Portability | MPTCs, fundeps |
---|---|
Stability | provisional |
Maintainer | Edward Kmett <ekmett@gmail.com> |
Safe Haskell | Trustworthy |
The co-Yoneda lemma states that
f a
is isomorphic to (forall r. (a -> r) -> f a)
This is described in a rather intuitive fashion by Dan Piponi in
- newtype Yoneda f a = Yoneda {
- runYoneda :: forall b. (a -> b) -> f b
- liftYoneda :: Functor f => f a -> Yoneda f a
- lowerYoneda :: Yoneda f a -> f a
- maxF :: (Functor f, Ord (f a)) => Yoneda f a -> Yoneda f a -> Yoneda f a
- minF :: (Functor f, Ord (f a)) => Yoneda f a -> Yoneda f a -> Yoneda f a
- maxM :: (Monad m, Ord (m a)) => Yoneda m a -> Yoneda m a -> Yoneda m a
- minM :: (Monad m, Ord (m a)) => Yoneda m a -> Yoneda m a -> Yoneda m a
- yonedaToRan :: Yoneda f a -> Ran Identity f a
- ranToYoneda :: Ran Identity f a -> Yoneda f a
- yonedaToRift :: Yoneda f a -> Rift Identity f a
- riftToYoneda :: Rift Identity f a -> Yoneda f a
Documentation
liftYoneda :: Functor f => f a -> Yoneda f aSource
lowerYoneda :: Yoneda f a -> f aSource
as a right Kan extension
yonedaToRan :: Yoneda f a -> Ran Identity f aSource
Yoneda f
is the right Kan extension of f
along the Identity
functor.
yonedaToRan
.ranToYoneda
≡id
ranToYoneda
.yonedaToRan
≡id
ranToYoneda :: Ran Identity f a -> Yoneda f aSource
as a right Kan lift
yonedaToRift :: Yoneda f a -> Rift Identity f aSource
Yoneda f
is the right Kan lift of f
along the Identity
functor.
yonedaToRift
.riftToYoneda
≡id
riftToYoneda
.yonedaToRift
≡id
riftToYoneda :: Rift Identity f a -> Yoneda f aSource