Task

Create a function, compose,   whose two arguments   f   and   g,   are both functions with one argument.



The result of compose is to be a function of one argument, (lets call the argument   x),   which works like applying function    f    to the result of applying function    g    to    x.



Example

 compose(f, g) (x) = f(g(x))



Reference: Function composition

Hint: In some languages, implementing compose correctly requires creating a closure.




public class Compose {
 
    // Java doesn't have function type so we define an interface
    // of function objects instead
    public interface Fun<A,B> {
        B call(A x);
    }
 
    public static <A,B,C> Fun<A,C> compose(final Fun<B,C> f, final Fun<A,B> g) {
        return new Fun<A,C>() {
            public C call(A x) {
                return f.call(g.call(x));
            }
        };
    }
 
    public static void main(String[] args) {
        Fun<Double,Double> sin = new Fun<Double,Double>() {
            public Double call(Double x) {
                return Math.sin(x);
            }
        };
        Fun<Double,Double> asin = new Fun<Double,Double>() {
            public Double call(Double x) {
                return Math.asin(x);
            }
        };
 
        Fun<Double,Double> sin_asin = compose(sin, asin);
 
        System.out.println(sin_asin.call(0.5)); // prints "0.5"
    }
}