Does JDK8's Optional class satisfy the Monad laws? Yes, it does.

jdk8_optional_monad_laws.java

/**
 * ```
 * Does JDK8's Optional class satisfy the Monad laws?
 * =================================================
 *   1.  Left identity:  true
 *   2.  Right identity: true
 *   3.  Associativity:  true
 *
 * Yes, it does. 
 * ```
 *
 * To install the JDK8 Early Access release via Ubuntu PPA, see:
 *   http://www.webupd8.org/2012/09/install-oracle-java-8-in-ubuntu-via-ppa.html
 *
 * For more info on the monad laws, see:
 *   [1] http://learnyouahaskell.com/a-fistful-of-monads#monad-laws
 *   [2] http://eed3si9n.com/learning-scalaz/Monad+laws.html
 *   [3] http://en.wikipedia.org/wiki/Monad_(functional_programming)#Monad_laws
 *
 * NOTE: Code below does *not* use lambdas, because the mainline Java 8 Early
 *   Access builds installed by the PPA do not yet include lambda expressions.
 *
 * @author Marc Siegel <marc.siegel@timgroup.com>
 */
import java.util.function.Function;
import java.util.Optional;

class jdk8_optional_monad_laws {
    public static void main (String[] args) throws java.lang.Exception
    {
        System.out.println("");
        System.out.println("Does JDK8's Optional class satisfy the Monad laws?");
        System.out.println("=================================================");
        System.out.println("  1.  Left identity:  " + satisfiesLaw1LeftIdentity());
        System.out.println("  2.  Right identity: " + satisfiesLaw2RightIdentity());
        System.out.println("  3.  Associativity:  " + satisfiesLaw3Associativity());
        System.out.println("");
        System.out.println(satisfiesLaw1LeftIdentity() 
                           && satisfiesLaw2RightIdentity()
                           && satisfiesLaw3Associativity()
                           ? "Yes, it does."
                           : "No, it doesn't.");
    }

    // Input values for the monad law tests below
    static int value = 42;
    static Optional monadicValue = Optional.of(value);

    // With lambdas, this entire thing goes away (pass `Optional.of` directly)
    static Function optionalOf = new Function<Integer, Optional<Integer>>() { 
        @Override public Optional<Integer> apply(Integer n) { return Optional.of(n); }
    };

    // With lambdas, this becomes `n -> Optional.of(n * 2)`
    static Function f = new Function<Integer, Optional<Integer>>() { 
        @Override public Optional<Integer> apply(Integer n) { return Optional.of(n * 2); } 
    };

    // With lambdas, this becomes `n -> Optional.of(n * 5)`
    static Function g = new Function<Integer, Optional<Integer>>() { 
        @Override public Optional<Integer> apply(Integer n) { return Optional.of(n * 5); } 
    };

    // With lambdas, this becomes `n -> f(n).flatMap(g)`
    static Function f_flatMap_g = new Function<Integer, Optional<Integer>>() { 
        @Override public Optional<Integer> apply(Integer n) { return ((Optional<Integer>) f.apply(n)).flatMap(g); }  
        // NOTE (2013-11-11): Bug in latest JDK8 requires this cast:  ^^^^^^^^^^^^^^^^^^^
    };


    /**
     * Monad law 1, Left Identity
     *
     * From LYAHFGG [1] above: 
     *   The first monad law states that if we take a value, put it in a default context 
     *   with return and then feed it to a function by using >>=, it’s the same as just 
     *   taking the value and applying the function to it
     */
    public static boolean satisfiesLaw1LeftIdentity() {
        return Optional.of(value).flatMap(f)
            .equals(f.apply(value));
    }

    /**
     * Monad law 2, Right Identity
     *
     * From LYAHFGG [1] above: 
     *   The second law states that if we have a monadic value and we use >>= to feed 
     *   it to return, the result is our original monadic value.
     */
    public static boolean satisfiesLaw2RightIdentity() {
        return monadicValue.flatMap(optionalOf)
            .equals(monadicValue);
    }

    /**
     * Monad law 3, Associativity
     *
     * From LYAHFGG [1] above: 
     *   The final monad law says that when we have a chain of monadic function 
     *   applications with >>=, it shouldn’t matter how they’re nested.
     */
    public static boolean satisfiesLaw3Associativity() {
        return monadicValue.flatMap(f).flatMap(g)
            .equals(monadicValue.flatMap(f_flatMap_g));
    }
}