scalaz

IsomorphismMonoid

trait IsomorphismMonoid[F, G] extends Monoid[F] with IsomorphismSemigroup[F, G]

Source
Isomorphism.scala
Linear Supertypes
IsomorphismSemigroup[F, G], Monoid[F], Semigroup[F], AnyRef, Any
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Inherited
  1. IsomorphismMonoid
  2. IsomorphismSemigroup
  3. Monoid
  4. Semigroup
  5. AnyRef
  6. Any
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  1. Public
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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
    Definition Classes
    Monoid
  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. implicit abstract def G: Monoid[G]

  2. abstract def iso: Isomorphism.<=>[F, G]

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. 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 tbe by-name parameter f2 if result can be determined by f1.

    Definition Classes
    IsomorphismSemigroupSemigroup
  5. 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[({type λ[α]=F})#λ] is discarded; it is a phantom type. As such, the functor cannot support scalaz.Bind.

    Definition Classes
    Monoid
  6. 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[({type λ[α]=F})#λ] is discarded; it is a phantom type. As such, the functor cannot support scalaz.Bind.

    Definition Classes
    Semigroup
  7. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  8. 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.

    Definition Classes
    Monoid
    Note

    category.monoid = this

  9. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  10. 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

  11. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  12. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any
  13. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  14. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any
  15. def hashCode(): Int

    Definition Classes
    AnyRef → Any
  16. final def ifEmpty[B](a: F)(t: ⇒ B)(f: ⇒ B)(implicit eq: Equal[F]): B

    Definition Classes
    Monoid
  17. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any
  18. def isMZero(a: F)(implicit eq: Equal[F]): Boolean

    Whether a == zero.

    Whether a == zero.

    Definition Classes
    Monoid
  19. def monoidLaw: MonoidLaw

    Definition Classes
    Monoid
  20. val monoidSyntax: MonoidSyntax[F]

    Definition Classes
    Monoid
  21. 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)

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

    Definition Classes
    Monoid
  22. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  23. final def notify(): Unit

    Definition Classes
    AnyRef
  24. final def notifyAll(): Unit

    Definition Classes
    AnyRef
  25. final def onEmpty[A, B](a: F)(v: ⇒ B)(implicit eq: Equal[F], mb: Monoid[B]): B

    Definition Classes
    Monoid
  26. final def onNotEmpty[B](a: F)(v: ⇒ B)(implicit eq: Equal[F], mb: Monoid[B]): B

    Definition Classes
    Monoid
  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. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  32. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  33. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  34. def zero: F

    The identity element for append.

    The identity element for append.

    Definition Classes
    IsomorphismMonoidMonoid

Inherited from IsomorphismSemigroup[F, G]

Inherited from Monoid[F]

Inherited from Semigroup[F]

Inherited from AnyRef

Inherited from Any

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