Safe Haskell	None
Language	Haskell2010

Proarrow.Category.Instance.Kleisli

Synopsis

newtype KLEISLI (p :: CAT k) = KL k
data Kleisli (a :: KLEISLI p) (b :: KLEISLI p) where
- Kleisli :: forall {k} (p :: CAT k) (a1 :: k) (b1 :: k). {..} -> Kleisli ('KL a1 :: KLEISLI p) ('KL b1 :: KLEISLI p)
arr :: forall {k} (p :: PRO k k) (a :: k) (b :: k). Promonad p => (a ~> b) -> Kleisli ('KL a :: KLEISLI p) ('KL b :: KLEISLI p)
data KleisliFree (p :: k +-> k) (a :: KLEISLI p) (b :: k) where
- KleisliFree :: forall {k} (p :: k +-> k) (a1 :: k) (b :: k). p a1 b -> KleisliFree p ('KL a1 :: KLEISLI p) b
data KleisliForget (p :: k +-> k) (a :: k) (b :: KLEISLI p) where
- KleisliForget :: forall {k} (p :: k +-> k) (a :: k) (b1 :: k). p a b1 -> KleisliForget p a ('KL b1 :: KLEISLI p)
type LIFTEDF (f :: j -> k) = KLEISLI (Costar f :.: Star f)
pattern LiftF :: forall {k1} {k2} (f :: k1 -> k2) (a :: k1) (b :: k1). Functor f => (Ob a, Ob b) => (f a ~> f b) -> Kleisli ('KL a :: KLEISLI (Costar f :.: Star f)) ('KL b :: KLEISLI (Costar f :.: Star f))

Documentation

newtype KLEISLI (p :: CAT k) Source Comments #

Constructors

KL k

Instances

Instances details

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 #

(Strong k p, Promonad p, Monoidal k) => MonoidalAction k (KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Methods

withObAct :: forall (a :: k) (x :: KLEISLI p) r. (Ob a, Ob x) => (Ob (Act a x) => r) -> r Source Comments #

unitor :: forall (x :: KLEISLI p). Ob x => Act (Unit :: k) x ~> x Source Comments #

unitorInv :: forall (x :: KLEISLI p). Ob x => x ~> Act (Unit :: k) x Source Comments #

multiplicator :: forall (a :: k) (b :: k) (x :: KLEISLI p). (Ob a, Ob b, Ob x) => Act a (Act b x) ~> Act (a ** b) x Source Comments #

multiplicatorInv :: forall (a :: k) (b :: k) (x :: KLEISLI p). (Ob a, Ob b, Ob x) => Act (a ** b) x ~> Act a (Act b x) Source Comments #

Promonad p => Profunctor (KleisliForget p :: j -> KLEISLI p -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Methods

dimap :: forall (c :: j) (a :: j) (b :: KLEISLI p) (d :: KLEISLI p). (c ~> a) -> (b ~> d) -> KleisliForget p a b -> KleisliForget p c d Source Comments #

(\\) :: forall (a :: j) (b :: KLEISLI p) r. ((Ob a, Ob b) => r) -> KleisliForget p a b -> r Source Comments #

Promonad p => Adjunction (KleisliFree p :: KLEISLI p -> k -> Type) (KleisliForget p :: k -> KLEISLI p -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Methods

unit :: forall (a :: k). Ob a => (KleisliForget p :.: KleisliFree p) a a Source Comments #

counit :: (KleisliFree p :.: KleisliForget p) :~> ((~>) :: CAT (KLEISLI p)) 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 #

(Promonad p, MonoidalProfunctor p) => Monoidal (KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Associated Types

type Unit
Instance details Defined in Proarrow.Category.Instance.Kleisli type Unit = 'KL (Unit :: k) :: KLEISLI p

Methods

withOb2 :: forall (a :: KLEISLI p) (b :: KLEISLI p) r. (Ob a, Ob b) => (Ob (a ** b) => r) -> r Source Comments #

leftUnitor :: forall (a :: KLEISLI p). Ob a => ((Unit :: KLEISLI p) ** a) ~> a Source Comments #

leftUnitorInv :: forall (a :: KLEISLI p). Ob a => a ~> ((Unit :: KLEISLI p) ** a) Source Comments #

rightUnitor :: forall (a :: KLEISLI p). Ob a => (a ** (Unit :: KLEISLI p)) ~> a Source Comments #

rightUnitorInv :: forall (a :: KLEISLI p). Ob a => a ~> (a ** (Unit :: KLEISLI p)) Source Comments #

associator :: forall (a :: KLEISLI p) (b :: KLEISLI p) (c :: KLEISLI p). (Ob a, Ob b, Ob c) => ((a ** b) ** c) ~> (a ** (b ** c)) Source Comments #

associatorInv :: forall (a :: KLEISLI p) (b :: KLEISLI p) (c :: KLEISLI p). (Ob a, Ob b, Ob c) => (a ** (b ** c)) ~> ((a ** b) ** c) Source Comments #

(Promonad p, MonoidalProfunctor p, SymMonoidal k) => SymMonoidal (KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Methods

swap :: forall (a :: KLEISLI p) (b :: KLEISLI p). (Ob a, Ob b) => (a ** b) ~> (b ** a) Source Comments #

(Distributive k, Promonad p, DistributiveProfunctor p) => Distributive (KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Methods

distL :: forall (a :: KLEISLI p) (b :: KLEISLI p) (c :: KLEISLI p). (Ob a, Ob b, Ob c) => (a ** (b || c)) ~> ((a ** b) || (a ** c)) Source Comments #

distR :: forall (a :: KLEISLI p) (b :: KLEISLI p) (c :: KLEISLI p). (Ob a, Ob b, Ob c) => ((a || b) ** c) ~> ((a ** c) || (b ** c)) Source Comments #

distL0 :: forall (a :: KLEISLI p). Ob a => (a ** (InitialObject :: KLEISLI p)) ~> (InitialObject :: KLEISLI p) Source Comments #

distR0 :: forall (a :: KLEISLI p). Ob a => ((InitialObject :: KLEISLI p) ** a) ~> (InitialObject :: KLEISLI p) Source Comments #

Promonad p => CategoryOf (KLEISLI p) Source Comments #

Every promonad makes a category.

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Kleisli type (~>) = Kleisli :: KLEISLI p -> KLEISLI p -> Type

(HasBinaryCoproducts k, Promonad p, MonoidalProfunctor (Coprod p)) => HasBinaryCoproducts (KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Methods

withObCoprod :: forall (a :: KLEISLI p) (b :: KLEISLI p) r. (Ob a, Ob b) => (Ob (a || b) => r) -> r Source Comments #

lft :: forall (a :: KLEISLI p) (b :: KLEISLI p). (Ob a, Ob b) => a ~> (a || b) Source Comments #

rgt :: forall (a :: KLEISLI p) (b :: KLEISLI p). (Ob a, Ob b) => b ~> (a || b) Source Comments #

(|||) :: forall (x :: KLEISLI p) (a :: KLEISLI p) (y :: KLEISLI p). (x ~> a) -> (y ~> a) -> (x || y) ~> a Source Comments #

(+++) :: forall (a :: KLEISLI p) (b :: KLEISLI p) (x :: KLEISLI p) (y :: KLEISLI p). (a ~> x) -> (b ~> y) -> (a || b) ~> (x || y) Source Comments #

(Cartesian k, Promonad p, MonoidalProfunctor p) => HasBinaryProducts (KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Methods

withObProd :: forall (a :: KLEISLI p) (b :: KLEISLI p) r. (Ob a, Ob b) => (Ob (a && b) => r) -> r Source Comments #

fst :: forall (a :: KLEISLI p) (b :: KLEISLI p). (Ob a, Ob b) => (a && b) ~> a Source Comments #

snd :: forall (a :: KLEISLI p) (b :: KLEISLI p). (Ob a, Ob b) => (a && b) ~> b Source Comments #

(&&&) :: forall (a :: KLEISLI p) (x :: KLEISLI p) (y :: KLEISLI p). (a ~> x) -> (a ~> y) -> a ~> (x && y) Source Comments #

(***) :: forall (a :: KLEISLI p) (b :: KLEISLI p) (x :: KLEISLI p) (y :: KLEISLI p). (a ~> x) -> (b ~> y) -> (a && b) ~> (x && y) Source Comments #

StarAutonomous (KLEISLI (Cont r)) Source Comments #

Instance details

Defined in Proarrow.Promonad.Cont

Methods

dual :: forall (a :: KLEISLI (Cont r)) (b :: KLEISLI (Cont r)). (a ~> b) -> Dual b ~> Dual a Source Comments #

dualInv :: forall (a :: KLEISLI (Cont r)) (b :: KLEISLI (Cont r)). (Ob a, Ob b) => (Dual a ~> Dual b) -> b ~> a Source Comments #

linDist :: forall (a :: KLEISLI (Cont r)) (b :: KLEISLI (Cont r)) (c :: KLEISLI (Cont r)). (Ob a, Ob b, Ob c) => ((a ** b) ~> Dual c) -> a ~> Dual (b ** c) Source Comments #

linDistInv :: forall (a :: KLEISLI (Cont r)) (b :: KLEISLI (Cont r)) (c :: KLEISLI (Cont r)). (Ob a, Ob b, Ob c) => (a ~> Dual (b ** c)) -> (a ** b) ~> Dual c Source Comments #

Closed (KLEISLI (Cont r)) Source Comments #

Instance details

Defined in Proarrow.Promonad.Cont

Methods

withObExp :: forall (a :: KLEISLI (Cont r)) (b :: KLEISLI (Cont r)) r0. (Ob a, Ob b) => (Ob (a ~~> b) => r0) -> r0 Source Comments #

curry :: forall (a :: KLEISLI (Cont r)) (b :: KLEISLI (Cont r)) (c :: KLEISLI (Cont r)). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Comments #

uncurry :: forall (b :: KLEISLI (Cont r)) (c :: KLEISLI (Cont r)) (a :: KLEISLI (Cont r)). (Ob b, Ob c) => (a ~> (b ~~> c)) -> (a ** b) ~> c Source Comments #

(^^^) :: forall (a :: KLEISLI (Cont r)) (b :: KLEISLI (Cont r)) (x :: KLEISLI (Cont r)) (y :: KLEISLI (Cont r)). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Comments #

(HasInitialObject k, Promonad p) => HasInitialObject (KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.Kleisli type InitialObject = 'KL (InitialObject :: k) :: KLEISLI p

Methods

initiate :: forall (a :: KLEISLI p). Ob a => (InitialObject :: KLEISLI p) ~> a Source Comments #

(HasTerminalObject k, Promonad p) => HasTerminalObject (KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Associated Types

type TerminalObject
Instance details Defined in Proarrow.Category.Instance.Kleisli type TerminalObject = 'KL (TerminalObject :: k) :: KLEISLI p

Methods

terminate :: forall (a :: KLEISLI p). Ob a => a ~> (TerminalObject :: KLEISLI p) Source Comments #

Promonad p => Profunctor (KleisliFree p :: KLEISLI p -> k -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Methods

dimap :: forall (c :: KLEISLI p) (a :: KLEISLI p) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> KleisliFree p a b -> KleisliFree p c d Source Comments #

(\\) :: forall (a :: KLEISLI p) (b :: k) r. ((Ob a, Ob b) => r) -> KleisliFree p a b -> r Source Comments #

Promonad p => Promonad (Kleisli :: KLEISLI p -> KLEISLI p -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Methods

id :: forall (a :: KLEISLI p). Ob a => Kleisli a a Source Comments #

(.) :: forall (b :: KLEISLI p) (c :: KLEISLI p) (a :: KLEISLI p). Kleisli b c -> Kleisli a b -> Kleisli a c Source Comments #

(Strong k p, Promonad p, Monoidal k) => Strong k (Kleisli :: KLEISLI p -> KLEISLI p -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Methods

act :: forall (a :: k) (b :: k) (x :: KLEISLI p) (y :: KLEISLI p). (a ~> b) -> Kleisli x y -> Kleisli (Act a x) (Act b y) Source Comments #

(Promonad p, MonoidalProfunctor p) => MonoidalProfunctor (Kleisli :: KLEISLI p -> KLEISLI p -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Methods

par0 :: Kleisli (Unit :: KLEISLI p) (Unit :: KLEISLI p) Source Comments #

par :: forall (x1 :: KLEISLI p) (x2 :: KLEISLI p) (y1 :: KLEISLI p) (y2 :: KLEISLI p). Kleisli x1 x2 -> Kleisli y1 y2 -> Kleisli (x1 ** y1) (x2 ** y2) Source Comments #

Promonad p => Profunctor (Kleisli :: KLEISLI p -> KLEISLI p -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

Methods

dimap :: forall (c :: KLEISLI p) (a :: KLEISLI p) (b :: KLEISLI p) (d :: KLEISLI p). (c ~> a) -> (b ~> d) -> Kleisli a b -> Kleisli c d Source Comments #

(\\) :: forall (a :: KLEISLI p) (b :: KLEISLI p) r. ((Ob a, Ob b) => r) -> Kleisli a b -> r Source Comments #

type Act (y :: k) ('KL x :: KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

type Act (y :: k) ('KL x :: KLEISLI p) = 'KL (Act y x) :: KLEISLI p

type UN ('KL :: j -> KLEISLI p) ('KL k :: KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

type UN ('KL :: j -> KLEISLI p) ('KL k :: KLEISLI p) = k

type Unit Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

type Unit = 'KL (Unit :: k) :: KLEISLI p

type (~>) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

type (~>) = Kleisli :: KLEISLI p -> KLEISLI p -> Type

type InitialObject Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

type InitialObject = 'KL (InitialObject :: k) :: KLEISLI p

type TerminalObject Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

type TerminalObject = 'KL (TerminalObject :: k) :: KLEISLI p

type Ob (a :: KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

type Ob (a :: KLEISLI p) = (Is ('KL :: k -> KLEISLI p) a, Ob (UN ('KL :: k -> KLEISLI p) a))

type (a :: KLEISLI p) ** (b :: KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

type (a :: KLEISLI p) ** (b :: KLEISLI p) = 'KL (UN ('KL :: k -> KLEISLI p) a ** UN ('KL :: k -> KLEISLI p) b) :: KLEISLI p

type (a :: KLEISLI p) || (b :: KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

type (a :: KLEISLI p) || (b :: KLEISLI p) = 'KL (UN ('KL :: k -> KLEISLI p) a || UN ('KL :: k -> KLEISLI p) b) :: KLEISLI p

type (a :: KLEISLI p) && (b :: KLEISLI p) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Kleisli

type (a :: KLEISLI p) && (b :: KLEISLI p) = 'KL (UN ('KL :: k -> KLEISLI p) a && UN ('KL :: k -> KLEISLI p) b) :: KLEISLI p

type (a :: KLEISLI (Cont r)) ~~> (b :: KLEISLI (Cont r)) Source Comments #

Instance details

Defined in Proarrow.Promonad.Cont

type (a :: KLEISLI (Cont r)) ~~> (b :: KLEISLI (Cont r)) = ExpSA a b

type Dual ('KL a :: KLEISLI (Cont r)) Source Comments #

Instance details

Defined in Proarrow.Promonad.Cont

type Dual ('KL a :: KLEISLI (Cont r)) = 'KL (a -> r) :: KLEISLI (Cont r)

data Kleisli (a :: KLEISLI p) (b :: KLEISLI p) where Source Comments #

Constructors

Kleisli
Fields :: forall {k} (p :: CAT k) (a1 :: k) (b1 :: k). { runKleisli :: p a1 b1 } -> Kleisli ('KL a1 :: KLEISLI p) ('KL b1 :: KLEISLI p)

Instances

Instances details

Promonad p => Promonad (Kleisli :: KLEISLI p -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods id :: forall (a :: KLEISLI p). Ob a => Kleisli a a Source Comments # (.) :: forall (b :: KLEISLI p) (c :: KLEISLI p) (a :: KLEISLI p). Kleisli b c -> Kleisli a b -> Kleisli a c Source Comments #
(Strong k p, Promonad p, Monoidal k) => Strong k (Kleisli :: KLEISLI p -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods act :: forall (a :: k) (b :: k) (x :: KLEISLI p) (y :: KLEISLI p). (a ~> b) -> Kleisli x y -> Kleisli (Act a x) (Act b y) Source Comments #
(Promonad p, MonoidalProfunctor p) => MonoidalProfunctor (Kleisli :: KLEISLI p -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods par0 :: Kleisli (Unit :: KLEISLI p) (Unit :: KLEISLI p) Source Comments # par :: forall (x1 :: KLEISLI p) (x2 :: KLEISLI p) (y1 :: KLEISLI p) (y2 :: KLEISLI p). Kleisli x1 x2 -> Kleisli y1 y2 -> Kleisli (x1 y1) (x2 y2) Source Comments #
Promonad p => Profunctor (Kleisli :: KLEISLI p -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods dimap :: forall (c :: KLEISLI p) (a :: KLEISLI p) (b :: KLEISLI p) (d :: KLEISLI p). (c ~> a) -> (b ~> d) -> Kleisli a b -> Kleisli c d Source Comments # (\\) :: forall (a :: KLEISLI p) (b :: KLEISLI p) r. ((Ob a, Ob b) => r) -> Kleisli a b -> r Source Comments #

arr :: forall {k} (p :: PRO k k) (a :: k) (b :: k). Promonad p => (a ~> b) -> Kleisli ('KL a :: KLEISLI p) ('KL b :: KLEISLI p) Source Comments #

data KleisliFree (p :: k +-> k) (a :: KLEISLI p) (b :: k) where Source Comments #

Constructors

KleisliFree :: forall {k} (p :: k +-> k) (a1 :: k) (b :: k). p a1 b -> KleisliFree p ('KL a1 :: KLEISLI p) b

Instances

Instances details

Promonad p => Adjunction (KleisliFree p :: KLEISLI p -> k -> Type) (KleisliForget p :: k -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods unit :: forall (a :: k). Ob a => (KleisliForget p :.: KleisliFree p) a a Source Comments # counit :: (KleisliFree p :.: KleisliForget p) :~> ((~>) :: CAT (KLEISLI p)) Source Comments #
Promonad p => Profunctor (KleisliFree p :: KLEISLI p -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods dimap :: forall (c :: KLEISLI p) (a :: KLEISLI p) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> KleisliFree p a b -> KleisliFree p c d Source Comments # (\\) :: forall (a :: KLEISLI p) (b :: k) r. ((Ob a, Ob b) => r) -> KleisliFree p a b -> r Source Comments #

data KleisliForget (p :: k +-> k) (a :: k) (b :: KLEISLI p) where Source Comments #

Constructors

KleisliForget :: forall {k} (p :: k +-> k) (a :: k) (b1 :: k). p a b1 -> KleisliForget p a ('KL b1 :: KLEISLI p)

Instances

Instances details

Promonad p => Profunctor (KleisliForget p :: j -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods dimap :: forall (c :: j) (a :: j) (b :: KLEISLI p) (d :: KLEISLI p). (c ~> a) -> (b ~> d) -> KleisliForget p a b -> KleisliForget p c d Source Comments # (\\) :: forall (a :: j) (b :: KLEISLI p) r. ((Ob a, Ob b) => r) -> KleisliForget p a b -> r Source Comments #
Promonad p => Adjunction (KleisliFree p :: KLEISLI p -> k -> Type) (KleisliForget p :: k -> KLEISLI p -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods unit :: forall (a :: k). Ob a => (KleisliForget p :.: KleisliFree p) a a Source Comments # counit :: (KleisliFree p :.: KleisliForget p) :~> ((~>) :: CAT (KLEISLI p)) Source Comments #

type LIFTEDF (f :: j -> k) = KLEISLI (Costar f :.: Star f) Source Comments #

Categories lifted by a functor: f a ~> f b.

pattern LiftF :: forall {k1} {k2} (f :: k1 -> k2) (a :: k1) (b :: k1). Functor f => (Ob a, Ob b) => (f a ~> f b) -> Kleisli ('KL a :: KLEISLI (Costar f :.: Star f)) ('KL b :: KLEISLI (Costar f :.: Star f)) Source Comments #