Safe Haskell	None
Language	Haskell2010

Proarrow.Profunctor.Identity

Documentation

newtype Id (a :: k) (b :: k) Source Comments #

Constructors

Id
Fields unId :: a ~> b

Instances

Instances details

(Strong m ((~>) :: CAT k), MonoidalAction m k) => Strong m (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Identity Methods act :: forall (a :: m) (b :: m) (x :: k) (y :: k). (a ~> b) -> Id x y -> Id (Act a x) (Act b y) Source Comments #
Monoidal k => MonoidalProfunctor (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Identity Methods par0 :: Id (Unit :: k) (Unit :: k) Source Comments # par :: forall (x1 :: k) (x2 :: k) (y1 :: k) (y2 :: k). Id x1 x2 -> Id y1 y2 -> Id (x1 y1) (x2 y2) Source Comments #
CategoryOf k => Profunctor (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Identity Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> Id a b -> Id c d Source Comments # (\\) :: forall (a :: k) (b :: k) r. ((Ob a, Ob b) => r) -> Id a b -> r Source Comments #
CategoryOf k => Corepresentable (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Identity Methods coindex :: forall (a :: k) (b :: k). Id a b -> ((Id :: k -> k -> Type) %% a) ~> b Source Comments # cotabulate :: forall (a :: k) (b :: k). Ob a => (((Id :: k -> k -> Type) %% a) ~> b) -> Id a b Source Comments # corepMap :: forall (a :: k) (b :: k). (a ~> b) -> ((Id :: k -> k -> Type) %% a) ~> ((Id :: k -> k -> Type) %% b) Source Comments #
CategoryOf k => Representable (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Identity Methods index :: forall (a :: k) (b :: k). Id a b -> a ~> ((Id :: k -> k -> Type) % b) Source Comments # tabulate :: forall (b :: k) (a :: k). Ob b => (a ~> ((Id :: k -> k -> Type) % b)) -> Id a b Source Comments # repMap :: forall (a :: k) (b :: k). (a ~> b) -> ((Id :: k -> k -> Type) % a) ~> ((Id :: k -> k -> Type) % b) Source Comments #
CategoryOf j => HasColimits (Id :: j -> j -> Type) k Source Comments #
Instance details Defined in Proarrow.Category.Colimit Methods colimit :: forall (d :: j +-> k). Representable d => (d :.: (Id :: j -> j -> Type)) :~> Colimit (Id :: j -> j -> Type) d Source Comments # colimitUniv :: forall (d :: j +-> k) (p :: j +-> k). (Representable d, Representable p) => ((d :.: (Id :: j -> j -> Type)) :~> p) -> Colimit (Id :: j -> j -> Type) d :~> p Source Comments # colimitUniv' :: forall (d :: j +-> k) p (b :: j) (c :: k). (Representable d, Corepresentable p) => (((Id :: j -> j -> Type) :.: p) :~> RepCostar d) -> p b c -> RepCostar (Colimit (Id :: j -> j -> Type) d) b c Source Comments #
CategoryOf j => HasLimits (Id :: j -> j -> Type) k Source Comments #
Instance details Defined in Proarrow.Category.Limit Methods limit :: forall (d :: j +-> k). Representable d => (Limit (Id :: j -> j -> Type) d :.: (Id :: j -> j -> Type)) :~> d Source Comments # limitUniv :: forall (d :: j +-> k) (p :: j +-> k). (Representable d, Representable p) => ((p :.: (Id :: j -> j -> Type)) :~> d) -> p :~> Limit (Id :: j -> j -> Type) d Source Comments #
CategoryOf k => Adjunction (Id :: k -> k -> Type) (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Adjunction Methods unit :: forall (a :: k). Ob a => ((Id :: k -> k -> Type) :.: (Id :: k -> k -> Type)) a a Source Comments # counit :: ((Id :: k -> k -> Type) :.: (Id :: k -> k -> Type)) :~> ((~>) :: CAT k) Source Comments #
Dagger k => DaggerProfunctor (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Identity Methods dagger :: forall (a :: k) (b :: k). Id a b -> Id b a Source Comments #
CategoryOf k => Cotraversable (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods cotraverse :: forall (p :: k +-> k). (DistributiveProfunctor p, Strong k p, SelfAction k) => (p :.: (Id :: k -> k -> Type)) :~> ((Id :: k -> k -> Type) :.: p) Source Comments #
CategoryOf k => Traversable (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods traverse :: forall (p :: k +-> k). (DistributiveProfunctor p, Strong k p, SelfAction k) => ((Id :: k -> k -> Type) :.: p) :~> (p :.: (Id :: k -> k -> Type)) Source Comments #
CategoryOf k => Promonad (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Identity Methods id :: forall (a :: k). Ob a => Id a a Source Comments # (.) :: forall (b :: k) (c :: k) (a :: k). Id b c -> Id a b -> Id a c Source Comments #
CategoryOf k => Procomonad (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad Methods extract :: (Id :: k -> k -> Type) :~> ((~>) :: CAT k) Source Comments # duplicate :: (Id :: k -> k -> Type) :~> ((Id :: k -> k -> Type) :.: (Id :: k -> k -> Type)) Source Comments #
Strong Type (Coprod (Id :: Type -> Type -> Type)) Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct Methods act :: forall a b (x :: COPROD Type) (y :: COPROD Type). (a ~> b) -> Coprod (Id :: Type -> Type -> Type) x y -> Coprod (Id :: Type -> Type -> Type) (Act a x) (Act b y) Source Comments #
Costrong (COPROD LINEAR) (Coprod (Id :: LINEAR -> LINEAR -> Type)) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear Methods coact :: forall (a :: COPROD LINEAR) (x :: COPROD LINEAR) (y :: COPROD LINEAR). (Ob a, Ob x, Ob y) => Coprod (Id :: LINEAR -> LINEAR -> Type) (Act a x) (Act a y) -> Coprod (Id :: LINEAR -> LINEAR -> Type) x y Source Comments #
Costrong (COPROD Type) (Coprod (Id :: Type -> Type -> Type)) Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct Methods coact :: forall (a :: COPROD Type) (x :: COPROD Type) (y :: COPROD Type). (Ob a, Ob x, Ob y) => Coprod (Id :: Type -> Type -> Type) (Act a x) (Act a y) -> Coprod (Id :: Type -> Type -> Type) x y Source Comments #
HasCoproducts k => Strong (COPROD k) (Coprod (Id :: k -> k -> Type) :: COPROD k -> COPROD k -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct Methods act :: forall (a :: COPROD k) (b :: COPROD k) (x :: COPROD k) (y :: COPROD k). (a ~> b) -> Coprod (Id :: k -> k -> Type) x y -> Coprod (Id :: k -> k -> Type) (Act a x) (Act b y) Source Comments #
HasCoproducts k => MonoidalProfunctor (Coprod (Id :: k -> k -> Type) :: COPROD k -> COPROD k -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryCoproduct Methods par0 :: Coprod (Id :: k -> k -> Type) (Unit :: COPROD k) (Unit :: COPROD k) Source Comments # par :: forall (x1 :: COPROD k) (x2 :: COPROD k) (y1 :: COPROD k) (y2 :: COPROD k). Coprod (Id :: k -> k -> Type) x1 x2 -> Coprod (Id :: k -> k -> Type) y1 y2 -> Coprod (Id :: k -> k -> Type) (x1 y1) (x2 y2) Source Comments #
type Colimit (Id :: j -> j -> Type) (d :: j +-> k) Source Comments #
Instance details Defined in Proarrow.Category.Colimit type Colimit (Id :: j -> j -> Type) (d :: j +-> k) = d
type Limit (Id :: j -> j -> Type) (d :: j +-> k) Source Comments #
Instance details Defined in Proarrow.Category.Limit type Limit (Id :: j -> j -> Type) (d :: j +-> k) = d
type (Id :: k -> k -> Type) %% (a :: k) Source Comments #
Instance details Defined in Proarrow.Profunctor.Identity type (Id :: k -> k -> Type) %% (a :: k) = a
type (Id :: k -> k -> Type) % (a :: k) Source Comments #
Instance details Defined in Proarrow.Profunctor.Identity type (Id :: k -> k -> Type) % (a :: k) = a