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, conjunction, disjunction, MapMonoid, stringInstance
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Semigroup
  2. AnyRef
  3. Any
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

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( ... ) @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: Any): 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[_]
    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. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  23. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  24. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native()

Inherited from AnyRef

Inherited from Any

Ungrouped