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:

  • Method Summary

    Modifier and Type
    Method
    Description
    static <A,B> Monoid<Pair<A,B>>
    compose(Monoid<A> ma, Monoid<B> mb)
    Composes a monoid with another.
    static <A> Monoid<A>
    dual(Monoid<A> monoid)
    Return the dual Monoid.
    default A
    intersperse(Iterable<? extends A> as, A a)
    Intersperses the given value between each two elements of the collection, and sums the result.
    default A
    multiply(int n, A a)
    Returns a value summed n times (a + a + ...
    default A
    multiply1p(int n, A a)
    Returns a value summed n + 1 times ( a + a + ...
    default A
    sum(Iterable<A> as)
    Sums the given values.
    default A
    sumNonEmpty(A head, Iterable<A> tail)
    Reduce a 'non-empty' Iterable with Semigroup.append(Object, Object)
    A
    zero()
    The identity element value for this monoid.

    Methods inherited from interface Semigroup

    append

  • Method Details

    • zero

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

    • sum

      default A sum(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(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, 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,