A - A type.public interface Monoid<A> extends Semigroup<A>
A Monoid is a Semigroup (types with an associative binary operation) that has an
identity element zero.
Given a type A, instances of Monoid should satisfy the following laws:
combine(combine(x,y),z) == combine(x,combine(y,z)) for any x,y,z of type
A.combine(zero(), x) == x == combine(x, zero()) for any x of type A.Example: String is a Monoid with zero "" (empty String) and String concatenation
+ as combine operation.
Please note that some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers.
Folding:| Modifier and Type | Method and Description |
|---|---|
static <A> Monoid<Function<A,A>> |
endoMonoid()
The monoid of endomorphisms under composition.
|
static <T> T |
fold(Monoid<T> monoid,
Foldable<T> foldable)
Folds the elements of
Foldable from the left, starting with monoid.zero()
and successively calling monoid::combine. |
static <T> T |
foldLeft(Monoid<T> monoid,
Foldable<T> foldable)
Folds the elements of
Foldable from the left, starting with monoid.zero()
and successively calling monoid::combine. |
static <T,U> U |
foldMap(Monoid<U> monoid,
Foldable<T> foldable,
Function<? super T,? extends U> mapper)
Maps this elements to a
Monoid and applies foldLeft, starting with monoid.zero(): |
static <T> T |
foldRight(Monoid<T> monoid,
Foldable<T> foldable)
Folds this elements from the right, starting with
monoid.zero() and successively calling monoid::combine. |
static <A> Monoid<A> |
of(A zero,
Semigroup<A> semigroup)
Factory method for monoids, taking a zero and a Semigroup.
|
A |
zero()
The unique neutral element regarding Semigroup.combine(Object, Object).
|
static <A> Monoid<A> of(A zero, Semigroup<A> semigroup)
A - Value typezero - The zero of the Monoid.semigroup - The associative binary operation of the Monoid. Please note that
Semigroup is a FunctionalInterface.NullPointerException - if semigroup is nullstatic <A> Monoid<Function<A,A>> endoMonoid()
A - Value typeA zero()
static <T> T fold(Monoid<T> monoid, Foldable<T> foldable)
Foldable from the left, starting with monoid.zero()
and successively calling monoid::combine.T - type of the foldable elementsmonoid - A monoid, providing a zero and a combine function.foldable - A foldableNullPointerException - if monoid or foldable is nullstatic <T> T foldLeft(Monoid<T> monoid, Foldable<T> foldable)
Foldable from the left, starting with monoid.zero()
and successively calling monoid::combine.T - type of the foldable elementsmonoid - A monoid, providing a zero and a combine function.foldable - A foldableNullPointerException - if monoid is nullstatic <T,U> U foldMap(Monoid<U> monoid, Foldable<T> foldable, Function<? super T,? extends U> mapper)
Monoid and applies foldLeft, starting with monoid.zero():
foldLeft(monoid.zero(), (ys, x) -> monoid.combine(ys, mapper.apply(x)));
T - type of the foldable elementsU - Component type of the given monoid.monoid - A Monoidfoldable - A foldablemapper - A mapperNullPointerException - if monoid or mapper is nullstatic <T> T foldRight(Monoid<T> monoid, Foldable<T> foldable)
monoid.zero() and successively calling monoid::combine.T - type of the foldable elementsmonoid - A monoid, providing a zero and a combine function.foldable - A foldableNullPointerException - if monoid is nullCopyright © 2017. All Rights Reserved.