Packages

t

scalaz

IsomorphismMonoid

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

Source
Monoid.scala
Linear Supertypes
IsomorphismSemigroup[F, G], Monoid[F], Semigroup[F], AnyRef, Any
Ordering
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  2. By Inheritance
Inherited
  1. IsomorphismMonoid
  2. IsomorphismSemigroup
  3. Monoid
  4. Semigroup
  5. AnyRef
  6. Any
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Visibility
  1. Public
  2. All

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]
    Definition Classes
    IsomorphismMonoid → IsomorphismSemigroup
  2. abstract def iso: Isomorphism.<=>[F, G]
    Definition Classes
    IsomorphismSemigroup

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

    Definition Classes
    IsomorphismSemigroup → Semigroup
  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[λ[α => F]] 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[λ[α => F]] 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[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native()
  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[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  14. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  15. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  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. 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
  23. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  24. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  25. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  26. final def onEmpty[A, B](a: F)(v: ⇒ B)(implicit eq: Equal[F], mb: Monoid[B]): B
    Definition Classes
    Monoid
  27. final def onNotEmpty[B](a: F)(v: ⇒ B)(implicit eq: Equal[F], mb: Monoid[B]): B
    Definition Classes
    Monoid
  28. def semigroupLaw: SemigroupLaw
    Definition Classes
    Semigroup
  29. val semigroupSyntax: SemigroupSyntax[F]
    Definition Classes
    Semigroup
  30. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  31. def toString(): String
    Definition Classes
    AnyRef → Any
  32. def unfoldlSum[S](seed: S)(f: (S) ⇒ Maybe[(S, F)]): F
    Definition Classes
    Monoid
  33. 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
  34. def unfoldrSum[S](seed: S)(f: (S) ⇒ Maybe[(F, S)]): F
    Definition Classes
    Monoid
  35. 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
  36. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  37. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  38. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native()
  39. def zero: F

    The identity element for append.

    The identity element for append.

    Definition Classes
    IsomorphismMonoid → Monoid

Inherited from IsomorphismSemigroup[F, G]

Inherited from Monoid[F]

Inherited from Semigroup[F]

Inherited from AnyRef

Inherited from Any

Ungrouped