Copyright	(C) 2013-2016 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	GADTs, TFs, MPTCs
Safe Haskell	Trustworthy
Language	Haskell2010

Data.Functor.Contravariant.Yoneda

Description

Synopsis

newtype Yoneda (f :: Type -> Type) a = Yoneda {
- runYoneda :: forall r. (r -> a) -> f r
}
liftYoneda :: Contravariant f => f a -> Yoneda f a
lowerYoneda :: Yoneda f a -> f a

Documentation

newtype Yoneda (f :: Type -> Type) a Source #

Yoneda embedding for a presheaf

Constructors

Yoneda
Fields runYoneda :: forall r. (r -> a) -> f r

Instances details

Instance details

Associated Types

type Rep (Yoneda f)
Instance details Defined in Data.Functor.Contravariant.Yoneda type Rep (Yoneda f) = Rep f

Methods

tabulate :: (a -> Rep (Yoneda f)) -> Yoneda f a #

index :: Yoneda f a -> a -> Rep (Yoneda f) #

Instance details

Methods

contramap :: (a' -> a) -> Yoneda f a -> Yoneda f a' #

(>$) :: b -> Yoneda f b -> Yoneda f a #

Instance details

Methods

unit :: a -> Yoneda g (Yoneda f a) #

leftAdjunct :: (b -> Yoneda f a) -> a -> Yoneda g b #

rightAdjunct :: (a -> Yoneda g b) -> b -> Yoneda f a #

Instance details

type Rep (Yoneda f) = Rep f

liftYoneda . lowerYoneda ≡ id
lowerYoneda . liftYoneda ≡ id