Implementing compose using only Function<> in java 8

Question

In the book Functional Programming in Java the author builds a compose function using only the Function<T, U> interface (the interface however is not one shipped with Java 8 but very similar though) the snippet of which is show below

public interface Function<T, U> {
  U apply(T arg);
}

though I could understand the method version of compose below, which takes in 2 functions and return a composed function

public static final Function<Integer, Integer> compose (final Function<Integer, Integer> f1, 
                                   final Function<Integer, Integer> f2) {
         arg -> f1.apply(f2.apply(arg));
}

I just couldn't get my head around the below compose implementation with Function<> and lambdas

static Function<Function<Integer, Integer>,
            Function<Function<Integer, Integer>,
                    Function<Integer, Integer>>> compose =
            x -> y -> z -> x.apply(y.apply(z));

PS: couldn't get my mind out of this and move forward with remaining sections :(

Answer 1

Referring to a Function<Integer, Integer> as an integer function, what you have there is a function that maps {an integer function} to {a function mapping an integer function to another integer function}.

Specifically, when given an integer function x, it returns a function that, given an integer function y, returns an integer function that maps an integer z to x(y(z)).

Given a function x
Returns a function that:
    Given a function y
    Returns a function that:
        Given an integer z
        Returns x(y(z))