trait IsomorphismSemiLattice[F, G] extends SemiLattice[F] with IsomorphismBand[F, G]
- Source
- SemiLattice.scala
- Alphabetic
- By Inheritance
- IsomorphismSemiLattice
- IsomorphismBand
- IsomorphismSemigroup
- SemiLattice
- Band
- Semigroup
- AnyRef
- Any
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- Public
- Protected
Type Members
- trait BandLaw extends SemigroupLaw
Band instances must satisfy scalaz.Semigroup.SemigroupLaw and 1 additional law:
Band instances must satisfy scalaz.Semigroup.SemigroupLaw and 1 additional law:
- idempotency:
forall a. append(a, a) == a
- Definition Classes
- Band
- idempotency:
- trait SemiLatticeLaw extends BandLaw
- Definition Classes
- SemiLattice
- 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, c
inF
, the equationappend(append(a, b), c) = append(a, append(b , c))
holds.
- Definition Classes
- Semigroup
- closure:
Abstract Value Members
- implicit abstract def G: SemiLattice[G]
- Definition Classes
- IsomorphismSemiLattice → IsomorphismBand → 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
f1
andf2
.The binary operation to combine
f1
andf2
.Implementations should not evaluate the by-name parameter
f2
if result can be determined byf1
.- Definition Classes
- IsomorphismSemigroup → Semigroup
- final def apply: Apply[[α]F]
An scalaz.Apply, that implements
ap
withappend
.An scalaz.Apply, that implements
ap
withappend
. Note that the type parameterα
inApply[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
- def bandLaw: BandLaw
- Definition Classes
- Band
- val bandSyntax: BandSyntax[F]
- Definition Classes
- Band
- def clone(): AnyRef
- Attributes
- protected[lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @native()
- 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
- 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 isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- def multiply1(value: F, n: Int): F
The default definition exploits idempotency to optimise to
O(1)
- 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()
- def semiLatticeLaw: SemiLatticeLaw
- Definition Classes
- SemiLattice
- val semiLatticeSyntax: SemiLatticeSyntax[F]
- Definition Classes
- SemiLattice
- 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
- def unfoldlSumOpt[S](seed: S)(f: (S) => Maybe[(S, F)]): Maybe[F]
Unfold
seed
to the left and sum using #append. - def unfoldrSumOpt[S](seed: S)(f: (S) => Maybe[(F, S)]): Maybe[F]
Unfold
seed
to the right and sum using #append. - 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()