FFunctor.Adjunction

Documentation

class (FFunctor ff, FFunctor uu) => Adjunction ff uu | ff -> uu, uu -> ff where

An adjunction between $\mathrm{Hask}^{\mathrm{Hask}}$ and $\mathrm{Hask}^{\mathrm{Hask}}$.

Minimal complete definition

unit, counit | leftAdjunct, rightAdjunct

Methods

unit :: forall g. Functor g => g ~> uu (ff g)

counit :: forall g. Functor g => ff (uu g) ~> g

leftAdjunct :: forall g h. (Functor g, Functor h) => (ff g ~> h) -> g ~> uu h

rightAdjunct :: forall g h. (Functor g, Functor h) => (g ~> uu h) -> ff g ~> h

Instances

Adjunction (EnvT e) (ReaderT e)

Defined in FFunctor.Adjunction

Methods

unit :: forall (g :: Type -> Type). Functor g => g ~> ReaderT e (EnvT e g)

counit :: forall (g :: Type -> Type). Functor g => EnvT e (ReaderT e g) ~> g

leftAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (EnvT e g ~> h) -> g ~> ReaderT e h

rightAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (g ~> ReaderT e h) -> EnvT e g ~> h

Adjunction (StoreT s) (StateT s)

Defined in FFunctor.Adjunction

Methods

unit :: forall (g :: Type -> Type). Functor g => g ~> StateT s (StoreT s g)

counit :: forall (g :: Type -> Type). Functor g => StoreT s (StateT s g) ~> g

leftAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (StoreT s g ~> h) -> g ~> StateT s h

rightAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (g ~> StateT s h) -> StoreT s g ~> h

Adjunction (TracedT m) (WriterT m)

Defined in FFunctor.Adjunction

Methods

unit :: forall (g :: Type -> Type). Functor g => g ~> WriterT m (TracedT m g)

counit :: forall (g :: Type -> Type). Functor g => TracedT m (WriterT m g) ~> g

leftAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (TracedT m g ~> h) -> g ~> WriterT m h

rightAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (g ~> WriterT m h) -> TracedT m g ~> h

Functor f => Adjunction (Day f) (Curried f)

Defined in FFunctor.Adjunction

Methods

unit :: forall (g :: Type -> Type). Functor g => g ~> Curried f (Day f g)

counit :: forall (g :: Type -> Type). Functor g => Day f (Curried f g) ~> g

leftAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (Day f g ~> h) -> g ~> Curried f h

rightAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (g ~> Curried f h) -> Day f g ~> h

Adjunction (IdentityT :: (Type -> Type) -> Type -> Type) (IdentityT :: (Type -> Type) -> Type -> Type)

Defined in FFunctor.Adjunction

Methods

unit :: forall (g :: Type -> Type). Functor g => g ~> IdentityT (IdentityT g)

counit :: forall (g :: Type -> Type). Functor g => IdentityT (IdentityT g) ~> g

leftAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (IdentityT g ~> h) -> g ~> IdentityT h

rightAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (g ~> IdentityT h) -> IdentityT g ~> h

Functor f => Adjunction ((:*:) f) (Exp1 f)

Defined in FFunctor.Adjunction

Methods

unit :: forall (g :: Type -> Type). Functor g => g ~> Exp1 f (f :*: g)

counit :: forall (g :: Type -> Type). Functor g => (f :*: Exp1 f g) ~> g

leftAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => ((f :*: g) ~> h) -> g ~> Exp1 f h

rightAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (g ~> Exp1 f h) -> (f :*: g) ~> h

(Adjunction ff uu, Adjunction gg vv) => Adjunction (FCompose ff gg) (FCompose vv uu)

Defined in FFunctor.Adjunction

Methods

unit :: forall (g :: Type -> Type). Functor g => g ~> FCompose vv uu (FCompose ff gg g)

counit :: forall (g :: Type -> Type). Functor g => FCompose ff gg (FCompose vv uu g) ~> g

leftAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (FCompose ff gg g ~> h) -> g ~> FCompose vv uu h

rightAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (g ~> FCompose vv uu h) -> FCompose ff gg g ~> h

Functor f => Adjunction (Lan f) (Precompose f)

Defined in FFunctor.Adjunction

Methods

unit :: forall (g :: Type -> Type). Functor g => g ~> Precompose f (Lan f g)

counit :: forall (g :: Type -> Type). Functor g => Lan f (Precompose f g) ~> g

leftAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (Lan f g ~> h) -> g ~> Precompose f h

rightAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (g ~> Precompose f h) -> Lan f g ~> h

Functor f => Adjunction (Precompose f) (Ran f)

Defined in FFunctor.Adjunction

Methods

unit :: forall (g :: Type -> Type). Functor g => g ~> Ran f (Precompose f g)

counit :: forall (g :: Type -> Type). Functor g => Precompose f (Ran f g) ~> g

leftAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (Precompose f g ~> h) -> g ~> Ran f h

rightAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (g ~> Ran f h) -> Precompose f g ~> h

Adjunction f u => Adjunction (Compose f :: (Type -> Type) -> Type -> Type) (Compose u :: (Type -> Type) -> Type -> Type)

Defined in FFunctor.Adjunction

Methods

unit :: forall (g :: Type -> Type). Functor g => g ~> Compose u (Compose f g)

counit :: forall (g :: Type -> Type). Functor g => Compose f (Compose u g) ~> g

leftAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (Compose f g ~> h) -> g ~> Compose u h

rightAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (g ~> Compose u h) -> Compose f g ~> h

(Adjunction ff uu, Adjunction gg vv) => Adjunction (Sum ff gg) (Product uu vv)

Defined in FFunctor.Adjunction

Methods

unit :: forall (g :: Type -> Type). Functor g => g ~> Product uu vv (Sum ff gg g)

counit :: forall (g :: Type -> Type). Functor g => Sum ff gg (Product uu vv g) ~> g

leftAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (Sum ff gg g ~> h) -> g ~> Product uu vv h

rightAdjunct :: forall (g :: Type -> Type) (h :: Type -> Type). (Functor g, Functor h) => (g ~> Product uu vv h) -> Sum ff gg g ~> h