Data.Profunctor.Optic.Types

Optic

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

type Optic' p s a = Optic p s s a a

Constraints

type Affine p = (Choice p, Strong p)

type Coaffine p = (Choice p, Closed p)

type Traversing p = (Representable p, Applicative' (Rep p))

type Cotraversing p = (Corepresentable p, Coapplicative (Corep p))

type Traversing1 p = (Representable p, Apply (Rep p))

type Cotraversing1 p = (Corepresentable p, Coapply (Corep p))

type CoerceL p = Bifunctor p

type CoerceR p = forall x. Contravariant (p x)

type Mapping p = (Representable p, Distributive (Rep p))

type Comapping p = (Corepresentable p, Traversable (Corep p))

type Mapping1 p = (Representable p, Distributive1 (Rep p))

type Comapping1 p = (Corepresentable p, Traversable1 (Corep p))

Equality

type Equality s t a b = forall p. Optic p s t a b

\( \mathsf{Equality}\;A = A \cong A \)

type Equality' s a = Equality s s a a

Iso

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

\( \mathsf{Iso}\;S\;A = S \cong A \)

type Iso' s a = Iso s s a a

Prism

type Prism s t a b = forall p. Choice p => Optic p s t a b

\( \mathsf{Prism}\;S\;A = \exists D, S \cong D + A \)

type Coprism s t a b = forall p. Cochoice p => Optic p s t a b

\( \mathsf{Prism}\;S\;A = \exists D, S + D \cong A \)

type Prism' s a = Prism s s a a

type Coprism' t b = Coprism t t b b

Lens

type Lens s t a b = forall p. Strong p => Optic p s t a b

\( \mathsf{Lens}\;S\;A = \exists C, S \cong C \times A \)

type Colens s t a b = forall p. Costrong p => Optic p s t a b

\( \mathsf{Lens}\;S\;A = \exists C, S \times C \cong A \)

type Lens' s a = Lens s s a a

type Colens' t b = Lens t t b b

Grate

type Grate s t a b = forall p. Closed p => Optic p s t a b

\( \mathsf{Grate}\;S\;A = \exists I, S \cong I \to A \)

type Grate' s a = Grate s s a a

Traversal

type Traversal0 s t a b = forall p. Affine p => Optic p s t a b

\( \mathsf{Traversal0}\;S\;A = \exists C, D, S \cong D + C \times A \)

type Cotraversal0 s t a b = forall p. Coaffine p => Optic p s t a b

\( \mathsf{Cotraversal0}\;S\;A = \exists D, I, S \cong I \to D + A \)

type Traversal s t a b = forall p. (Affine p, Traversing p) => Optic p s t a b

\( \mathsf{Traversal}\;S\;A = \exists F : \mathsf{Traversable}, S \equiv F\,A \)

type Cotraversal s t a b = forall p. (Coaffine p, Cotraversing p) => Optic p s t a b

\( \mathsf{Cotraversal}\;S\;A = \exists F : \mathsf{Distributive}, S \equiv F\,A \)

type Traversal1 s t a b = forall p. (Strong p, Traversing1 p) => Optic p s t a b

\( \mathsf{Traversal1}\;S\;A = \exists F : \mathsf{Traversable1}, S \equiv F\,A \)

type Cotraversal1 s t a b = forall p. (Closed p, Cotraversing1 p) => Optic p s t a b

\( \mathsf{Cotraversal1}\;S\;A = \exists F : \mathsf{Distributive1}, S \equiv F\,A \)

type Traversal0' s a = Traversal0 s s a a

type Cotraversal0' t b = Cotraversal0 t t b b

type Traversal' s a = Traversal s s a a

type Cotraversal' t b = Cotraversal t t b b

type Traversal1' s a = Traversal1 s s a a

type Cotraversal1' t b = Cotraversal1 t t b b

Fold

type Fold0 s a = forall p. (Affine p, CoerceR p) => Optic' p s a

type Fold s a = forall p. (Affine p, Traversing p, CoerceR p) => Optic' p s a

type Fold1 s a = forall p. (Strong p, Traversing1 p, CoerceR p) => Optic' p s a

Setter

type Setter s t a b = forall p. (Affine p, Traversing p, Mapping p) => Optic p s t a b

\( \mathsf{Setter}\;S\;A = \exists F : \mathsf{Functor}, S \equiv F\,A \)

type Resetter s t a b = forall p. (Coaffine p, Cotraversing p, Comapping p) => Optic p s t a b

\( \mathsf{Setter}\;S\;A = \exists F : \mathsf{Functor}, F\,S \equiv A \)

type Setter' s a = Setter s s a a

type Resetter' s a = Resetter s s a a

View

type View s a = forall p. (Strong p, CoerceR p) => Optic' p s a

type Review t b = forall p. (Closed p, CoerceL p) => Optic' p t b

Re

newtype Re p s t a b

The Re type and its instances witness the symmetry between the parameters of a Profunctor.

Constructors

Re

Fields

• runRe :: p b a -> p t s

Instances

(Profunctor p, forall x. Contravariant (p x)) => Bifunctor (Re p s t)

Defined in Data.Profunctor.Optic.Types

Methods

bimap :: (a -> b) -> (c -> d) -> Re p s t a c -> Re p s t b d

first :: (a -> b) -> Re p s t a c -> Re p s t b c

second :: (b -> c) -> Re p s t a b -> Re p s t a c

Cochoice p => Choice (Re p s t)

Defined in Data.Profunctor.Optic.Types

Methods

left' :: Re p s t a b -> Re p s t (Either a c) (Either b c)

right' :: Re p s t a b -> Re p s t (Either c a) (Either c b)

Choice p => Cochoice (Re p s t)

Defined in Data.Profunctor.Optic.Types

Methods

unleft :: Re p s t (Either a d) (Either b d) -> Re p s t a b

unright :: Re p s t (Either d a) (Either d b) -> Re p s t a b

Costrong p => Strong (Re p s t)

Defined in Data.Profunctor.Optic.Types

Methods

first' :: Re p s t a b -> Re p s t (a, c) (b, c)

second' :: Re p s t a b -> Re p s t (c, a) (c, b)

Strong p => Costrong (Re p s t)

Defined in Data.Profunctor.Optic.Types

Methods

unfirst :: Re p s t (a, d) (b, d) -> Re p s t a b

unsecond :: Re p s t (d, a) (d, b) -> Re p s t a b

Profunctor p => Profunctor (Re p s t)

Defined in Data.Profunctor.Optic.Types

Methods

dimap :: (a -> b) -> (c -> d) -> Re p s t b c -> Re p s t a d

lmap :: (a -> b) -> Re p s t b c -> Re p s t a c

rmap :: (b -> c) -> Re p s t a b -> Re p s t a c

(#.) :: Coercible c b => q b c -> Re p s t a b -> Re p s t a c

(.#) :: Coercible b a => Re p s t b c -> q a b -> Re p s t a c

Bifunctor p => Contravariant (Re p s t a)

Defined in Data.Profunctor.Optic.Types

Methods

contramap :: (a0 -> b) -> Re p s t a b -> Re p s t a a0

(>$) :: b -> Re p s t a b -> Re p s t a a0

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

Reverse an optic to obtain its dual.

re . re  ≡ id

re :: Iso s t a b   -> Iso b a t s
re :: Lens s t a b  -> Colens b a t s
re :: Prism s t a b -> Coprism b a t s
re :: Traversal s t a b  -> Cotraversal b a t s
re :: View s t a b  -> Review b a t s

>>> 5 ^. re left'
Left 5

between :: (c -> d) -> (a -> b) -> (b -> c) -> a -> d

Can be used to rewrite

\g -> f . g . h

to

between f h

module Data.Profunctor.Types

Orphan instances

Contravariant f => Bifunctor (Costar f)

Methods

bimap :: (a -> b) -> (c -> d) -> Costar f a c -> Costar f b d

first :: (a -> b) -> Costar f a c -> Costar f b c

second :: (b -> c) -> Costar f a b -> Costar f a c

Coapplicative f => Choice (Costar f)

Methods

left' :: Costar f a b -> Costar f (Either a c) (Either b c)

right' :: Costar f a b -> Costar f (Either c a) (Either c b)

Apply f => Apply (Star f a)

Methods

(<.>) :: Star f a (a0 -> b) -> Star f a a0 -> Star f a b

(.>) :: Star f a a0 -> Star f a b -> Star f a b

(<.) :: Star f a a0 -> Star f a b -> Star f a a0

liftF2 :: (a0 -> b -> c) -> Star f a a0 -> Star f a b -> Star f a c

Apply (Costar f a)

Methods

(<.>) :: Costar f a (a0 -> b) -> Costar f a a0 -> Costar f a b

(.>) :: Costar f a a0 -> Costar f a b -> Costar f a b

(<.) :: Costar f a a0 -> Costar f a b -> Costar f a a0

liftF2 :: (a0 -> b -> c) -> Costar f a a0 -> Costar f a b -> Costar f a c