Packages

trait Monoid[F] extends Semigroup[F]

Provides an identity element (zero) to the binary append operation in scalaz.Semigroup, subject to the monoid laws.

Example instances:

  • Monoid[Int]: zero and append are 0 and Int#+ respectively
  • Monoid[List[A]]: zero and append are Nil and List#++ respectively

References:

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

scalaz.syntax.MonoidOps

scalaz.Monoid.MonoidLaw

Linear Supertypes
Semigroup[F], AnyRef, Any
Known Subclasses
IsomorphismMonoid
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  1. Monoid
  2. Semigroup
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  2. Protected

Type Members

  1. trait MonoidLaw extends SemigroupLaw

    Monoid instances must satisfy scalaz.Semigroup.SemigroupLaw and 2 additional laws:

    Monoid instances must satisfy scalaz.Semigroup.SemigroupLaw and 2 additional laws:

    • left identity: forall a. append(zero, a) == a
    • right identity : forall a. append(a, zero) == a
  2. trait SemigroupApply extends Apply[[α]F]
    Attributes
    protected[this]
    Definition Classes
    Semigroup
  3. trait SemigroupCompose extends Compose[[α, β]F]
    Attributes
    protected[this]
    Definition Classes
    Semigroup
  4. 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.
    Definition Classes
    Semigroup

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.

    Definition Classes
    Semigroup
  2. abstract def zero: F

    The identity element for append.

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 applicative: Applicative[[α]F]

    A monoidal applicative functor, that implements point and ap with the operations zero and append respectively.

    A monoidal applicative functor, that implements point and ap with the operations zero and append respectively. Note that the type parameter α in Applicative[λ[α => F]] is discarded; it is a phantom type. As such, the functor cannot support scalaz.Bind.

  5. 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.

    Definition Classes
    Semigroup
  6. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  7. final def category: Category[[α, β]F]

    Every Monoid gives rise to a scalaz.Category, for which the type parameters are phantoms.

    Every Monoid gives rise to a scalaz.Category, for which the type parameters are phantoms.

    Note

    category.monoid = this

  8. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native()
  9. 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.

    Definition Classes
    Semigroup
    Note

    compose.semigroup = this

  10. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  11. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  12. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.Throwable])
  13. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  14. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  15. final def ifEmpty[B](a: F)(t: => B)(f: => B)(implicit eq: Equal[F]): B
  16. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  17. def isMZero(a: F)(implicit eq: Equal[F]): Boolean

    Whether a == zero.

  18. def monoidLaw: MonoidLaw
  19. val monoidSyntax: MonoidSyntax[F]
  20. def multiply(value: F, n: Int): F

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

  21. 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

    Definition Classes
    Semigroup
  22. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  23. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  24. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  25. final def onEmpty[A, B](a: F)(v: => B)(implicit eq: Equal[F], mb: Monoid[B]): B
  26. final def onNotEmpty[B](a: F)(v: => B)(implicit eq: Equal[F], mb: Monoid[B]): B
  27. def semigroupLaw: SemigroupLaw
    Definition Classes
    Semigroup
  28. val semigroupSyntax: SemigroupSyntax[F]
    Definition Classes
    Semigroup
  29. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  30. def toString(): String
    Definition Classes
    AnyRef → Any
  31. def unfoldlSum[S](seed: S)(f: (S) => Maybe[(S, F)]): F
  32. 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.

    Definition Classes
    Semigroup
  33. def unfoldrSum[S](seed: S)(f: (S) => Maybe[(F, S)]): F
  34. 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.

    Definition Classes
    Semigroup
  35. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  36. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException])
  37. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()

Inherited from Semigroup[F]

Inherited from AnyRef

Inherited from Any

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