Safe Haskell	None
Language	GHC2024

Proarrow.Profunctor.Costar

Documentation

data Costar (f :: j -> k) (a :: j) (b :: k) where Source Comments #

Constructors

Costar
Fields :: forall {j} {k} (a :: j) (f :: j -> k) (b :: k). Ob a => { unCostar :: f a ~> b } -> Costar f a b

Instances

Instances details

(Functor f, Discrete j, Thin k) => ThinProfunctor (Costar f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Costar Methods arr :: forall (a :: k) (b :: j). (Ob a, Ob b, HasArrow (Costar f) a b) => Costar f a b Source Comments # withArr :: forall (a :: k) (b :: j) r. Costar f a b -> (HasArrow (Costar f) a b => r) -> r Source Comments #
(Cartesian j, Cartesian k, Functor f) => MonoidalProfunctor (Costar f :: j -> k -> Type) Source Comments #	Every functor between cartesian categories is a colax monoidal functor.
Instance details Defined in Proarrow.Profunctor.Costar Methods par0 :: Costar f (Unit :: j) (Unit :: k) Source Comments # par :: forall (x1 :: j) (x2 :: k) (y1 :: j) (y2 :: k). Costar f x1 x2 -> Costar f y1 y2 -> Costar f (x1 y1) (x2 y2) Source Comments #
Functor f => Profunctor (Costar f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Costar Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Costar f a b -> Costar f c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Costar f a b -> r Source Comments #
Functor f => Corepresentable (Costar f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Costar Methods coindex :: forall (a :: k) (b :: j). Costar f a b -> (Costar f %% a) ~> b Source Comments # cotabulate :: forall (a :: k) (b :: j). Ob a => ((Costar f %% a) ~> b) -> Costar f a b Source Comments # corepMap :: forall (a :: k) (b :: k). (a ~> b) -> (Costar f %% a) ~> (Costar f %% b) Source Comments #
(Functor f, Functor g, Adjunction (Star f) (Star g)) => Adjunction (Costar f :: k -> j -> Type) (Costar g :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Adjunction Methods unit :: forall (a :: j). Ob a => (Costar g :.: Costar f) a a Source Comments # counit :: (Costar f :.: Costar g) :~> ((~>) :: CAT k) Source Comments #
Functor f => Adjunction (Star f :: k -> j -> Type) (Costar f :: j -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Adjunction Methods unit :: forall (a :: j). Ob a => (Costar f :.: Star f) a a Source Comments # counit :: (Star f :.: Costar f) :~> ((~>) :: CAT k) Source Comments #
(Functor t, Traversable (Star t)) => Cotraversable (Costar t :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Costar Methods cotraverse :: forall (p :: k +-> k). (DistributiveProfunctor p, Strong k p, SelfAction k) => (p :.: Costar t) :~> (Costar t :.: p) Source Comments #
Monad m => Procomonad (Costar (Prelude m) :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Costar Methods extract :: Costar (Prelude m) :~> ((~>) :: CAT Type) Source Comments # duplicate :: Costar (Prelude m) :~> (Costar (Prelude m) :.: Costar (Prelude m)) Source Comments #
type (Costar f :: k -> j -> Type) %% (a :: k) Source Comments #
Instance details Defined in Proarrow.Profunctor.Costar type (Costar f :: k -> j -> Type) %% (a :: k) = f a
type HasArrow (Costar f :: k -> j -> Type) (a :: k) (b :: j) Source Comments #
Instance details Defined in Proarrow.Profunctor.Costar type HasArrow (Costar f :: k -> j -> Type) (a :: k) (b :: j) = f a ~ b

composeCostar :: forall {k} {j} (g :: k -> Type) (f :: j -> k). Functor g => (Costar f :.: Costar g) :~> Costar (Compose g f) Source Comments #

costrength :: forall {d} {k} {m} (f :: d -> k) (a :: m) (b :: d). (Functor f, Strong m (Costar f), Ob a, Ob b) => f (Act a b) ~> Act a (f b) Source Comments #