Copyright	(c) Edward Kmett 2014
License	BSD3
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Hask.Prof

Description

Prof  :: (j -> k -> *) -> (i -> j -> *) -> i -> k -> *
ProfR :: (i -> j -> *) -> (i -> k -> *) -> j -> k -> *

Documentation

data Prof :: (j -> k -> *) -> (i -> j -> *) -> i -> k -> * where Source

Constructors

Prof :: p b c -> q a b -> Prof p q a c

Instances

(Corepresentable j * k p, Corepresentable i * j q, Composed k (Hom k ), Functor j k (Corep j k p), Category j (Hom j ), Category k (Hom k )) => Corepresentable i * k (Prof j k i p q)
(Representable k * j p, Representable j * i q, Composed i (Hom i ), Functor j i (Rep j i q), Category i (Hom i ), Category j (Hom j )) => Representable k * i (Prof j k i p q)
Post k1 (k -> ) (Contravariant k) p => Contravariant * k (Prof k k k p q a)
Post k1 (k -> ) (Functor k ) p => Functor k * (Prof k k k p q a)
Functor k (k1 -> ) q => Functor k (k -> ) (Prof k k k p q)
Contravariant (k1 -> ) k q => Contravariant (k -> ) k (Prof k k k p q)
Curried (k -> k -> ) (k -> k -> ) (k -> k -> *) (Prof k k k) (ProfR k k k)
Functor (k -> k -> ) ((k -> k -> ) -> k -> k -> *) (Prof k k k)
Functor (k -> k -> ) (k -> k -> ) (Prof k k k p)
Category i ((~>) i) => Tensor (i -> i -> *) (Prof i i i)
Category i ((~>) i) => Semitensor (i -> i -> *) (Prof i i i)
type Corep i * k (Prof j k i p q) = · k j i (Corep j * k p) (Corep i * j q)
type Rep k * i (Prof j k i p q) = · i j k (Rep j * i q) (Rep k * j p)
type Curryable (k2 -> k1 -> ) (k2 -> k -> ) (k -> k1 -> ) (Prof k k1 k2) = Const (k -> k1 -> ) Constraint ()
type I (k -> k -> *) (Prof k k k) = (~>) k
type Tensorable (k -> k -> ) (Prof k k k) = Profunctor k k

associateProf :: Iso (Prof (Prof p q) r) (Prof (Prof p' q') r') (Prof p (Prof q r)) (Prof p' (Prof q' r')) Source

newtype ProfR p q a b Source

Constructors

ProfR
Fields runProfR :: forall x. p x a -> q x b

Instances

Post k2 (k -> ) (Contravariant k) q => Contravariant * k (ProfR k k k p q a)
Post k2 (k -> ) (Functor k ) q => Functor k * (ProfR k k k p q a)
Post k1 (k -> ) (Contravariant k) p => Functor k (k -> *) (ProfR k k k p q)
Post k1 (k -> ) (Functor k ) p => Contravariant (k -> *) k (ProfR k k k p q)
Curried (k -> k -> ) (k -> k -> ) (k -> k -> *) (Prof k k k) (ProfR k k k)
Contravariant ((k -> k -> ) -> k -> k -> ) (k -> k -> *) (ProfR k k k)
Functor (k -> k -> ) (k -> k -> ) (ProfR k k k p)
type I (k -> k -> *) (ProfR k k k) = (~>) k

(Corepresentable j * k p, Corepresentable i * j q, Composed k (Hom k ), Functor j k (Corep j k p), Category j (Hom j ), Category k (Hom k )) => Corepresentable i * k (Prof j k i p q)
(Representable k * j p, Representable j * i q, Composed i (Hom i ), Functor j i (Rep j i q), Category i (Hom i ), Category j (Hom j )) => Representable k * i (Prof j k i p q)
Post k1 (k -> ) (Contravariant k) p => Contravariant * k (Prof k k k p q a)
Post k1 (k -> ) (Functor k ) p => Functor k * (Prof k k k p q a)
Functor k (k1 -> ) q => Functor k (k -> ) (Prof k k k p q)
Contravariant (k1 -> ) k q => Contravariant (k -> ) k (Prof k k k p q)
Curried (k -> k -> ) (k -> k -> ) (k -> k -> *) (Prof k k k) (ProfR k k k)
Functor (k -> k -> ) ((k -> k -> ) -> k -> k -> *) (Prof k k k)
Functor (k -> k -> ) (k -> k -> ) (Prof k k k p)
Category i ((~>) i) => Tensor (i -> i -> *) (Prof i i i)
Category i ((~>) i) => Semitensor (i -> i -> *) (Prof i i i)
type Corep i * k (Prof j k i p q) = · k j i (Corep j * k p) (Corep i * j q)
type Rep k * i (Prof j k i p q) = · i j k (Rep j * i q) (Rep k * j p)
type Curryable (k2 -> k1 -> ) (k2 -> k -> ) (k -> k1 -> ) (Prof k k1 k2) = Const (k -> k1 -> ) Constraint ()
type I (k -> k -> *) (Prof k k k) = (~>) k
type Tensorable (k -> k -> ) (Prof k k k) = Profunctor k k

Post k2 (k -> ) (Contravariant k) q => Contravariant * k (ProfR k k k p q a)
Post k2 (k -> ) (Functor k ) q => Functor k * (ProfR k k k p q a)
Post k1 (k -> ) (Contravariant k) p => Functor k (k -> *) (ProfR k k k p q)
Post k1 (k -> ) (Functor k ) p => Contravariant (k -> *) k (ProfR k k k p q)
Curried (k -> k -> ) (k -> k -> ) (k -> k -> *) (Prof k k k) (ProfR k k k)
Contravariant ((k -> k -> ) -> k -> k -> ) (k -> k -> *) (ProfR k k k)
Functor (k -> k -> ) (k -> k -> ) (ProfR k k k p)
type I (k -> k -> *) (ProfR k k k) = (~>) k