Package io.atlassian.fugue

Interface Monoid<A>

  • All Superinterfaces:
    Semigroup<A>
    public interface Monoid<A>
extends Semigroup<A>
    A Monoid is an algebraic structure consisting of an associative binary operation across the values of a given type (a monoid is a Semigroup) and an identity element for this operation. Implementations must follow the monoidal laws:
    • Left Identity; forall x. append(zero(), x) == x
    • Right Identity; forall x. append(x, zero()) == x
    • Associativity; forall x y z. append(append(x, y), z) == append(x, append(y, z))
    Methods sum(Iterable) and multiply(int, Object) can be overriden for performance reason, especially if sum(Iterable) can be implemented to not require evaluation of the whole iterable. All other default methods should not be overriden.
    Since:
    3.1
    See Also:
    Semigroup

    • Method Detail

      • zero

        A zero()
        The identity element value for this monoid.
        Returns:
        The identity element for this monoid.

      • sum

        default A sum​(java.lang.Iterable<A> as)
        Sums the given values.
        Parameters:
        as - The values to sum.
        Returns:
        The sum of the given values.

      • multiply

        default A multiply​(int n,
                   A a)
        Returns a value summed n times (a + a + ... + a). The default definition uses peasant multiplication, exploiting associativity to only require `O(log n)` uses of Semigroup.append(Object, Object).
        Parameters:
        n - multiplier
        a - the value to be reapeatly summed
        Returns:
        a summed n times. If n <= 0, returns zero()

      • intersperse

        default A intersperse​(java.lang.Iterable<? extends A> as,
                      A a)
        Intersperses the given value between each two elements of the collection, and sums the result.
        Parameters:
        as - An iterable of values.
        a - The value to intersperse between values of the given iterable.
        Returns:
        The sum of the given values and the interspersed value.

      • sumNonEmpty

        default A sumNonEmpty​(A head,
                      java.lang.Iterable<A> tail)
        Description copied from interface: Semigroup
        Reduce a 'non-empty' Iterable with Semigroup.append(Object, Object)
        Specified by:
        sumNonEmpty in interface Semigroup<A>
        Parameters:
        head - the head of the 'non-empty' Iterable
        tail - the tail (maybe an empty Iterable).
        Returns:
        the sum of all elements.

      • multiply1p

        default A multiply1p​(int n,
                     A a)
        Description copied from interface: Semigroup
        Returns a value summed n + 1 times ( a + a + ... + a) The default definition uses peasant multiplication, exploiting associativity to only require `O(log n)` uses of Semigroup.append(Object, Object).
        Specified by:
        multiply1p in interface Semigroup<A>
        Parameters:
        n - multiplier
        a - the value to be reapeatly summed n + 1 times
        Returns:
        a summed n times. If n <= 0, returns zero()

      • compose

        static <A,​B> Monoid<Pair<A,​B>> compose​(Monoid<A> ma,
                                                   Monoid<B> mb)
        Composes a monoid with another.

      • dual

        static <A> Monoid<A> dual​(Monoid<A> monoid)
        Return the dual Monoid.
        Parameters:
        monoid - a monoid.
        Returns:
        a Monoid appending in reverse order,