Data.Functor.Day.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)

Operator alias for Data.Functor.Day.Hom.Hom (right-associative / precedence 5)

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

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

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

The curry function for the internal hom object Hom

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

The uncurry function for the internal hom object Hom

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

The composition map for the internal hom object Hom

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

The evaluation map for the internal hom object Hom

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

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

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

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

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

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

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

Every functor f pairs with f ⊸ Identity.