Safe Haskell	None
Language	Haskell2010

Optics.Iso

Contents

Isomorphisms

Synopsis

data An_Iso :: OpticKind
type Iso s t a b = Optic An_Iso '[] s t a b
type Iso' s a = Optic' An_Iso '[] s a
toIso :: Is k An_Iso => Optic k is s t a b -> Optic An_Iso is s t a b
iso :: (s -> a) -> (b -> t) -> Iso s t a b
withIso :: Is k An_Iso => Optic k is s t a b -> ((s -> a) -> (b -> t) -> r) -> r
mapping :: (Is k An_Iso, Functor f, Functor g) => Optic k '[] s t a b -> Iso (f s) (g t) (f a) (g b)
curried :: Iso ((a, b) -> c) ((d, e) -> f) (a -> b -> c) (d -> e -> f)
uncurried :: Iso (a -> b -> c) (d -> e -> f) ((a, b) -> c) ((d, e) -> f)
flipped :: Iso (a -> b -> c) (a' -> b' -> c') (b -> a -> c) (b' -> a' -> c')
class Bifunctor p => Swapped p where
module Optics.Optic

Documentation

data An_Iso :: OpticKind #

Tag for an iso.

Instances

ReversibleOptic An_Iso #
Instance details Defined in Optics.Internal.Re Associated Types type ReversedOptic An_Iso :: OpticKind # Methods re :: Optic An_Iso [] s t a b -> Optic (ReversedOptic An_Iso) [] b a t s #
Is An_Iso A_Review #
Instance details Defined in Optics.Internal.Optic.Subtyping Methods implies :: proxy An_Iso A_Review p -> (Constraints An_Iso p -> r) -> Constraints A_Review p -> r
Is An_Iso A_LensyReview #
Instance details Defined in Optics.Internal.Optic.Subtyping Methods implies :: proxy An_Iso A_LensyReview p -> (Constraints An_Iso p -> r) -> Constraints A_LensyReview p -> r
Is An_Iso A_Fold #
Instance details Defined in Optics.Internal.Optic.Subtyping Methods implies :: proxy An_Iso A_Fold p -> (Constraints An_Iso p -> r) -> Constraints A_Fold p -> r
Is An_Iso An_AffineFold #
Instance details Defined in Optics.Internal.Optic.Subtyping Methods implies :: proxy An_Iso An_AffineFold p -> (Constraints An_Iso p -> r) -> Constraints An_AffineFold p -> r
Is An_Iso A_Getter #
Instance details Defined in Optics.Internal.Optic.Subtyping Methods implies :: proxy An_Iso A_Getter p -> (Constraints An_Iso p -> r) -> Constraints A_Getter p -> r
Is An_Iso A_PrismaticGetter #
Instance details Defined in Optics.Internal.Optic.Subtyping Methods implies :: proxy An_Iso A_PrismaticGetter p -> (Constraints An_Iso p -> r) -> Constraints A_PrismaticGetter p -> r
Is An_Iso A_Setter #
Instance details Defined in Optics.Internal.Optic.Subtyping Methods implies :: proxy An_Iso A_Setter p -> (Constraints An_Iso p -> r) -> Constraints A_Setter p -> r
Is An_Iso A_Traversal #
Instance details Defined in Optics.Internal.Optic.Subtyping Methods implies :: proxy An_Iso A_Traversal p -> (Constraints An_Iso p -> r) -> Constraints A_Traversal p -> r
Is An_Iso An_AffineTraversal #
Instance details Defined in Optics.Internal.Optic.Subtyping Methods implies :: proxy An_Iso An_AffineTraversal p -> (Constraints An_Iso p -> r) -> Constraints An_AffineTraversal p -> r
Is An_Iso A_Prism #
Instance details Defined in Optics.Internal.Optic.Subtyping Methods implies :: proxy An_Iso A_Prism p -> (Constraints An_Iso p -> r) -> Constraints A_Prism p -> r
Is An_Iso A_Lens #
Instance details Defined in Optics.Internal.Optic.Subtyping Methods implies :: proxy An_Iso A_Lens p -> (Constraints An_Iso p -> r) -> Constraints A_Lens p -> r
Is An_Equality An_Iso #
Instance details Defined in Optics.Internal.Optic.Subtyping Methods implies :: proxy An_Equality An_Iso p -> (Constraints An_Equality p -> r) -> Constraints An_Iso p -> r
Arrow arr => ArrowOptic An_Iso arr #
Instance details Defined in Optics.Arrow Methods overA :: Optic An_Iso [] s t a b -> arr a b -> arr s t #
ViewableOptic An_Iso r #
Instance details Defined in Optics.Internal.View Associated Types type ViewResult An_Iso r :: * # Methods view :: Optic' An_Iso is s r -> s -> ViewResult An_Iso r #
PermeableOptic An_Iso r #
Instance details Defined in Optics.Internal.Passthrough Methods passthrough :: Optic An_Iso is s t a b -> (a -> (r, b)) -> s -> (ViewResult An_Iso r, t) #
type ReversedOptic An_Iso #
Instance details Defined in Optics.Internal.Re type ReversedOptic An_Iso = An_Iso
type ViewResult An_Iso r #
Instance details Defined in Optics.Internal.View type ViewResult An_Iso r = r

type Iso s t a b = Optic An_Iso '[] s t a b #

Type synonym for a type-modifying iso.

type Iso' s a = Optic' An_Iso '[] s a #

Type synonym for a type-preserving iso.

toIso :: Is k An_Iso => Optic k is s t a b -> Optic An_Iso is s t a b #

Explicitly cast an optic to an iso.

iso :: (s -> a) -> (b -> t) -> Iso s t a b #

Build an iso from a pair of inverse functions.

withIso :: Is k An_Iso => Optic k is s t a b -> ((s -> a) -> (b -> t) -> r) -> r #

Extract the two components of an isomorphism.

Isomorphisms

mapping :: (Is k An_Iso, Functor f, Functor g) => Optic k '[] s t a b -> Iso (f s) (g t) (f a) (g b) #

This can be used to lift any Iso into an arbitrary Functor.

curried :: Iso ((a, b) -> c) ((d, e) -> f) (a -> b -> c) (d -> e -> f) #

The canonical isomorphism for currying and uncurrying a function.

curried = iso curry uncurry

>>> view curried fst 3 4
3

uncurried :: Iso (a -> b -> c) (d -> e -> f) ((a, b) -> c) ((d, e) -> f) #

The canonical isomorphism for uncurrying and currying a function.

uncurried = iso uncurry curry

uncurried = from curried

>>> (view uncurried (+)) (1,2)
3

flipped :: Iso (a -> b -> c) (a' -> b' -> c') (b -> a -> c) (b' -> a' -> c') #

The isomorphism for flipping a function.

>>> (view flipped (,)) 1 2
(2,1)

class Bifunctor p => Swapped p where #

This class provides for symmetric bifunctors.

Minimal complete definition

swapped

Methods

swapped :: Iso (p a b) (p c d) (p b a) (p d c) #

swapped . swapped ≡ id
first f . swapped = swapped . second f
second g . swapped = swapped . first g
bimap f g . swapped = swapped . bimap g f

>>> view swapped (1,2)
(2,1)

Instances

Swapped Either #
Instance details Defined in Optics.Iso Methods swapped :: Iso (Either a b) (Either c d) (Either b a) (Either d c) #
Swapped (,) #
Instance details Defined in Optics.Iso Methods swapped :: Iso (a, b) (c, d) (b, a) (d, c) #

module Optics.Optic