trait IsomorphismMonoid[F, G] extends Monoid[F] with IsomorphismSemigroup[F, G]
- Source
- Isomorphism.scala
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- By Inheritance
- IsomorphismMonoid
- IsomorphismSemigroup
- Monoid
- Semigroup
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- Any
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Type Members
- 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
- left identity:
- trait SemigroupApply extends Apply[[α]F]
- Attributes
- protected[this]
- Definition Classes
- Semigroup
- trait SemigroupCompose extends Compose[[α, β]F]
- Attributes
- protected[this]
- Definition Classes
- Semigroup
- 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 inF. This is enforced by the type system. - associativity:
∀ a, b, cinF, the equationappend(append(a, b), c) = append(a, append(b , c))holds.
- Definition Classes
- Semigroup
- closure:
Abstract Value Members
- implicit abstract def G: Monoid[G]
- Definition Classes
- IsomorphismMonoid → IsomorphismSemigroup
- abstract def iso: Isomorphism.<=>[F, G]
- Definition Classes
- IsomorphismSemigroup
Concrete Value Members
- final def !=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- final def ##: Int
- Definition Classes
- AnyRef → Any
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- def append(f1: F, f2: => F): F
The binary operation to combine
f1andf2.The binary operation to combine
f1andf2.Implementations should not evaluate the by-name parameter
f2if result can be determined byf1.- Definition Classes
- IsomorphismSemigroup → Semigroup
- final def applicative: Applicative[[α]F]
A monoidal applicative functor, that implements
pointandapwith the operationszeroandappendrespectively.A monoidal applicative functor, that implements
pointandapwith the operationszeroandappendrespectively. Note that the type parameterαinApplicative[λ[α => F]]is discarded; it is a phantom type. As such, the functor cannot support scalaz.Bind.- Definition Classes
- Monoid
- final def apply: Apply[[α]F]
An scalaz.Apply, that implements
apwithappend.An scalaz.Apply, that implements
apwithappend. Note that the type parameterαinApply[λ[α => F]]is discarded; it is a phantom type. As such, the functor cannot support scalaz.Bind.- Definition Classes
- Semigroup
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- final def category: Category[[α, β]F]
Every
Monoidgives rise to a scalaz.Category, for which the type parameters are phantoms.Every
Monoidgives rise to a scalaz.Category, for which the type parameters are phantoms.- Definition Classes
- Monoid
- Note
category.monoid=this
- def clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @native()
- final def compose: Compose[[α, β]F]
Every
Semigroupgives rise to a scalaz.Compose, for which the type parameters are phantoms.Every
Semigroupgives rise to a scalaz.Compose, for which the type parameters are phantoms.- Definition Classes
- Semigroup
- Note
compose.semigroup=this
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def equals(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef → Any
- def finalize(): Unit
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.Throwable])
- final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
- def hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
- final def ifEmpty[B](a: F)(t: => B)(f: => B)(implicit eq: Equal[F]): B
- Definition Classes
- Monoid
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- def isMZero(a: F)(implicit eq: Equal[F]): Boolean
Whether
a==zero.Whether
a==zero.- Definition Classes
- Monoid
- def monoidLaw: MonoidLaw
- Definition Classes
- Monoid
- val monoidSyntax: MonoidSyntax[F]
- Definition Classes
- Monoid
- def multiply(value: F, n: Int): F
For
n = 0,zeroForn = 1,append(zero, value)Forn = 2,append(append(zero, value), value)For
n = 0,zeroForn = 1,append(zero, value)Forn = 2,append(append(zero, value), value)- Definition Classes
- Monoid
- def multiply1(value: F, n: Int): F
For
n = 0,valueForn = 1,append(value, value)Forn = 2,append(append(value, value), value) - final def ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- final def notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
- final def notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
- final def onEmpty[A, B](a: F)(v: => B)(implicit eq: Equal[F], mb: Monoid[B]): B
- Definition Classes
- Monoid
- final def onNotEmpty[B](a: F)(v: => B)(implicit eq: Equal[F], mb: Monoid[B]): B
- Definition Classes
- Monoid
- def semigroupLaw: SemigroupLaw
- Definition Classes
- Semigroup
- val semigroupSyntax: SemigroupSyntax[F]
- Definition Classes
- Semigroup
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- def toString(): String
- Definition Classes
- AnyRef → Any
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
- def zero: F
The identity element for
append.The identity element for
append.- Definition Classes
- IsomorphismMonoid → Monoid