root/scalaz/Isomorphism

Isomorphism

object Isomorphism extends Isomorphisms
class Object
trait Matchable
class Any

Type members

Inherited classlikes

trait Iso[Arr[_, _], A, B]

Isomorphism for arrows of kind * -> * -> *

Isomorphism for arrows of kind * -> * -> *

Inherited from
Isomorphisms
trait Iso2[Arr[_[_], _[_]], F[_], G[_]]

Isomorphism for arrows of kind (* -> ) -> ( -> *) -> *

Isomorphism for arrows of kind (* -> ) -> ( -> *) -> *

Inherited from
Isomorphisms
trait Iso3[Arr[_[_, _], _[_, _]], F[_, _], G[_, _]]

Isomorphism for arrows of kind (* -> * -> ) -> ( -> * -> *) -> *

Isomorphism for arrows of kind (* -> * -> ) -> ( -> * -> *) -> *

Inherited from
Isomorphisms
trait IsoBifunctorTemplate[F[_, _], G[_, _]]

Convenience template trait to implement <~~>

Convenience template trait to implement <~~>

Inherited from
Isomorphisms
object IsoFunctor
Inherited from
Isomorphisms
trait IsoFunctorTemplate[F[_], G[_]]

Convenience template trait to implement <~>

Convenience template trait to implement <~>

Inherited from
Isomorphisms
object IsoSet
Inherited from
Isomorphisms

Inherited types

type <=>[A, B] = IsoSet[A, B]

Alias for IsoSet

Alias for IsoSet

Inherited from
Isomorphisms
type <~>[F[_], G[_]] = IsoFunctor[F, G]

Alias for IsoFunctor

Alias for IsoFunctor

Inherited from
Isomorphisms
type <~~>[F[_, _], G[_, _]] = IsoBifunctor[F, G]

Alias for IsoBifunctor

Alias for IsoBifunctor

Inherited from
Isomorphisms
type IsoBifunctor[F[_, _], G[_, _]] = Iso3[~~>, F, G]
Inherited from
Isomorphisms
type IsoFunctor[F[_], G[_]] = Iso2[[F[_], G[_]] =>> NaturalTransformation[F, G], F, G]

Natural isomorphism between functors

Natural isomorphism between functors

Inherited from
Isomorphisms
type IsoSet[A, B] = Iso[Function1, A, B]

Set isomorphism

Set isomorphism

Inherited from
Isomorphisms

Value members

Inherited methods

def commutative[A, B](i: IsoSet[A, B]): IsoSet[B, A]

Set isomorphism is commutative

Set isomorphism is commutative

Inherited from
Isomorphisms
def naturalCommutative[F[_], G[_]](i: IsoFunctor[F, G]): IsoFunctor[G, F]

Natural isomorphism is commutative

Natural isomorphism is commutative

Inherited from
Isomorphisms
def naturalRefl[F[_]]: IsoFunctor[F, F]

Natural isomorphism is reflexive

Natural isomorphism is reflexive

Inherited from
Isomorphisms
def refl[A]: IsoSet[A, A]

Set isomorphism is reflexive

Set isomorphism is reflexive

Inherited from
Isomorphisms