Packages

trait Semigroup[F] extends AnyRef

An associative binary operation, circumscribed by type and the semigroup laws. Unlike scalaz.Monoid, there is not necessarily a zero.

Self Type
Semigroup[F]
Source
Semigroup.scala
See also

scalaz.Semigroup.SemigroupLaw

scalaz.syntax.SemigroupOps

http://mathworld.wolfram.com/Semigroup.html

Linear Supertypes
AnyRef, Any
Known Subclasses
Band, ComposeSemigroup, IsomorphismBand, IsomorphismMonoid, IsomorphismSemiLattice, IsomorphismSemigroup, Monoid, SemiLattice
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Type Members

  1. trait SemigroupApply extends Apply[[α]F]
    Attributes
    protected[this]
  2. trait SemigroupCompose extends Compose[[α, β]F]
    Attributes
    protected[this]
  3. trait SemigroupLaw extends AnyRef

    A semigroup in type F must satisfy two laws:

    A semigroup in type F must satisfy two laws:

    • closure: ∀ a, b in F, append(a, b) is also in F. This is enforced by the type system.
    • associativity: ∀ a, b, c in F, the equation append(append(a, b), c) = append(a, append(b , c)) holds.

Abstract Value Members

  1. abstract def append(f1: F, f2: => F): F

    The binary operation to combine f1 and f2.

    The binary operation to combine f1 and f2.

    Implementations should not evaluate the by-name parameter f2 if result can be determined by f1.

Concrete Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. final def apply: Apply[[α]F]

    An scalaz.Apply, that implements ap with append.

    An scalaz.Apply, that implements ap with append. Note that the type parameter α in Apply[λ[α => F]] is discarded; it is a phantom type. As such, the functor cannot support scalaz.Bind.

  5. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  6. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native()
  7. final def compose: Compose[[α, β]F]

    Every Semigroup gives rise to a scalaz.Compose, for which the type parameters are phantoms.

    Every Semigroup gives rise to a scalaz.Compose, for which the type parameters are phantoms.

    Note

    compose.semigroup = this

  8. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  9. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  10. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable])
  11. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  12. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  13. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  14. def multiply1(value: F, n: Int): F

    For n = 0, value For n = 1, append(value, value) For n = 2, append(append(value, value), value)

    For n = 0, value For n = 1, append(value, value) For n = 2, append(append(value, value), value)

    The default definition uses peasant multiplication, exploiting associativity to only require O(log n) uses of append

  15. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  16. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  17. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  18. def semigroupLaw: SemigroupLaw
  19. val semigroupSyntax: SemigroupSyntax[F]
  20. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  21. def toString(): String
    Definition Classes
    AnyRef → Any
  22. def unfoldlSumOpt[S](seed: S)(f: (S) => Maybe[(S, F)]): Maybe[F]

    Unfold seed to the left and sum using #append.

    Unfold seed to the left and sum using #append. Semigroups with right absorbing elements may override this method to not unfold more than is necessary to determine the result.

  23. def unfoldrSumOpt[S](seed: S)(f: (S) => Maybe[(F, S)]): Maybe[F]

    Unfold seed to the right and sum using #append.

    Unfold seed to the right and sum using #append. Semigroups with left absorbing elements may override this method to not unfold more than is necessary to determine the result.

  24. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  25. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  26. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()

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