Hom.md

Module Data.Functor.Day.Hom

The internal hom in the category of functors with Day convolution as the monoidal tensor.

Hom

newtype Hom f g a

This is the internal hom in the category of functors with Day convolution as the monoidal tensor.

Instances

(Functor f) => Functor (Hom f g)
(Extend f, Bind g) => Apply (Hom f g)
(Comonad f, Monad g) => Applicative (Hom f g)
(Comonad f, Monad g) => Bind (Hom f g)
(Comonad f, Monad g) => Monad (Hom f g)
(Comonad f) => MonadTrans (Hom f)

type (⊸)

infixr 5 type Hom as ype (⊸

hom

hom :: forall f g a. (forall r. f (a -> r) -> g r) -> Hom f g a

runHom

runHom :: forall f g a r. Hom f g a -> f (a -> r) -> g r

curryHom

curryHom :: forall f g h. (f ⊗ g ⊸ h) ~> f ⊸ g ⊸ h

The curry function for the internal hom object Hom

uncurryHom

uncurryHom :: forall f g h. Functor f => Functor g => (f ⊸ g ⊸ h) ~> f ⊗ g ⊸ h

The uncurry function for the internal hom object Hom

introHom

introHom :: forall f g h. (f ⊗ g ~> h) -> f ~> g ⊸ h

elimHom

elimHom :: forall f g h. Functor g => (f ~> g ⊸ h) -> f ⊗ g ~> h

introHom'

introHom' :: forall f g. Functor f => (f ~> g) -> Identity ~> f ⊸ g

elimHom'

elimHom' :: forall f g. Functor f => (Identity ~> f ⊸ g) -> f ~> g

composeHom

composeHom :: forall f g h. Functor f => (g ⊸ h) ⊗ (f ⊸ g) ~> f ⊸ h

The composition map for the internal hom object Hom

evalHom

evalHom :: forall f g. Functor f => (f ⊸ g) ⊗ f ~> g

The evaluation map for the internal hom object Hom

pairingHom

pairingHom :: forall f g. f ⋈ g -> f ~> g ⊸ Identity

Hom generalizes pairings which have been applied to their first argument.

pairHom

pairHom :: forall f. Functor f => f ⋈ (f ⊸ Identity)

Every functor f pairs with f ⊸ Identity.