Type Members

1.  final case class Format[A, B](getOption: (A) => Option[B], reverseGet: (B) => A) extends Product with Serializable

   A normalizing optic, isomorphic to Prism but with different laws, specifically getOption need not be injective; i.e., distinct inputs may have the same getOption result, which combined with a subsequent reverseGet yield a normalized form for A.

   A normalizing optic, isomorphic to Prism but with different laws, specifically getOption need not be injective; i.e., distinct inputs may have the same getOption result, which combined with a subsequent reverseGet yield a normalized form for A. Composition with stronger optics (Prism and Iso) yields another Format.

2.  final case class SplitEpi[A, B](get: (A) => B, reverseGet: (B) => A) extends Product with Serializable

   A split epimorphism, which we can think of as a weaker Iso[A, B] where B is a smaller .

   A split epimorphism, which we can think of as a weaker Iso[A, B] where B is a smaller . type. So reverseGet andThen get remains an identity but get andThen reverseGet is merely idempotent (i.e., it normalizes values in A). The following statements hold:

   • reverseGet is a section of get,
   • get is a retraction of reverseGet,
   • B is a retract of A,
   • the pair (get, reverseGet) is a splitting of the idempotent get andThen reverseGet.

   get

   any function A => B.

   reverseGet

   a section of get such that reverseGet andThen get is an identity.

   See also

   Split Epimorphism at nLab

3.  final case class SplitMono[A, B](get: (A) => B, reverseGet: (B) => A) extends Product with Serializable

   A split monomorphism, which we can think of as a weaker Iso[A, B] where A is a smaller .

   A split monomorphism, which we can think of as a weaker Iso[A, B] where A is a smaller . type. So get andThen reverseGet andThen remains an identity but reverseGet andThen get is merely idempotent (i.e., it normalizes values in B). The following statements hold:

   • reverseGet is a retraction of get,
   • get is a section of reverseGet,
   • A is a retract of B,
   • the pair (reverseGet, get) is a splitting of the idempotent reverseGet andThen get.

   get

   section of reverseGet such that get andThen reverseGet is an identity

   reverseGet

   any function B => A

   See also

   Split Monomorphism at nLab

4.  final case class Wedge[A, B](get: (A) => B, reverseGet: (B) => A) extends Product with Serializable

   Composition of a SplitMono and a SplitEpi, yielding an even weaker structure where neither get andThen reverseGet and reverseGet andThen get is an identity but both are idempotent.