Safe Haskell	None
Language	Haskell2010

Proarrow.Profunctor.Star

Documentation

data Star (f :: k1 -> k2) (a :: k2) (b :: k1) where Source Comments #

Constructors

Star
Fields :: forall {k1} {k2} (b :: k1) (a :: k2) (f :: k1 -> k2). Ob b => { unStar :: a ~> f b } -> Star f a b

Instances

Instances details

Functor f => Strong Type (Star f :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods act :: (a ~> b) -> Star f x y -> Star f (Act a x) (Act b y) Source Comments #
(Functor f, Applicative f) => Strong (SUBCAT Traversable) (Star (Prelude f) :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods act :: forall (a :: SUBCAT Traversable) (b :: SUBCAT Traversable) x y. (a ~> b) -> Star (Prelude f) x y -> Star (Prelude f) (Act a x) (Act b y) Source Comments #
(Applicative f, Monoidal j, Monoidal k) => MonoidalProfunctor (Star f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods par0 :: Star f (Unit :: k) (Unit :: j) Source Comments # par :: forall (x1 :: k) (x2 :: j) (y1 :: k) (y2 :: j). Star f x1 x2 -> Star f y1 y2 -> Star f (x1 y1) (x2 y2) Source Comments #
Functor f => Profunctor (Star f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Star f a b -> Star f c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Star f a b -> r Source Comments #
(Functor f, Thin j, Discrete k) => ThinProfunctor (Star f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods arr :: forall (a :: k) (b :: j). (Ob a, Ob b, HasArrow (Star f) a b) => Star f a b Source Comments # withArr :: forall (a :: k) (b :: j) r. Star f a b -> (HasArrow (Star f) a b => r) -> r Source Comments #
Functor f => Representable (Star f :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods index :: forall (a :: k) (b :: j). Star f a b -> a ~> (Star f % b) Source Comments # tabulate :: forall (b :: j) (a :: k). Ob b => (a ~> (Star f % b)) -> Star f a b Source Comments # repMap :: forall (a :: j) (b :: j). (a ~> b) -> (Star f % a) ~> (Star f % b) Source Comments #
Functor j => HasColimits (Star j :: i -> a -> Type) k Source Comments #
Instance details Defined in Proarrow.Category.Colimit Methods colimit :: forall (d :: i +-> k). Representable d => (d :.: Star j) :~> Colimit (Star j) d Source Comments # colimitUniv :: forall (d :: i +-> k) (p :: a +-> k). (Representable d, Representable p) => ((d :.: Star j) :~> p) -> Colimit (Star j) d :~> p Source Comments # colimitUniv' :: forall (d :: i +-> k) p (b :: a) (c :: k). (Representable d, Corepresentable p) => ((Star j :.: p) :~> RepCostar d) -> p b c -> RepCostar (Colimit (Star j) d) b c Source Comments #
Adjunction (Star ((,) a) :: Type -> Type -> Type) (Star ((->) a) :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Adjunction Methods unit :: Ob a0 => (Star ((->) a) :.: Star ((,) a)) a0 a0 Source Comments # counit :: (Star ((,) a) :.: Star ((->) a)) :~> ((~>) :: CAT Type) 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 #
Traversable (Star Maybe) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods traverse :: forall (p :: Type +-> Type). (DistributiveProfunctor p, Strong Type p, SelfAction Type) => (Star Maybe :.: p) :~> (p :.: Star Maybe) Source Comments #
Traversable (Star []) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods traverse :: forall (p :: Type +-> Type). (DistributiveProfunctor p, Strong Type p, SelfAction Type) => (Star [] :.: p) :~> (p :.: Star []) Source Comments #
Monad m => Promonad (Star (Prelude m) :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods id :: Ob a => Star (Prelude m) a a Source Comments # (.) :: Star (Prelude m) b c -> Star (Prelude m) a b -> Star (Prelude m) a c Source Comments #
Monad m => Strong Type (Updating a b :: Type -> KlCat m -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods act :: forall a0 b0 x (y :: KlCat m). (a0 ~> b0) -> Updating a b x y -> Updating a b (Act a0 x) (Act b0 y) Source Comments #
(Alternative f, Monoidal k, Distributive j) => MonoidalProfunctor (CoprodDom (Star f) :: k -> COPROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods par0 :: CoprodDom (Star f) (Unit :: k) (Unit :: COPROD j) Source Comments # par :: forall (x1 :: k) (x2 :: COPROD j) (y1 :: k) (y2 :: COPROD j). CoprodDom (Star f) x1 x2 -> CoprodDom (Star f) y1 y2 -> CoprodDom (Star f) (x1 y1) (x2 y2) Source Comments #
Monad m => Profunctor (Updating a b :: Type -> KlCat m -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods dimap :: forall c a0 (b0 :: KlCat m) (d :: KlCat m). (c ~> a0) -> (b0 ~> d) -> Updating a b a0 b0 -> Updating a b c d Source Comments # (\\) :: forall a0 (b0 :: KlCat m) r. ((Ob a0, Ob b0) => r) -> Updating a b a0 b0 -> r Source Comments #
(Functor f, Distributive j, Distributive k) => MonoidalProfunctor (Coprod (Star f) :: COPROD k -> COPROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods par0 :: Coprod (Star f) (Unit :: COPROD k) (Unit :: COPROD j) Source Comments # par :: forall (x1 :: COPROD k) (x2 :: COPROD j) (y1 :: COPROD k) (y2 :: COPROD j). Coprod (Star f) x1 x2 -> Coprod (Star f) y1 y2 -> Coprod (Star f) (x1 y1) (x2 y2) Source Comments #
Profunctor j => Adjunction (Star ((:.:) j :: (i2 +-> k) -> i1 -> i2 -> Type) :: (i1 -> i2 -> Type) -> (i2 +-> k) -> Type) (Star (Rift ('OP j) :: (i2 +-> i1) -> k -> i2 -> Type) :: (k -> i2 -> Type) -> (i2 +-> i1) -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Rift Methods unit :: forall (a :: i2 +-> k). Ob a => (Star (Rift ('OP j) :: (i2 +-> i1) -> k -> i2 -> Type) :.: Star ((:.:) j :: (i2 +-> k) -> i1 -> i2 -> Type)) a a Source Comments # counit :: (Star ((:.:) j :: (i2 +-> k) -> i1 -> i2 -> Type) :.: Star (Rift ('OP j) :: (i2 +-> i1) -> k -> i2 -> Type)) :~> ((~>) :: CAT (i1 -> i2 -> Type)) Source Comments #
(SymMonoidal j, SymMonoidal k, Profunctor p) => Adjunction (Star (Day p) :: (k -> j -> Type) -> (j +-> k) -> Type) (Star (DayExp p) :: (k -> j -> Type) -> (k -> j -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods unit :: forall (a :: j +-> k). Ob a => (Star (DayExp p) :.: Star (Day p)) a a Source Comments # counit :: (Star (Day p) :.: Star (DayExp p)) :~> ((~>) :: CAT (k -> j -> Type)) Source Comments #
Profunctor j2 => Adjunction (Star (Precompose j2 :: (j1 +-> k) -> k -> i -> Type) :: (k -> i -> Type) -> (j1 +-> k) -> Type) (Star (Ran ('OP j2) :: (i +-> k) -> k -> j1 -> Type) :: (k -> j1 -> Type) -> (i +-> k) -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Ran Methods unit :: forall (a :: j1 +-> k). Ob a => (Star (Ran ('OP j2) :: (i +-> k) -> k -> j1 -> Type) :.: Star (Precompose j2 :: (j1 +-> k) -> k -> i -> Type)) a a Source Comments # counit :: (Star (Precompose j2 :: (j1 +-> k) -> k -> i -> Type) :.: Star (Ran ('OP j2) :: (i +-> k) -> k -> j1 -> Type)) :~> ((~>) :: CAT (k -> i -> Type)) Source Comments #
type Colimit (Star j :: i -> a -> Type) (d :: i +-> k) Source Comments #
Instance details Defined in Proarrow.Category.Colimit type Colimit (Star j :: i -> a -> Type) (d :: i +-> k) = d :.: Star j
type (Star f :: k -> j -> Type) % (a :: j) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star type (Star f :: k -> j -> Type) % (a :: j) = f a
type HasArrow (Star f :: k -> j -> Type) (a :: k) (b :: j) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star type HasArrow (Star f :: k -> j -> Type) (a :: k) (b :: j) = a ~ f b

composeStar :: forall {k} {k1} (f :: k -> Type) (g :: k1 -> k). Functor f => (Star f :.: Star g) :~> Star (Compose f g) Source Comments #

data CoprodDom (p :: j +-> k) (a :: k) (b :: COPROD j) where Source Comments #

Constructors

Co
Fields :: forall {j} {k} (p :: j +-> k) (a :: k) (b1 :: j). { unCo :: p a b1 } -> CoprodDom p a ('COPR b1)

Instances

Instances details

(Alternative f, Monoidal k, Distributive j) => MonoidalProfunctor (CoprodDom (Star f) :: k -> COPROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods par0 :: CoprodDom (Star f) (Unit :: k) (Unit :: COPROD j) Source Comments # par :: forall (x1 :: k) (x2 :: COPROD j) (y1 :: k) (y2 :: COPROD j). CoprodDom (Star f) x1 x2 -> CoprodDom (Star f) y1 y2 -> CoprodDom (Star f) (x1 y1) (x2 y2) Source Comments #
Profunctor p => Profunctor (CoprodDom p :: k -> COPROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods dimap :: forall (c :: k) (a :: k) (b :: COPROD j) (d :: COPROD j). (c ~> a) -> (b ~> d) -> CoprodDom p a b -> CoprodDom p c d Source Comments # (\\) :: forall (a :: k) (b :: COPROD j) r. ((Ob a, Ob b) => r) -> CoprodDom p a b -> r Source Comments #

strength :: forall {k1} {k2} {m} (f :: k1 -> k2) (a :: m) (b :: k1). (Functor f, Strong m (Star f), Ob a, Ob b) => Act a (f b) ~> f (Act a b) Source Comments #