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

(.#..) :: (Kan 'Right t u b ~ v a, Category v) => v c d -> ((v a :. v b0) := c) -> (v a :. v b0) := d

(.#...) :: (Kan 'Right t u b ~ v a, Kan 'Right t u b ~ v b0, Category v, Covariant (v a), Covariant (v b0)) => v d e -> ((v a :. (v b0 :. v c)) := d) -> (v a :. (v b0 :. v c)) := e

(.#....) :: (Kan 'Right t u b ~ v a, Kan 'Right t u b ~ v b0, Kan 'Right t u b ~ v c, Category v, Covariant (v a), Covariant (v b0), Covariant (v c)) => v e f -> ((v a :. (v b0 :. (v c :. v d))) := e) -> (v a :. (v b0 :. (v c :. v d))) := f

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

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

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

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

(<$||=) :: (Covariant j, Interpreted u0) => (Primary (Kan 'Left t u b) a -> Primary u0 b0) -> (j := Kan 'Left t u b a) -> j := u0 b0

(<$$||=) :: (Covariant j, Covariant k, Interpreted u0) => (Primary (Kan 'Left t u b) a -> Primary u0 b0) -> ((j :. k) := Kan 'Left t u b a) -> (j :. k) := u0 b0

(<$$$||=) :: (Covariant j, Covariant k, Covariant l, Interpreted u0) => (Primary (Kan 'Left t u b) a -> Primary u0 b0) -> ((j :. (k :. l)) := Kan 'Left t u b a) -> (j :. (k :. l)) := u0 b0

(<$$$$||=) :: (Covariant j, Covariant k, Covariant l, Covariant m, Interpreted u0) => (Primary (Kan 'Left t u b) a -> Primary u0 b0) -> ((j :. (k :. (l :. m))) := Kan 'Left t u b a) -> (j :. (k :. (l :. m))) := u0 b0

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

(=||$$>) :: (Covariant j, Covariant k, Interpreted u0) => (Kan 'Left t u b a -> u0 b0) -> ((j :. k) := Primary (Kan 'Left t u b) a) -> (j :. k) := Primary u0 b0

(=||$$$>) :: (Covariant j, Covariant k, Covariant l, Interpreted u0) => (Kan 'Left t u b a -> u0 b0) -> ((j :. (k :. l)) := Primary (Kan 'Left t u b) a) -> (j :. (k :. l)) := Primary u0 b0

(=||$$$$>) :: (Covariant j, Covariant k, Covariant l, Covariant m, Interpreted u0) => (Kan 'Left t u b a -> u0 b0) -> ((j :. (k :. (l :. m))) := Primary (Kan 'Left t u b) a) -> (j :. (k :. (l :. m))) := 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

(<$||=) :: (Covariant j, Interpreted u0) => (Primary (Kan 'Right t u b) a -> Primary u0 b0) -> (j := Kan 'Right t u b a) -> j := u0 b0

(<$$||=) :: (Covariant j, Covariant k, Interpreted u0) => (Primary (Kan 'Right t u b) a -> Primary u0 b0) -> ((j :. k) := Kan 'Right t u b a) -> (j :. k) := u0 b0

(<$$$||=) :: (Covariant j, Covariant k, Covariant l, Interpreted u0) => (Primary (Kan 'Right t u b) a -> Primary u0 b0) -> ((j :. (k :. l)) := Kan 'Right t u b a) -> (j :. (k :. l)) := u0 b0

(<$$$$||=) :: (Covariant j, Covariant k, Covariant l, Covariant m, Interpreted u0) => (Primary (Kan 'Right t u b) a -> Primary u0 b0) -> ((j :. (k :. (l :. m))) := Kan 'Right t u b a) -> (j :. (k :. (l :. m))) := u0 b0

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

(=||$$>) :: (Covariant j, Covariant k, Interpreted u0) => (Kan 'Right t u b a -> u0 b0) -> ((j :. k) := Primary (Kan 'Right t u b) a) -> (j :. k) := Primary u0 b0

(=||$$$>) :: (Covariant j, Covariant k, Covariant l, Interpreted u0) => (Kan 'Right t u b a -> u0 b0) -> ((j :. (k :. l)) := Primary (Kan 'Right t u b) a) -> (j :. (k :. l)) := Primary u0 b0

(=||$$$$>) :: (Covariant j, Covariant k, Covariant l, Covariant m, Interpreted u0) => (Kan 'Right t u b a -> u0 b0) -> ((j :. (k :. (l :. m))) := Primary (Kan 'Right t u b) a) -> (j :. (k :. (l :. m))) := 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