Safe Haskell	None
Language	GHC2024

Proarrow.Profunctor.Composition

Synopsis

data ((p :: j +-> k) :.: (q :: i +-> j)) (a :: k) (c :: i) where
- (:.:) :: forall {j} {k} {i} (p :: j +-> k) (a :: k) (b :: j) (q :: i +-> j) (c :: i). p a b -> q b c -> (p :.: q) a c
o :: forall {i} {j} {k} (p :: j +-> k) (q :: j +-> k) (r :: i +-> j) (s :: i +-> j). Prof p q -> Prof r s -> Prof (p :.: r) (q :.: s)

Documentation

data ((p :: j +-> k) :.: (q :: i +-> j)) (a :: k) (c :: i) where Source Comments #

Constructors

(:.:) :: forall {j} {k} {i} (p :: j +-> k) (a :: k) (b :: j) (q :: i +-> j) (c :: i). p a b -> q b c -> (p :.: q) a c

Instances

Instances details

(Strong m p, Strong m q) => Strong m (p :.: q :: d -> c -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Composition Methods act :: forall (a :: m) (b :: m) (x :: d) (y :: c). (a ~> b) -> (p :.: q) x y -> (p :.: q) (Act a x) (Act b y) Source Comments #
(MonoidalProfunctor p, MonoidalProfunctor q) => MonoidalProfunctor (p :.: q :: k -> j2 -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Composition Methods par0 :: (p :.: q) (Unit :: k) (Unit :: j2) Source Comments # par :: forall (x1 :: k) (x2 :: j2) (y1 :: k) (y2 :: j2). (p :.: q) x1 x2 -> (p :.: q) y1 y2 -> (p :.: q) (x1 y1) (x2 y2) Source Comments #
(Profunctor p, Profunctor q) => Profunctor (p :.: q :: k -> j2 -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Composition Methods dimap :: forall (c :: k) (a :: k) (b :: j2) (d :: j2). (c ~> a) -> (b ~> d) -> (p :.: q) a b -> (p :.: q) c d Source Comments # (\\) :: forall (a :: k) (b :: j2) r. ((Ob a, Ob b) => r) -> (p :.: q) a b -> r Source Comments #
(Corepresentable p, Corepresentable q) => Corepresentable (p :.: q :: k -> j2 -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Composition Methods coindex :: forall (a :: k) (b :: j2). (p :.: q) a b -> ((p :.: q) %% a) ~> b Source Comments # cotabulate :: forall (a :: k) (b :: j2). Ob a => (((p :.: q) %% a) ~> b) -> (p :.: q) a b Source Comments # corepMap :: forall (a :: k) (b :: k). (a ~> b) -> ((p :.: q) %% a) ~> ((p :.: q) %% b) Source Comments #
(Representable p, Representable q) => Representable (p :.: q :: k -> j2 -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Composition Methods index :: forall (a :: k) (b :: j2). (p :.: q) a b -> a ~> ((p :.: q) % b) Source Comments # tabulate :: forall (b :: j2) (a :: k). Ob b => (a ~> ((p :.: q) % b)) -> (p :.: q) a b Source Comments # repMap :: forall (a :: j2) (b :: j2). (a ~> b) -> ((p :.: q) % a) ~> ((p :.: q) % b) Source Comments #
(Corepresentable j2, HasColimits j1 k, HasColimits j2 k) => HasColimits (j1 :.: j2 :: i -> a -> Type) k Source Comments #
Instance details Defined in Proarrow.Category.Colimit Methods colimit :: forall (d :: k +-> i). Corepresentable d => ((j1 :.: j2) :.: Colimit (j1 :.: j2) d) :~> d Source Comments # colimitUniv :: forall (d :: k +-> i) (p :: k +-> a). (Corepresentable d, Profunctor p) => (((j1 :.: j2) :.: p) :~> d) -> p :~> Colimit (j1 :.: j2) d Source Comments #
(Representable j1, HasLimits j1 k, HasLimits j2 k) => HasLimits (j1 :.: j2 :: a -> i -> Type) k Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods limit :: forall (d :: i +-> k). Representable d => (Limit (j1 :.: j2) d :.: (j1 :.: j2)) :~> d Source Comments # limitUniv :: forall (d :: i +-> k) (p :: a +-> k). (Representable d, Profunctor p) => ((p :.: (j1 :.: j2)) :~> d) -> p :~> Limit (j1 :.: j2) d Source Comments #
(Proadjunction l1 r1, Proadjunction l2 r2) => Proadjunction (l1 :.: l2 :: i -> k -> Type) (r2 :.: r1 :: k -> i -> Type) Source Comments #
Instance details Defined in Proarrow.Adjunction Methods unit :: forall (a :: k). Ob a => ((r2 :.: r1) :.: (l1 :.: l2)) a a Source Comments # counit :: ((l1 :.: l2) :.: (r2 :.: r1)) :~> ((~>) :: CAT i) Source Comments #
(Cotraversable p, Cotraversable q) => Cotraversable (p :.: q :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods cotraverse :: forall (p0 :: k +-> k). (DistributiveProfunctor p0, Strong k p0, SelfAction k) => (p0 :.: (p :.: q)) :~> ((p :.: q) :.: p0) Source Comments #
(Traversable p, Traversable q) => Traversable (p :.: q :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods traverse :: forall (p0 :: k +-> k). (DistributiveProfunctor p0, Strong k p0, SelfAction k) => ((p :.: q) :.: p0) :~> (p0 :.: (p :.: q)) Source Comments #
Proadjunction p q => Promonad (q :.: p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Adjunction Methods id :: forall (a :: k). Ob a => (q :.: p) a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). (q :.: p) b c -> (q :.: p) a b -> (q :.: p) a c Source Comments #
Proadjunction p q => Procomonad (p :.: q :: i -> i -> Type) Source Comments #
Instance details Defined in Proarrow.Adjunction Methods extract :: (p :.: q) :~> ((~>) :: CAT i) Source Comments # duplicate :: (p :.: q) :~> ((p :.: q) :.: (p :.: q)) Source Comments #
(Profunctor f, Profunctor g, MonoidalProfunctor (Coprod f), MonoidalProfunctor (Coprod g)) => MonoidalProfunctor (Coprod (f :.: g) :: COPROD k -> COPROD j2 -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Composition Methods par0 :: Coprod (f :.: g) (Unit :: COPROD k) (Unit :: COPROD j2) Source Comments # par :: forall (x1 :: COPROD k) (x2 :: COPROD j2) (y1 :: COPROD k) (y2 :: COPROD j2). Coprod (f :.: g) x1 x2 -> Coprod (f :.: g) y1 y2 -> Coprod (f :.: g) (x1 y1) (x2 y2) Source Comments #
Functor ((:.:) :: (j +-> k) -> (i +-> j) -> k -> i -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods map :: forall (a :: j +-> k) (b :: j +-> k). (a ~> b) -> ((:.:) a :: (i +-> j) -> k -> i -> Type) ~> ((:.:) b :: (i +-> j) -> k -> i -> Type) Source Comments #
Profunctor p => Functor ((:.:) p :: (i +-> j) -> k -> i -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Composition Methods map :: forall (a :: i +-> j) (b :: i +-> j). (a ~> b) -> (p :.: a) ~> (p :.: b) Source Comments #
type Colimit (j1 :.: j2 :: i -> a -> Type) (d :: k +-> i) Source Comments #
Instance details Defined in Proarrow.Category.Colimit type Colimit (j1 :.: j2 :: i -> a -> Type) (d :: k +-> i) = Colimit j2 (Colimit j1 d)
type Limit (j1 :.: j2 :: a -> i -> Type) (d :: i +-> k) Source Comments #
Instance details Defined in Proarrow.Category.Limit type Limit (j1 :.: j2 :: a -> i -> Type) (d :: i +-> k) = Limit j1 (Limit j2 d)
type (p :.: q :: k -> j1 -> Type) %% (a :: k) Source Comments #
Instance details Defined in Proarrow.Profunctor.Composition type (p :.: q :: k -> j1 -> Type) %% (a :: k) = q %% (p %% a)
type (p :.: q :: k -> j1 -> Type) % (a :: j1) Source Comments #
Instance details Defined in Proarrow.Profunctor.Composition type (p :.: q :: k -> j1 -> Type) % (a :: j1) = p % (q % a)

o :: forall {i} {j} {k} (p :: j +-> k) (q :: j +-> k) (r :: i +-> j) (s :: i +-> j). Prof p q -> Prof r s -> Prof (p :.: r) (q :.: s) Source Comments #

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