Data.Functor.Yoneda · kan-extensions-5.2.7

newtypenewtype Yoneda (f :: Type -> Type) a

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Yoneda f a can be viewed as the partial application of fmap to its second argument.

Constructors

Yoneda
- runYoneda :: forall b. (a -> b) -> f b

Instances31MonadTrans, ComonadTrans, MonadFree, Monad, Functor, MonadFix, …

MonadTrans YonedaDefined in kan-extensions-5.2.7 · Data.Functor.Yoneda
ComonadTrans YonedaDefined in kan-extensions-5.2.7 · Data.Functor.Yoneda
(Functor f, MonadFree f m) => MonadFree f (Yoneda m)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Monad m => Monad (Yoneda m)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Functor (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
MonadFix m => MonadFix (Yoneda m)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Applicative f => Applicative (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Foldable f => Foldable (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Traversable f => Traversable (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Alternative f => Alternative (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
MonadPlus m => MonadPlus (Yoneda m)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Foldable1 f => Foldable1 (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Eq1 f => Eq1 (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Ord1 f => Ord1 (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
(Read1 f, Functor f) => Read1 (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Show1 f => Show1 (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Distributive f => Distributive (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Comonad w => Comonad (Yoneda w)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Alt f => Alt (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Apply f => Apply (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Bind m => Bind (Yoneda m)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Extend w => Extend (Yoneda w)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Plus f => Plus (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Traversable1 f => Traversable1 (Yoneda f)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Representable g => Representable (Yoneda g)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Adjunction f g => Adjunction (Yoneda f) (Yoneda g)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
(Eq1 f, Eq a) => Eq (Yoneda f a)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
(Ord1 f, Ord a) => Ord (Yoneda f a)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
(Functor f, Read (f a)) => Read (Yoneda f a)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
Show (f a) => Show (Yoneda f a)Defined in kan-extensions-5.2.7 · Data.Functor.Yoneda
type Rep (Yoneda g) = Rep gDefined in kan-extensions-5.2.7 · Data.Functor.Yoneda

valueliftYoneda :: Functor f => f a -> Yoneda f a

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The natural isomorphism between f and Yoneda f given by the Yoneda lemma is witnessed by liftYoneda and lowerYoneda

liftYoneda . lowerYoneda ≡ id
lowerYoneda . liftYoneda ≡ id

lowerYoneda (liftYoneda fa) =         -- definition
lowerYoneda (Yoneda (f -> fmap f a)) -- definition
(f -> fmap f fa) id                  -- beta reduction
fmap id fa                            -- functor law
fa