Data.Lens.Iso

iso :: forall s t a b. (s -> a) -> (b -> t) -> Iso s t a b

Create an Iso from a pair of morphisms.

withIso :: forall s t a b r. AnIso s t a b -> ((s -> a) -> (b -> t) -> r) -> r

Extracts the pair of morphisms from an isomorphism.

cloneIso :: forall s t a b. AnIso s t a b -> Iso s t a b

Extracts an Iso from AnIso.

re :: forall p s t a b. Optic (Re p a b) s t a b -> Optic p b a t s

Reverses an optic.

au :: forall s t a b e. AnIso s t a b -> ((b -> t) -> e -> s) -> e -> a

auf :: forall s t a b e r p. Profunctor p => AnIso s t a b -> (p r a -> e -> b) -> p r s -> e -> t

under :: forall s t a b. AnIso s t a b -> (t -> s) -> b -> a

non :: forall a. Eq a => a -> Iso' (Maybe a) a

If a1 is obtained from a by removing a single value, then Maybe a1 is isomorphic to a.

curried :: forall a b c d e f. Iso (Tuple a b -> c) (Tuple d e -> f) (a -> b -> c) (d -> e -> f)

uncurried :: forall a b c d e f. Iso (a -> b -> c) (d -> e -> f) (Tuple a b -> c) (Tuple d e -> f)

flipped :: forall a b c d e f. Iso (a -> b -> c) (d -> e -> f) (b -> a -> c) (e -> d -> f)

mapping :: forall s t a b f g. Functor f => Functor g => AnIso s t a b -> Iso (f s) (g t) (f a) (g b)

dimapping :: forall s ss t tt a aa b bb p q. Profunctor p => Profunctor q => AnIso s t a b -> AnIso ss tt aa bb -> Iso (p a ss) (q b tt) (p s aa) (q t bb)

newtype Re p s t a b

Constructors

• Re (p b a -> p t s)

Instances

• Newtype (Re p s t a b) _
• (Profunctor p) => Profunctor (Re p s t)
• (Choice p) => Cochoice (Re p s t)
• (Cochoice p) => Choice (Re p s t)
• (Strong p) => Costrong (Re p s t)
• (Costrong p) => Strong (Re p s t)

type Optic p s t a b = p a b -> p s t

type Iso' s a = Iso s s a a

type Iso s t a b = forall p. Profunctor p => Optic p s t a b

A generalized isomorphism.

data Exchange a b s t

The Exchange profunctor characterizes an Iso.

Constructors

• Exchange (s -> a) (b -> t)

Instances

• Functor (Exchange a b s)
• Profunctor (Exchange a b)

type AnIso' s a = AnIso s s a a

type AnIso s t a b = Optic (Exchange a b) s t a b