Safe Haskell	None
Language	Haskell2010

Proarrow.Category.Instance.Nat

Contents

Orphan instances

Documentation

data Nat (f :: j -> k) (g :: j -> k) where Source Comments #

Constructors

Nat
Fields :: forall {j} {k} (f :: j -> k) (g :: j -> k). (Functor f, Functor g) => { getNat :: f .~> g } -> Nat f g

Instances

Instances details

Promonad (Nat :: (j -> Type) -> (j -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: j -> Type). Ob a => Nat a a Source Comments # (.) :: forall (b :: j -> Type) (c :: j -> Type) (a :: j -> Type). Nat b c -> Nat a b -> Nat a c Source Comments #
Promonad (Nat :: (k1 -> k2 -> k3 -> k4 -> Type) -> (k1 -> k2 -> k3 -> k4 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: k1 -> k2 -> k3 -> k4 -> Type). Ob a => Nat a a Source Comments # (.) :: forall (b :: k1 -> k2 -> k3 -> k4 -> Type) (c :: k1 -> k2 -> k3 -> k4 -> Type) (a :: k1 -> k2 -> k3 -> k4 -> Type). Nat b c -> Nat a b -> Nat a c Source Comments #
Promonad (Nat :: (k1 -> k2 -> k3 -> Type) -> (k1 -> k2 -> k3 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: k1 -> k2 -> k3 -> Type). Ob a => Nat a a Source Comments # (.) :: forall (b :: k1 -> k2 -> k3 -> Type) (c :: k1 -> k2 -> k3 -> Type) (a :: k1 -> k2 -> k3 -> Type). Nat b c -> Nat a b -> Nat a c Source Comments #
Tambara (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Replacing a b :: Type -> Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods tambara :: forall (x :: Type -> Type) (x' :: Type -> Type) a0 b0. Nat x x' -> Replacing a b a0 b0 -> Replacing a b (Act x a0) (Act x' b0) Source Comments #
MonoidalProfunctor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods lift0 :: Nat (Unit :: Type -> Type) (Unit :: Type -> Type) Source Comments # lift2 :: forall (x1 :: Type -> Type) (x2 :: Type -> Type) (y1 :: Type -> Type) (y2 :: Type -> Type). Nat x1 x2 -> Nat y1 y2 -> Nat (x1 y1) (x2 y2) Source Comments #
Profunctor (Nat :: (k1 -> k2 -> k3 -> k4 -> Type) -> (k1 -> k2 -> k3 -> k4 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: k1 -> k2 -> k3 -> k4 -> Type) (a :: k1 -> k2 -> k3 -> k4 -> Type) (b :: k1 -> k2 -> k3 -> k4 -> Type) (d :: k1 -> k2 -> k3 -> k4 -> Type). (c ~> a) -> (b ~> d) -> Nat a b -> Nat c d Source Comments # (\\) :: forall (a :: k1 -> k2 -> k3 -> k4 -> Type) (b :: k1 -> k2 -> k3 -> k4 -> Type) r. ((Ob a, Ob b) => r) -> Nat a b -> r Source Comments #
Profunctor (Nat :: (k1 -> k2 -> k3 -> Type) -> (k1 -> k2 -> k3 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: k1 -> k2 -> k3 -> Type) (a :: k1 -> k2 -> k3 -> Type) (b :: k1 -> k2 -> k3 -> Type) (d :: k1 -> k2 -> k3 -> Type). (c ~> a) -> (b ~> d) -> Nat a b -> Nat c d Source Comments # (\\) :: forall (a :: k1 -> k2 -> k3 -> Type) (b :: k1 -> k2 -> k3 -> Type) r. ((Ob a, Ob b) => r) -> Nat a b -> r Source Comments #
Profunctor (Nat :: (k1 -> Type) -> (k1 -> Type) -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: k1 -> Type) (a :: k1 -> Type) (b :: k1 -> Type) (d :: k1 -> Type). (c ~> a) -> (b ~> d) -> Nat a b -> Nat c d Source Comments # (\\) :: forall (a :: k1 -> Type) (b :: k1 -> Type) r. ((Ob a, Ob b) => r) -> Nat a b -> r Source Comments #

newtype NatK j k Source Comments #

Constructors

NT (j -> k)

Instances

Instances details

CategoryOf (NatK j k) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Nat

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Nat type (~>) = Nat' :: NatK j k -> NatK j k -> Type

Promonad (Nat' :: NatK j k -> NatK j k -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Nat

Methods

id :: forall (a :: NatK j k). Ob a => Nat' a a Source Comments #

(.) :: forall (b :: NatK j k) (c :: NatK j k) (a :: NatK j k). Nat' b c -> Nat' a b -> Nat' a c Source Comments #

Profunctor (Nat' :: NatK j k -> NatK j k -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Nat

Methods

dimap :: forall (c :: NatK j k) (a :: NatK j k) (b :: NatK j k) (d :: NatK j k). (c ~> a) -> (b ~> d) -> Nat' a b -> Nat' c d Source Comments #

(\\) :: forall (a :: NatK j k) (b :: NatK j k) r. ((Ob a, Ob b) => r) -> Nat' a b -> r Source Comments #

type (~>) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Nat

type (~>) = Nat' :: NatK j k -> NatK j k -> Type

type Ob (f :: NatK j k) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Nat

type Ob (f :: NatK j k) = (Is ('NT :: (j -> k) -> NatK j k) f, Functor (UN ('NT :: (j -> k) -> NatK j k) f))

type UN ('NT :: (j -> k) -> NatK j k) ('NT f :: NatK j k) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Nat

type UN ('NT :: (j -> k) -> NatK j k) ('NT f :: NatK j k) = f

data Nat' (f :: NatK k k1) (g :: NatK k k1) where Source Comments #

Constructors

Nat'
Fields :: forall {k} {k1} (f1 :: k -> k1) (g1 :: k -> k1). (Functor f1, Functor g1) => { getNat' :: f1 .~> g1 } -> Nat' ('NT f1) ('NT g1)

Instances

Instances details

Promonad (Nat' :: NatK j k -> NatK j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods id :: forall (a :: NatK j k). Ob a => Nat' a a Source Comments # (.) :: forall (b :: NatK j k) (c :: NatK j k) (a :: NatK j k). Nat' b c -> Nat' a b -> Nat' a c Source Comments #
Profunctor (Nat' :: NatK j k -> NatK j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods dimap :: forall (c :: NatK j k) (a :: NatK j k) (b :: NatK j k) (d :: NatK j k). (c ~> a) -> (b ~> d) -> Nat' a b -> Nat' c d Source Comments # (\\) :: forall (a :: NatK j k) (b :: NatK j k) r. ((Ob a, Ob b) => r) -> Nat' a b -> r Source Comments #

Orphan instances

Monoidal (Type -> Type) Source Comments #

Instance details

Associated Types

type Unit
Instance details Defined in Proarrow.Category.Instance.Nat type Unit = Identity
type (f :: Type -> Type) ** (g :: Type -> Type)
Instance details Defined in Proarrow.Category.Instance.Nat type (f :: Type -> Type) ** (g :: Type -> Type) = Compose f g

Methods

par :: forall (a :: Type -> Type) (b :: Type -> Type) (c :: Type -> Type) (d :: Type -> Type). (a ~> b) -> (c ~> d) -> (a ** c) ~> (b ** d) Source Comments #

leftUnitor :: forall (a :: Type -> Type). Obj a -> ((Unit :: Type -> Type) ** a) ~> a Source Comments #

leftUnitorInv :: forall (a :: Type -> Type). Obj a -> a ~> ((Unit :: Type -> Type) ** a) Source Comments #

rightUnitor :: forall (a :: Type -> Type). Obj a -> (a ** (Unit :: Type -> Type)) ~> a Source Comments #

rightUnitorInv :: forall (a :: Type -> Type). Obj a -> a ~> (a ** (Unit :: Type -> Type)) Source Comments #

associator :: forall (a :: Type -> Type) (b :: Type -> Type) (c :: Type -> Type). Obj a -> Obj b -> Obj c -> ((a ** b) ** c) ~> (a ** (b ** c)) Source Comments #

associatorInv :: forall (a :: Type -> Type) (b :: Type -> Type) (c :: Type -> Type). Obj a -> Obj b -> Obj c -> (a ** (b ** c)) ~> ((a ** b) ** c) Source Comments #

CategoryOf (k1 -> k2 -> k3 -> k4 -> Type) Source Comments #

Instance details

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Nat type (~>) = Nat :: (k1 -> k2 -> k3 -> k4 -> Type) -> (k1 -> k2 -> k3 -> k4 -> Type) -> Type

CategoryOf (k1 -> k2 -> k3 -> Type) Source Comments #

Instance details

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Nat type (~>) = Nat :: (k1 -> k2 -> k3 -> Type) -> (k1 -> k2 -> k3 -> Type) -> Type

CategoryOf (k1 -> Type) Source Comments #

Instance details

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Nat type (~>) = Nat :: (k1 -> Type) -> (k1 -> Type) -> Type