Monoid

A monoid is a semigroup with an identity. A monoid is a specialization of a semigroup, so its operation must be associative. Additionally, op(x, id) == op(id, x) == x. For example, if we have Monoid[String], with op as string concatenation, then id = "".

Linear Supertypes

Semigroup[A], AnyRef, Any

Known Subclasses

AbGroup, CMonoid, Group, IterableMonoid, MapGroup, MapMonoid, OptionMonoid, SignAlgebra, StringMonoid

Abstract Value Members

abstract def id: A

Return the identity element for this monoid.
abstract def op(x: A, y: A): A

Definition Classes
Semigroup

Concrete Value Members

final def !=(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def ##(): Int

Definition Classes
AnyRef → Any
final def ==(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def asInstanceOf[T0]: T0

Definition Classes
Any
def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
final def eq(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def equals(arg0: Any): Boolean

Definition Classes
AnyRef → Any
def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
final def getClass(): Class[_]

Definition Classes
AnyRef → Any
def hashCode(): Int

Definition Classes
AnyRef → Any
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
final def notify(): Unit

Definition Classes
AnyRef
final def notifyAll(): Unit

Definition Classes
AnyRef
def sum(as: TraversableOnce[A]): A

Given a sequence of as, sum them using the monoid and return the total.
def sumOption(as: TraversableOnce[A]): Option[A]

Given a sequence of as, sum them using the semigroup and return the total.
Given a sequence of as, sum them using the semigroup and return the total.
If the sequence is empty, returns None. Otherwise, returns Some(total).

Definition Classes
Semigroup
def sumn(a: A, n: Int): A

Return a combined with itself n times.
Return a combined with itself n times.

Definition Classes
Monoid → Semigroup
def sumnAboveOne(a: A, n: Int): A

Attributes
protected
Definition Classes
Semigroup
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
def toString(): String

Definition Classes
AnyRef → Any
final def wait(): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )

trait Monoid[A] extends Semigroup[A]

Abstract Value Members

abstract def id: A

abstract def op(x: A, y: A): A

Concrete Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

final def asInstanceOf[T0]: T0

def clone(): AnyRef

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

def finalize(): Unit

final def getClass(): Class[_]

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

final def ne(arg0: AnyRef): Boolean

final def notify(): Unit

final def notifyAll(): Unit

def sum(as: TraversableOnce[A]): A

def sumOption(as: TraversableOnce[A]): Option[A]

def sumn(a: A, n: Int): A

def sumnAboveOne(a: A, n: Int): A

final def synchronized[T0](arg0: ⇒ T0): T0

def toString(): String

final def wait(): Unit

final def wait(arg0: Long, arg1: Int): Unit

final def wait(arg0: Long): Unit

Inherited from Semigroup[A]

Inherited from AnyRef

Inherited from Any

Ungrouped