A commutative zero group is a commutative group with an absorbing element
that satisfies combine(x, absorbing) == combine(absorbing, x) == absorbing
.
A commutative zero group is a commutative group with an absorbing element
that satisfies combine(x, absorbing) == combine(absorbing, x) == absorbing
.
- Companion
- object
Value members
Inherited methods
Return the absorbing element for this zero semigroup.
Return the absorbing element for this zero semigroup.
- Inherited from
- ZeroSemigroup
Associative operation which combines two values.
Associative operation which combines two values.
Example:
scala> import cats.kernel.instances.string._
scala> import cats.kernel.instances.int._
scala> import cats.kernel.instances.option._
scala> Semigroup[String].combine("Hello ", "World!")
res0: String = Hello World!
scala> Semigroup[Option[Int]].combine(None, Some(1))
res1: Option[Int] = Some(1)
- Inherited from
- Semigroup
Given a sequence of as
, sum them using the monoid and return the total.
Given a sequence of as
, sum them using the monoid and return the total.
Example:
scala> import cats.kernel.instances.string._
scala> Monoid[String].combineAll(List("One ", "Two ", "Three"))
res0: String = One Two Three
scala> Monoid[String].combineAll(List.empty)
res1: String = ""
- Inherited from
- Monoid
Return a
appended to itself n
times. If n
is negative, then
this returns inverse(a)
appended to itself n
times.
Return a
appended to itself n
times. If n
is negative, then
this returns inverse(a)
appended to itself n
times.
- Definition Classes
- Group -> Monoid -> Semigroup
- Inherited from
- Group
Return the identity element for this monoid.
Return the identity element for this monoid.
Example:
scala> import cats.kernel.instances.int._
scala> import cats.kernel.instances.string._
scala> Monoid[String].empty
res0: String = ""
scala> Monoid[Int].empty
res1: Int = 0
- Inherited from
- Monoid
Find the inverse of a
.
Find the inverse of a
.
combine(a, inverse(a))
= combine(inverse(a), a)
= empty
.
Example:
scala> import cats.kernel.instances.int._
scala> Group[Int].inverse(5)
res0: Int = -5
- Inherited from
- Group
Tests if a
is the absorbing element.
Tests if a
is the absorbing element.
- Inherited from
- ZeroSemigroup
Tests if a
is the identity.
Tests if a
is the identity.
Example:
scala> import cats.kernel.instances.string._
scala> Monoid[String].isEmpty("")
res0: Boolean = true
scala> Monoid[String].isEmpty("something")
res1: Boolean = false
- Inherited from
- Monoid
Remove the element b
from a
.
Remove the element b
from a
.
Equivalent to combine(a, inverse(b))
Example:
scala> import cats.kernel.instances.int._
scala> Group[Int].remove(5, 2)
res0: Int = 3
- Inherited from
- Group
- Definition Classes
- CommutativeZeroMonoid -> CommutativeZeroSemigroup -> CommutativeMonoid -> CommutativeSemigroup -> ZeroMonoid -> ZeroSemigroup -> Monoid -> Semigroup
- Inherited from
- CommutativeZeroMonoid