ZeroGroup

Return the absorbing element for this zero semigroup.

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)

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 = ""

Return a appended to itself n times. If n is negative, then this returns inverse(a) appended to itself n times.

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

Between each pair of elements insert middle This name matches the term used in Foldable and Reducible and a similar Haskell function.

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

Tests if a is the absorbing element.

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

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