I'm not a mathematician, sorry...
My question is best explained with an example:
I have lots of functions (programs in a functional programming language) in which the domain and codomain are lists of integers. These functions, given lists of integers return other lists.
Then I have other kinds of functions in which the domain is the previous mentioned functions, and the codomain is a real number. These functions given one of the previous ones return an error measure (this error is some measure of the difference between the returned list and the given list, the one given as input, but in sorted order).
So my question is if there is a branch of mathematics that studies this kind of stuff, these "functions of functions".
Any help is much appreciated.