A function with type A -> B is essentially equivalent to an object of type B^A. I can give you some relatively intuition for the case that A is finite. Imagine B^|A|, this is a list of B elements with one for every element in A. You can therefore interpret it as the return value for every possible input. Therefore it uniquely defines a function A -> B!
The type of pairs is just the cartesian product. Therefore (A×B)->C ~ C^(A×B) = (C^B)^A ~ A->B->C.
If you find this sort of thing, you might be interested in category theory :)
The type of pairs is just the cartesian product. Therefore (A×B)->C ~ C^(A×B) = (C^B)^A ~ A->B->C.
If you find this sort of thing, you might be interested in category theory :)