be considered as taking 2 or 3 arguments and then the compiler has to infer to decide?
The compiler is going to build up a sequence of functions. Consider the following (mathematical) function: f(x, y, z) = x^2 + y^2 + z^2. This is a function in three arguments. But if you bind any of them (say, x) to a value x', you end up with a function g(y,z) = f(x',y,z). This is a function in two arguments. Bind another variable, and you get another function, with one less argument. You need to bind all the variables in order to compute f for a point.
Say if I, as a code reader, meet such a function defined with three formal parameters, how can I draw the conclusion of its type (and it takes 2 arguments actually)?
You can derive this from the syntactic properties of types. Count the number of arrows that are not "in parentheses". That's how many arguments the function takes. f :: a -> b -> c is a function that takes an a, a b, and returns a c. g :: (a -> b) -> c takes one argument, which is expected to be a function from a to b. g returns a c. That stuff I mentioned before about variable binding and function application still applies. We can show that f and g have "isomorphic" types. But they are conceptually different types.