Freer Monads in java

Freer.java

import java.util.function.Function;

// straight forward port of freer monads to java
// see http://okmij.org/ftp/Computation/free-monad.html


// lightweight higher kinded polymorphism
// see http://ocamllabs.io/higher/lightweight-higher-kinded-polymorphism.pdf

interface App<F,A> {}

// freer monads have an exstential type
// so pattern matching on them requires a rank n type

interface View<R, F, A> {
    R pure(A pure);
    <X> R impure(App<F, X> now, Function<X, Freer<F, A>> after);
}

// the 2 constructors for freer monads

class Pure<F, A> extends Freer<F, A> {
    final A pure;
    Pure(A pure) {
        this.pure = pure;
    }
    <R> R match(View<R, F, A> view) {
        return view.pure(pure);
    }
}

class Impure<X, F, A> extends Freer<F, A> {
    final App<F, X> now;
    final Function<X, Freer<F,A>> after;
    Impure(App<F, X> now, Function<X, Freer<F, A>> after) {
        this.now = now;
        this.after = after;
    }

    <R> R match(View<R, F, A> view) {
        return view.impure(now, after);
    }
}

public abstract class Freer<F, A> implements App<App<Freer<?, ?>, F>, A> {
    abstract <R> R match(View<R, F, A> view);

    // monadic bind
    final <B> Freer<F, B> flatMap(Function<A, Freer<F, B>> lastly) {
        return match(new View<Freer<F, B>, F, A>() {
            public Freer<F, B> pure(A pure) {
                return lastly.apply(pure);
            }
            public <X> Freer<F, B> impure(App<F, X> now, Function<X, Freer<F, A>> after) {
                return new Impure<X, F, B>(now, x -> after.apply(x).flatMap(lastly) );
            }
        });
    }

    // convert a F a to Freer F a
    static <F, A> Freer<F, A> eta(App<F, A> effect) {
        return impure(effect, Freer::pure);
    }
}