Safe Haskell	None
Language	GHC2024

Proarrow.Profunctor.Identity

Documentation

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

Constructors

Id
Fields unId :: a ~> b

Instances

Instances details

(MonoidalAction m k, Costrong m (Hom k)) => Costrong m (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Identity

Methods

coact :: forall (a :: m) (x :: k) (y :: k). (Ob a, Ob x, Ob y) => Id (Act a x) (Act a y) -> Id x y Source Github #

(MonoidalAction m k, Strong m (Hom k)) => Strong m (Id :: k -> k -> Type) Source Github #

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 Github #

Thin k => ThinProfunctor (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Identity

Methods

arr :: forall (a :: k) (b :: k). (Ob a, Ob b, HasArrow (Id :: k -> k -> Type) a b) => Id a b Source Github #

withArr :: forall (a :: k) (b :: k) r. Id a b -> (HasArrow (Id :: k -> k -> Type) a b => r) -> r Source Github #

Monoidal k => MonoidalProfunctor (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Identity

Methods

par0 :: Id (Unit :: k) (Unit :: k) Source Github #

par :: forall (x1 :: k) (x2 :: k) (y1 :: k) (y2 :: k). Id x1 x2 -> Id y1 y2 -> Id (x1 ** y1) (x2 ** y2) Source Github #

CategoryOf k => Profunctor (Id :: k -> k -> Type) Source Github #

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 Github #

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

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

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

CategoryOf k => Corepresentable (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Identity

Methods

coindex :: forall (a :: k) (b :: k). Id a b -> ((Id :: k -> k -> Type) %% a) ~> b Source Github #

cotabulate :: forall (a :: k) (b :: k). Ob a => (((Id :: k -> k -> Type) %% a) ~> b) -> Id a b Source Github #

corepMap :: forall (a :: k) (b :: k). (a ~> b) -> ((Id :: k -> k -> Type) %% a) ~> ((Id :: k -> k -> Type) %% b) Source Github #

trivialCorep :: forall (a :: k). Ob a => Id a ((Id :: k -> k -> Type) %% a) Source Github #

CategoryOf k => Representable (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Identity

Methods

index :: forall (a :: k) (b :: k). Id a b -> a ~> ((Id :: k -> k -> Type) % b) Source Github #

tabulate :: forall (b :: k) (a :: k). Ob b => (a ~> ((Id :: k -> k -> Type) % b)) -> Id a b Source Github #

repMap :: forall (a :: k) (b :: k). (a ~> b) -> ((Id :: k -> k -> Type) % a) ~> ((Id :: k -> k -> Type) % b) Source Github #

trivialRep :: forall (a :: k). Ob a => Id ((Id :: k -> k -> Type) % a) a Source Github #

CategoryOf j => HasColimits (Id :: j -> j -> Type) k Source Github #

Instance details

Defined in Proarrow.Category.Colimit

Methods

colimit :: forall (d :: k +-> j). Corepresentable d => ((Id :: j -> j -> Type) :.: Colimit (Id :: j -> j -> Type) d) :~> d Source Github #

colimitUniv :: forall (d :: k +-> j) (p :: k +-> j). (Corepresentable d, Profunctor p) => (((Id :: j -> j -> Type) :.: p) :~> d) -> p :~> Colimit (Id :: j -> j -> Type) d Source Github #

CategoryOf j => HasLimits (Id :: j -> j -> Type) k Source Github #

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 Github #

limitUniv :: forall (d :: j +-> k) (p :: j +-> k). (Representable d, Profunctor p) => ((p :.: (Id :: j -> j -> Type)) :~> d) -> p :~> Limit (Id :: j -> j -> Type) d Source Github #

CategoryOf k => Proadjunction (Id :: k -> k -> Type) (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Adjunction

Methods

unit :: forall (a :: k). Ob a => ((Id :: k -> k -> Type) :.: (Id :: k -> k -> Type)) a a Source Github #

counit :: ((Id :: k -> k -> Type) :.: (Id :: k -> k -> Type)) :~> ((~>) :: CAT k) Source Github #

Costrong (COPROD Type) (Id :: Type -> Type -> Type) Source Github #

Instance details

Defined in Proarrow.Object.BinaryCoproduct

Methods

coact :: forall (a :: COPROD Type) x y. (Ob a, Ob x, Ob y) => Id (Act a x) (Act a y) -> Id x y Source Github #

(SymMonoidal k, Ob s) => MonoidalProfunctor (State s :: k -> k -> Type) Source Github #

Note: This is only premonoidal, not monoidal.

Instance details

Defined in Proarrow.Promonad.State

Methods

par0 :: State s (Unit :: k) (Unit :: k) Source Github #

par :: forall (x1 :: k) (x2 :: k) (y1 :: k) (y2 :: k). State s x1 x2 -> State s y1 y2 -> State s (x1 ** y1) (x2 ** y2) Source Github #

CategoryOf k => Involution (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Adjunction

Methods

involuted :: forall (a :: k) (a' :: k). (Ob a, Ob a') => Iso a a' ((Id :: k -> k -> Type) % ((Id :: k -> k -> Type) % a)) ((Id :: k -> k -> Type) % ((Id :: k -> k -> Type) % a')) Source Github #

Dagger k => DaggerProfunctor (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Identity

Methods

dagger :: forall (a :: k) (b :: k). Id a b -> Id b a Source Github #

SelfAction k => IsReader (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Equipment.Stateful

Associated Types

type WithWriter (Id :: k -> k -> Type)
Instance details Defined in Proarrow.Category.Equipment.Stateful type WithWriter (Id :: k -> k -> Type) = Id :: k -> k -> Type

SelfAction k => IsWriter (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Equipment.Stateful

Associated Types

type WithReader (Id :: k -> k -> Type)
Instance details Defined in Proarrow.Category.Equipment.Stateful type WithReader (Id :: k -> k -> Type) = Id :: k -> k -> Type

CategoryOf k => Cotraversable (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Distributive

Methods

cotraverse :: forall (p :: k +-> k). StrongDistributiveProfunctor p => (p :.: (Id :: k -> k -> Type)) :~> ((Id :: k -> k -> Type) :.: p) Source Github #

CategoryOf k => Traversable (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Monoidal.Distributive

Methods

traverse :: forall (p :: k +-> k). StrongDistributiveProfunctor p => ((Id :: k -> k -> Type) :.: p) :~> (p :.: (Id :: k -> k -> Type)) Source Github #

CategoryOf k => Promonad (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Profunctor.Identity

Methods

id :: forall (a :: k). Ob a => Id a a Source Github #

(.) :: forall (b :: k) (c :: k) (a :: k). Id b c -> Id a b -> Id a c Source Github #

CategoryOf k => Procomonad (Id :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Promonad

Methods

extract :: (Id :: k -> k -> Type) :~> ((~>) :: CAT k) Source Github #

duplicate :: (Id :: k -> k -> Type) :~> ((Id :: k -> k -> Type) :.: (Id :: k -> k -> Type)) Source Github #

(HasZeroObject k, HasBiproducts k, Ob a, Ob b) => CommutativeMonoid (Id a b :: Type) Source Github #

Instance details

Defined in Proarrow.Monoid

Strong Type (Coprod (Id :: Type -> Type -> Type)) Source Github #

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 Github #

HasCoproducts k => MonoidalProfunctor (Coprod (Id :: k -> k -> Type) :: COPROD k -> COPROD k -> Type) Source Github #

Instance details

Defined in Proarrow.Object.BinaryCoproduct

Methods

par0 :: Coprod (Id :: k -> k -> Type) (Unit :: COPROD k) (Unit :: COPROD k) Source Github #

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 Github #