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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

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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
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  2. final def ##(): Int
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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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  6. final def eq(arg0: AnyRef): Boolean
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  7. def equals(arg0: Any): Boolean
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  8. def finalize(): Unit
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  9. final def getClass(): Class[_]
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  10. def hashCode(): Int
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    @native()
  11. def invariantFunctorLaw: InvariantFunctorLaw
  12. val invariantFunctorSyntax: InvariantFunctorSyntax[F]
  13. final def isInstanceOf[T0]: Boolean
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  14. final def ne(arg0: AnyRef): Boolean
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  15. final def notify(): Unit
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  16. final def notifyAll(): Unit
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  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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  20. final def wait(arg0: Long, arg1: Int): Unit
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  21. final def wait(arg0: Long): Unit
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  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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