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 Summary

Modifier and Type	Method and Description
A	append(A a1, A a2) Combine the two given arguments.
static <A,B> Semigroup<Pair<A,B>>	compose(Semigroup<A> sa, Semigroup<B> sb) Composes a semigroup with another.
static <A> Semigroup<A>	dual(Semigroup<A> semigroup) Return the dual Semigroup of a semigroup
default A	multiply1p(int n, A a) Returns a value summed n + 1 times ( a + a + ...
default A	sumNonEmpty(A head, Iterable<A> tail) Reduce a 'non-empty' Iterable with append(Object, Object)

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,
                      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()

compose

static <A,B> Semigroup<Pair<A,B>> compose(Semigroup<A> sa,
                                          Semigroup<B> sb)

Composes a semigroup with another.

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