Pandora.Paradigm.Primary.Transformer.Kan

Documentation

data family Kan (v :: * -> k) (t :: * -> *) (u :: * -> *) b a

Instances

Contravariant (Kan ('Left :: Type -> Wye Type) t u b)

Defined in Pandora.Paradigm.Primary.Transformer.Kan

Methods

(>$<) :: (a -> b0) -> Kan 'Left t u b b0 -> Kan 'Left t u b a

contramap :: (a -> b0) -> Kan 'Left t u b b0 -> Kan 'Left t u b a

(>$) :: b0 -> Kan 'Left t u b b0 -> Kan 'Left t u b a

($<) :: Kan 'Left t u b b0 -> b0 -> Kan 'Left t u b a

full :: Kan 'Left t u b () -> Kan 'Left t u b a

(>&<) :: Kan 'Left t u b b0 -> (a -> b0) -> Kan 'Left t u b a

(>$$<) :: Contravariant u0 => (a -> b0) -> ((Kan 'Left t u b :. u0) := a) -> (Kan 'Left t u b :. u0) := b0

(>$$$<) :: (Contravariant u0, Contravariant v) => (a -> b0) -> ((Kan 'Left t u b :. (u0 :. v)) := b0) -> (Kan 'Left t u b :. (u0 :. v)) := a

(>$$$$<) :: (Contravariant u0, Contravariant v, Contravariant w) => (a -> b0) -> ((Kan 'Left t u b :. (u0 :. (v :. w))) := a) -> (Kan 'Left t u b :. (u0 :. (v :. w))) := b0

(>&&<) :: Contravariant u0 => ((Kan 'Left t u b :. u0) := a) -> (a -> b0) -> (Kan 'Left t u b :. u0) := b0

(>&&&<) :: (Contravariant u0, Contravariant v) => ((Kan 'Left t u b :. (u0 :. v)) := b0) -> (a -> b0) -> (Kan 'Left t u b :. (u0 :. v)) := a

(>&&&&<) :: (Contravariant u0, Contravariant v, Contravariant w) => ((Kan 'Left t u b :. (u0 :. (v :. w))) := a) -> (a -> b0) -> (Kan 'Left t u b :. (u0 :. (v :. w))) := b0

Covariant (Kan ('Right :: Type -> Wye Type) t u b)

Defined in Pandora.Paradigm.Primary.Transformer.Kan

Methods

(<$>) :: (a -> b0) -> Kan 'Right t u b a -> Kan 'Right t u b b0

comap :: (a -> b0) -> Kan 'Right t u b a -> Kan 'Right t u b b0

(<$) :: a -> Kan 'Right t u b b0 -> Kan 'Right t u b a

($>) :: Kan 'Right t u b a -> b0 -> Kan 'Right t u b b0

void :: Kan 'Right t u b a -> Kan 'Right t u b ()

loeb :: Kan 'Right t u b (a <:= Kan 'Right t u b) -> Kan 'Right t u b a

(<&>) :: Kan 'Right t u b a -> (a -> b0) -> Kan 'Right t u b b0

(<$$>) :: Covariant u0 => (a -> b0) -> ((Kan 'Right t u b :. u0) := a) -> (Kan 'Right t u b :. u0) := b0

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b0) -> ((Kan 'Right t u b :. (u0 :. v)) := a) -> (Kan 'Right t u b :. (u0 :. v)) := b0

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b0) -> ((Kan 'Right t u b :. (u0 :. (v :. w))) := a) -> (Kan 'Right t u b :. (u0 :. (v :. w))) := b0

(<&&>) :: Covariant u0 => ((Kan 'Right t u b :. u0) := a) -> (a -> b0) -> (Kan 'Right t u b :. u0) := b0

(<&&&>) :: (Covariant u0, Covariant v) => ((Kan 'Right t u b :. (u0 :. v)) := a) -> (a -> b0) -> (Kan 'Right t u b :. (u0 :. v)) := b0

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((Kan 'Right t u b :. (u0 :. (v :. w))) := a) -> (a -> b0) -> (Kan 'Right t u b :. (u0 :. (v :. w))) := b0

Interpreted (Kan ('Left :: Type -> Wye Type) t u b)

Defined in Pandora.Paradigm.Primary.Transformer.Kan

Associated Types

type Primary (Kan 'Left t u b) a

Methods

run :: Kan 'Left t u b a -> Primary (Kan 'Left t u b) a

unite :: Primary (Kan 'Left t u b) a -> Kan 'Left t u b a

(||=) :: Interpreted u0 => (Primary (Kan 'Left t u b) a -> Primary u0 b0) -> Kan 'Left t u b a -> u0 b0

(=||) :: Interpreted u0 => (Kan 'Left t u b a -> u0 b0) -> Primary (Kan 'Left t u b) a -> Primary u0 b0

Interpreted (Kan ('Right :: Type -> Wye Type) t u b)

Defined in Pandora.Paradigm.Primary.Transformer.Kan

Associated Types

type Primary (Kan 'Right t u b) a

Methods

run :: Kan 'Right t u b a -> Primary (Kan 'Right t u b) a

unite :: Primary (Kan 'Right t u b) a -> Kan 'Right t u b a

(||=) :: Interpreted u0 => (Primary (Kan 'Right t u b) a -> Primary u0 b0) -> Kan 'Right t u b a -> u0 b0

(=||) :: Interpreted u0 => (Kan 'Right t u b a -> u0 b0) -> Primary (Kan 'Right t u b) a -> Primary u0 b0

data Kan ('Left :: Type -> Wye Type) t u b a

Defined in Pandora.Paradigm.Primary.Transformer.Kan

data Kan ('Left :: Type -> Wye Type) t u b a = Lan ((t b -> a) -> u b)

data Kan ('Right :: Type -> Wye Type) t u b a

Defined in Pandora.Paradigm.Primary.Transformer.Kan

data Kan ('Right :: Type -> Wye Type) t u b a = Ran ((a -> t b) -> u b)

type Primary (Kan ('Left :: Type -> Wye Type) t u b) a

Defined in Pandora.Paradigm.Primary.Transformer.Kan

type Primary (Kan ('Left :: Type -> Wye Type) t u b) a = (t b -> a) -> u b

type Primary (Kan ('Right :: Type -> Wye Type) t u b) a

Defined in Pandora.Paradigm.Primary.Transformer.Kan

type Primary (Kan ('Right :: Type -> Wye Type) t u b) a = (a -> t b) -> u b