Safe Haskell	None
Language	GHC2024

Proarrow.Profunctor.Instance.Day

Contents

Orphan instances

Description

Day convolution of profunctors: Day p q convolves p and q along the tensors of the source and target categories, with unit DayUnit and internal hom DayExp. Monoidal profunctors are closed under it, and it preserves Procomonads.

Synopsis

data DayUnit (a :: k) (b :: k1) where
- DayUnit :: forall {k} {k1} (a :: k) (b :: k1). (a ~> (Unit :: k)) -> ((Unit :: k1) ~> b) -> DayUnit a b
data Day (p :: j +-> k) (q :: j +-> k) (a :: k) (b :: j) where
- Day :: forall {k} {j} (c :: k) (d :: j) (e :: k) (f :: j) (p :: j +-> k) (q :: j +-> k) (a :: k) (b :: j). (a ~> (c ** e)) -> p c d -> q e f -> ((d ** f) ~> b) -> Day p q a b
day :: forall j k p q (c :: k) (d :: j) (e :: k) (f :: j). (Monoidal j, Monoidal k, Profunctor p, Profunctor q) => p c d -> q e f -> Day p q (c ** e) (d ** f)
duoidal :: forall {i} j k (p :: j +-> k) (p' :: i +-> j) (q :: j +-> k) (q' :: i +-> j). (Monoidal j, Profunctor p, Profunctor p', Profunctor q, Profunctor q') => Day (p :.: p') (q :.: q') ~> (Day p q :.: Day p' q')
data DayExp (p :: k -> k1 -> Type) (q :: k -> k1 -> Type) (a :: k) (b :: k1) where
- DayExp :: forall {k} {k1} (p :: k -> k1 -> Type) (q :: k -> k1 -> Type) (a :: k) (b :: k1). (Ob a, Ob b) => (forall (c :: k) (d :: k1) (e :: k) (f :: k1). (e ~> (a ** c)) -> ((b ** d) ~> f) -> p c d -> q e f) -> DayExp p q a b
multDayExp :: forall j k (p :: j +-> k) (q :: j +-> k) (p' :: j +-> k) (q' :: j +-> k). (SymMonoidal j, SymMonoidal k, Profunctor p, Profunctor q, Profunctor p', Profunctor q') => Day (p ~~> q) (p' ~~> q') ~> (Day p p' ~~> Day q q')
day2comp :: forall k (p :: k +-> k) (q :: k +-> k). (MonStrong p, MonStrong q, Monoidal k) => Day p q ~> (p :.: q)

Documentation

data DayUnit (a :: k) (b :: k1) where Source Github #

The unit of Day convolution: a pair of arrows through the monoidal units.

Constructors

DayUnit :: forall {k} {k1} (a :: k) (b :: k1). (a ~> (Unit :: k)) -> ((Unit :: k1) ~> b) -> DayUnit a b

Instances

Instances details

(CategoryOf j, CategoryOf k) => Profunctor (DayUnit :: k -> j -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Instance.Day

Methods

dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> DayUnit a b -> DayUnit c d Source Github #

lmap :: forall (c :: k) (a :: k) (b :: j). (c ~> a) -> DayUnit a b -> DayUnit c b Source Github #

rmap :: forall (b :: j) (d :: j) (a :: k). (b ~> d) -> DayUnit a b -> DayUnit a d Source Github #

(\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> DayUnit a b -> r Source Github #

data Day (p :: j +-> k) (q :: j +-> k) (a :: k) (b :: j) where Source Github #

The Day convolution on profunctors.

Constructors

Day :: forall {k} {j} (c :: k) (d :: j) (e :: k) (f :: j) (p :: j +-> k) (q :: j +-> k) (a :: k) (b :: j). (a ~> (c ** e)) -> p c d -> q e f -> ((d ** f) ~> b) -> Day p q a b

Instances

Instances details

(w1 p1 q1, w2 p2 q2) => DayFl (w1 :: (j1 +-> j1) -> (j2 +-> j2) -> Constraint) (w2 :: (j1 +-> j1) -> (j2 +-> j2) -> Constraint) (Day p1 p2 :: j1 -> j1 -> Type) (Day q1 q2 :: j2 -> j2 -> Type) Source Github #
Instance details Defined in Proarrow.Optic.Day
(SymMonoidal j, SymMonoidal k, MonoidalProfunctor p, MonoidalProfunctor q) => MonoidalProfunctor (Day p q :: k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Day Methods one :: Day p q (Unit :: k) (Unit :: j) Source Github # () :: forall (x1 :: k) (x2 :: j) (y1 :: k) (y2 :: j). Day p q x1 x2 -> Day p q y1 y2 -> Day p q (x1 y1) (x2 ** y2) Source Github #
(Profunctor p, Profunctor q) => Profunctor (Day p q :: k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Day Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Day p q a b -> Day p q c d Source Github # lmap :: forall (c :: k) (a :: k) (b :: j). (c ~> a) -> Day p q a b -> Day p q c b Source Github # rmap :: forall (b :: j) (d :: j) (a :: k). (b ~> d) -> Day p q a b -> Day p q a d Source Github # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Day p q a b -> r Source Github #
(Procomonad p, Procomonad q, Monoidal k) => Procomonad (Day p q :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Day Methods proextract :: Day p q :~> ((~>) :: CAT k) Source Github # produplicate :: Day p q :~> (Day p q :.: Day p q) Source Github #
Functor (Day :: (j +-> k) -> (j +-> k) -> k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Day Methods map :: forall (a :: j +-> k) (b :: j +-> k). (a ~> b) -> Day a ~> Day b Source Github #
Profunctor p => Functor (Day p :: (j +-> k) -> k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Day Methods map :: forall (a :: j +-> k) (b :: j +-> k). (a ~> b) -> Day p a ~> Day p b Source Github #

day :: forall j k p q (c :: k) (d :: j) (e :: k) (f :: j). (Monoidal j, Monoidal k, Profunctor p, Profunctor q) => p c d -> q e f -> Day p q (c ** e) (d ** f) Source Github #

duoidal :: forall {i} j k (p :: j +-> k) (p' :: i +-> j) (q :: j +-> k) (q' :: i +-> j). (Monoidal j, Profunctor p, Profunctor p', Profunctor q, Profunctor q') => Day (p :.: p') (q :.: q') ~> (Day p q :.: Day p' q') Source Github #

data DayExp (p :: k -> k1 -> Type) (q :: k -> k1 -> Type) (a :: k) (b :: k1) where Source Github #

The internal hom of Day convolution, making the category of profunctors Closed.

Constructors

DayExp :: forall {k} {k1} (p :: k -> k1 -> Type) (q :: k -> k1 -> Type) (a :: k) (b :: k1). (Ob a, Ob b) => (forall (c :: k) (d :: k1) (e :: k) (f :: k1). (e ~> (a ** c)) -> ((b ** d) ~> f) -> p c d -> q e f) -> DayExp p q a b

Instances

Instances details

(Monoidal j, Monoidal k, Profunctor p, Profunctor q) => Profunctor (DayExp p q :: k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Day Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> DayExp p q a b -> DayExp p q c d Source Github # lmap :: forall (c :: k) (a :: k) (b :: j). (c ~> a) -> DayExp p q a b -> DayExp p q c b Source Github # rmap :: forall (b :: j) (d :: j) (a :: k). (b ~> d) -> DayExp p q a b -> DayExp p q a d Source Github # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> DayExp p q a b -> r Source Github #
(Monoidal j, Monoidal k, Profunctor p) => Functor (DayExp p :: (k -> j -> Type) -> k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Day Methods map :: forall (a :: k -> j -> Type) (b :: k -> j -> Type). (a ~> b) -> DayExp p a ~> DayExp p b Source Github #

multDayExp :: forall j k (p :: j +-> k) (q :: j +-> k) (p' :: j +-> k) (q' :: j +-> k). (SymMonoidal j, SymMonoidal k, Profunctor p, Profunctor q, Profunctor p', Profunctor q') => Day (p ~~> q) (p' ~~> q') ~> (Day p p' ~~> Day q q') Source Github #

day2comp :: forall k (p :: k +-> k) (q :: k +-> k). (MonStrong p, MonStrong q, Monoidal k) => Day p q ~> (p :.: q) Source Github #

Orphan instances

(Monoidal j, Monoidal k) => Monoidal (j +-> k) Source Github #

Instance details

Associated Types

type Unit
Instance details Defined in Proarrow.Profunctor.Instance.Day type Unit = DayUnit :: k -> j -> Type

Methods

withOb2 :: forall (a :: j +-> k) (b :: j +-> k) r. (Ob a, Ob b) => (Ob (a ** b) => r) -> r Source Github #

leftUnitor :: forall (a :: j +-> k). Ob a => ((Unit :: j +-> k) ** a) ~> a Source Github #

leftUnitorInv :: forall (a :: j +-> k). Ob a => a ~> ((Unit :: j +-> k) ** a) Source Github #

rightUnitor :: forall (a :: j +-> k). Ob a => (a ** (Unit :: j +-> k)) ~> a Source Github #

rightUnitorInv :: forall (a :: j +-> k). Ob a => a ~> (a ** (Unit :: j +-> k)) Source Github #

associator :: forall (a :: j +-> k) (b :: j +-> k) (c :: j +-> k). (Ob a, Ob b, Ob c) => ((a ** b) ** c) ~> (a ** (b ** c)) Source Github #

associatorInv :: forall (a :: j +-> k) (b :: j +-> k) (c :: j +-> k). (Ob a, Ob b, Ob c) => (a ** (b ** c)) ~> ((a ** b) ** c) Source Github #

(SymMonoidal j, SymMonoidal k) => SymMonoidal (j +-> k) Source Github #

Instance details

Methods

swap :: forall (a :: j +-> k) (b :: j +-> k). (Ob a, Ob b) => (a ** b) ~> (b ** a) Source Github #

(Monoidal j, Monoidal k) => Closed (j +-> k) Source Github #

Instance details

Methods

withObExp :: forall (a :: j +-> k) (b :: j +-> k) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: j +-> k) (b :: j +-> k) (c :: j +-> k). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: j +-> k) (b :: j +-> k). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: j +-> k) (b :: j +-> k) (x :: j +-> k) (y :: j +-> k). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

(SymMonoidal j, CopyDiscard k, Supplies CommutativeMonoid j) => CopyDiscard (j +-> k) Source Github #

Instance details

Methods

copy :: forall (a :: j +-> k). Ob a => a ~> (a ** a) Source Github #

discard :: forall (a :: j +-> k). Ob a => a ~> (Unit :: j +-> k) Source Github #

(Monoidal j, Monoidal k) => Distributive (j +-> k) Source Github #

Instance details

Methods

distL :: forall (a :: j +-> k) (b :: j +-> k) (c :: j +-> k). (Ob a, Ob b, Ob c) => (a ** (b || c)) ~> ((a ** b) || (a ** c)) Source Github #

distR :: forall (a :: j +-> k) (b :: j +-> k) (c :: j +-> k). (Ob a, Ob b, Ob c) => ((a || b) ** c) ~> ((a ** c) || (b ** c)) Source Github #

absorbL :: forall (a :: j +-> k). Ob a => (a ** (InitialObject :: j +-> k)) ~> (InitialObject :: j +-> k) Source Github #

absorbR :: forall (a :: j +-> k). Ob a => ((InitialObject :: j +-> k) ** a) ~> (InitialObject :: j +-> k) Source Github #

(SymMonoidal j, CopyDiscard k, Supplies CommutativeMonoid j, Profunctor p) => CocommutativeComonoid (p :: j +-> k) Source Github #

Instance details

(SymMonoidal j, CopyDiscard k, Supplies CommutativeMonoid j, Profunctor p) => Comonoid (p :: j +-> k) Source Github #

Instance details

Methods

counit :: p ~> (Unit :: j +-> k) Source Github #

comult :: p ~> (p ** p) Source Github #

(Profunctor p, MonoidalProfunctor p) => Monoid (p :: j +-> k) Source Github #

Instance details

Methods

mempty :: (Unit :: j +-> k) ~> p Source Github #

mappend :: (p ** p) ~> p Source Github #

(Monoidal j, Monoidal k) => MonoidalProfunctor (Prof :: (j +-> k) -> (j +-> k) -> Type) Source Github #

Instance details

Methods

one :: Prof (Unit :: j +-> k) (Unit :: j +-> k) Source Github #

(**) :: forall (x1 :: j +-> k) (x2 :: j +-> k) (y1 :: j +-> k) (y2 :: j +-> k). Prof x1 x2 -> Prof y1 y2 -> Prof (x1 ** y1) (x2 ** y2) Source Github #