Packages

trait InvariantFunctor[F[_]] extends AnyRef

Unary type constructor that supports an xmap operation that converts an F[A] to an F[B] given two functions, A => B and B => A.

An invariant functor must satisfy two laws:

  • identity - xmap(ma)(identity, identity) == ma
  • composite - xmap(xmap(ma, f1, g1), f2, g2) == xmap(ma, f2 compose f1, g1, compose g2)

Also known as an exponential functor.

Self Type
InvariantFunctor[F]
Source
InvariantFunctor.scala
See also

https://hackage.haskell.org/packages/archive/invariant/latest/doc/html/Data-Functor-Invariant.html

http://comonad.com/reader/2008/rotten-bananas/

scalaz.InvariantFunctor.InvariantFunctorLaw

Linear Supertypes
AnyRef, Any
Known Subclasses
Align, Alt, Applicative, ApplicativeError, ApplicativePlus, Apply, FlippedApply, Bind, BindRec, Cobind, Comonad, ComonadStore, Contravariant, Decidable, Distributive, Divide, Divisible, Functor, OverrideWiden, InvariantAlt, InvariantApplicative, IsomorphismAlign, IsomorphismAlt, IsomorphismApplicative, IsomorphismApplicativeError, IsomorphismApplicativePlus, IsomorphismApply, IsomorphismBind, IsomorphismBindRec, IsomorphismCobind, IsomorphismComonad, IsomorphismComonadStore, IsomorphismContravariant, IsomorphismDecidable, IsomorphismDistributive, IsomorphismDivide, IsomorphismDivisible, IsomorphismFunctor, IsomorphismInvariantAlt, IsomorphismInvariantApplicative, IsomorphismInvariantFunctor, IsomorphismMonad, IsomorphismMonadError, IsomorphismMonadPlus, IsomorphismMonadReader, IsomorphismMonadState, IsomorphismMonadTell, IsomorphismNondeterminism, IsomorphismTraverse, IsomorphismTraverse1, Monad, MonadError, MonadListen, MonadPlus, MonadReader, MonadState, MonadTell, Nondeterminism, SndCovariant, SemigroupApply, Traverse, Traverse1
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Type Members

  1. trait InvariantFunctorLaw extends AnyRef

Abstract Value Members

  1. abstract def xmap[A, B](ma: F[A], f: (A) ⇒ B, g: (B) ⇒ A): F[B]

    Converts ma to a value of type F[B] using the provided functions f and g.

Concrete Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
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  2. final def ##(): Int
    Definition Classes
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  3. final def ==(arg0: Any): Boolean
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  4. final def asInstanceOf[T0]: T0
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  5. def clone(): AnyRef
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    protected[lang]
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    @throws( ... ) @native()
  6. final def eq(arg0: AnyRef): Boolean
    Definition Classes
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  7. def equals(arg0: Any): Boolean
    Definition Classes
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  8. def finalize(): Unit
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    protected[lang]
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    @throws( classOf[java.lang.Throwable] )
  9. final def getClass(): Class[_]
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    @native()
  10. def hashCode(): Int
    Definition Classes
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    Annotations
    @native()
  11. def invariantFunctorLaw: InvariantFunctorLaw
  12. val invariantFunctorSyntax: InvariantFunctorSyntax[F]
  13. final def isInstanceOf[T0]: Boolean
    Definition Classes
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  14. final def ne(arg0: AnyRef): Boolean
    Definition Classes
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  15. final def notify(): Unit
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    @native()
  16. final def notifyAll(): Unit
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    @native()
  17. final def synchronized[T0](arg0: ⇒ T0): T0
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  18. def toString(): String
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  19. final def wait(): Unit
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    @throws( ... )
  20. final def wait(arg0: Long, arg1: Int): Unit
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    @throws( ... )
  21. final def wait(arg0: Long): Unit
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    @throws( ... ) @native()
  22. def xmapb[A, B](ma: F[A])(b: Bijection[A, B]): F[B]

    Converts ma to a value of type F[B] using the provided bijection.

  23. def xmapi[A, B](ma: F[A])(iso: Isomorphism.<=>[A, B]): F[B]

    Converts ma to a value of type F[B] using the provided isomorphism.

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