Packages

t

scalaz

IsomorphismSemigroup

trait IsomorphismSemigroup[F, G] extends Semigroup[F]

Source
Isomorphism.scala
Linear Supertypes
Semigroup[F], AnyRef, Any
Known Subclasses
IsomorphismMonoid
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Inherited
  1. IsomorphismSemigroup
  2. Semigroup
  3. AnyRef
  4. Any
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Visibility
  1. Public
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Type Members

  1. trait SemigroupApply extends Apply[[α]F]
    Attributes
    protected[this]
    Definition Classes
    Semigroup
  2. trait SemigroupCompose extends Compose[[α, β]F]
    Attributes
    protected[this]
    Definition Classes
    Semigroup
  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.
    Definition Classes
    Semigroup

Abstract Value Members

  1. implicit abstract def G: Semigroup[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 the by-name parameter f2 if result can be determined by f1.

    Definition Classes
    IsomorphismSemigroup → Semigroup
  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. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )
  8. 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

  9. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  10. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  11. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  12. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  13. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  14. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  15. 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
  16. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  17. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  18. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  19. def semigroupLaw: SemigroupLaw
    Definition Classes
    Semigroup
  20. val semigroupSyntax: SemigroupSyntax[F]
    Definition Classes
    Semigroup
  21. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  22. def toString(): String
    Definition Classes
    AnyRef → Any
  23. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  24. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  25. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @throws( ... )

Inherited from Semigroup[F]

Inherited from AnyRef

Inherited from Any

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