Package io.atlassian.fugue

Interface Semigroup<A>

  • All Known Subinterfaces:
    Monoid<A>
    public interface Semigroup<A>
    A Semigroup is an algebraic structure consisting of an associative binary operation across the values of a given type (the Semigroup type argument). Implementations must satisfy the law of associativity:
    • Associativity; forall x y z. append(append(x, y), z) == append(x, append(y, z))
    Methods sumNonEmpty(Object, Iterable) and multiply1p(int, Object) can be overriden for performance reason, especially if sumNonEmpty(Object, Iterable) can be implemented to not require evaluation of the whole iterable.
    Since:
    3.1
    See Also:
    Monoid

    • Method Detail

      • append

        A append​(A a1,
         A a2)
        Combine the two given arguments.
        Parameters:
        a1 - left value to combine
        a2 - right value to combine
        Returns:
        the combination of the left and right value.

      • sumNonEmpty

        default A sumNonEmpty​(A head,
                      java.lang.Iterable<A> tail)
        Reduce a 'non-empty' Iterable with append(Object, Object)
        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)
        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 append(Object, Object).
        Parameters:
        n - multiplier
        a - the value to be reapeatly summed n + 1 times
        Returns:
        a summed n times. If n <= 0, returns zero()

      • dual

        static <A> Semigroup<A> dual​(Semigroup<A> semigroup)
        Return the dual Semigroup of a semigroup
        Parameters:
        semigroup - base semigroup to create the dual from
        Returns:
        a semigroup appending in reverse order