Pandora.Pattern.Functor.Adjoint

Documentation

type (-|) = Adjoint infixl 8

class (Covariant target source t, Covariant source target u) => Adjoint source target t u where

When providing a new instance, you should ensure it satisfies:
* Left adjunction identity: phi cozero ≡ identity
* Right adjunction identity: psi zero ≡ identity
* Left adjunction interchange: phi f ≡ comap f . eta
* Right adjunction interchange: psi f ≡ epsilon . comap f

Minimal complete definition

(-|), (|-)

Methods

(-|) :: source (t a) b -> target a (u b) infixl 8

(|-) :: target a (u b) -> source (t a) b infixl 8

(|--------) :: target a (u b) -> source (t a) b infixl 1

(|-------) :: target a (u b) -> source (t a) b infixl 2

(|------) :: target a (u b) -> source (t a) b infixl 3

(|-----) :: target a (u b) -> source (t a) b infixl 4

(|----) :: target a (u b) -> source (t a) b infixl 5

(|---) :: target a (u b) -> source (t a) b infixl 6

(|--) :: target a (u b) -> source (t a) b infixl 7

(--------|) :: source (t a) b -> target a (u b) infixl 1

(-------|) :: source (t a) b -> target a (u b) infixl 2

(------|) :: source (t a) b -> target a (u b) infixl 3

(-----|) :: source (t a) b -> target a (u b) infixl 4

(----|) :: source (t a) b -> target a (u b) infixl 5

(---|) :: source (t a) b -> target a (u b) infixl 6

(--|) :: source (t a) b -> target a (u b) infixl 7

Instances

Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Exactly Exactly

Defined in Pandora.Paradigm.Primary.Functor.Exactly

Methods

(-|) :: (Exactly a -> b) -> a -> Exactly b

(|-) :: (a -> Exactly b) -> Exactly a -> b

(|--------) :: (a -> Exactly b) -> Exactly a -> b

(|-------) :: (a -> Exactly b) -> Exactly a -> b

(|------) :: (a -> Exactly b) -> Exactly a -> b

(|-----) :: (a -> Exactly b) -> Exactly a -> b

(|----) :: (a -> Exactly b) -> Exactly a -> b

(|---) :: (a -> Exactly b) -> Exactly a -> b

(|--) :: (a -> Exactly b) -> Exactly a -> b

(--------|) :: (Exactly a -> b) -> a -> Exactly b

(-------|) :: (Exactly a -> b) -> a -> Exactly b

(------|) :: (Exactly a -> b) -> a -> Exactly b

(-----|) :: (Exactly a -> b) -> a -> Exactly b

(----|) :: (Exactly a -> b) -> a -> Exactly b

(---|) :: (Exactly a -> b) -> a -> Exactly b

(--|) :: (Exactly a -> b) -> a -> Exactly b

Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Store s) (State s)

Defined in Pandora.Paradigm.Inventory

Methods

(-|) :: (Store s a -> b) -> a -> State s b

(|-) :: (a -> State s b) -> Store s a -> b

(|--------) :: (a -> State s b) -> Store s a -> b

(|-------) :: (a -> State s b) -> Store s a -> b

(|------) :: (a -> State s b) -> Store s a -> b

(|-----) :: (a -> State s b) -> Store s a -> b

(|----) :: (a -> State s b) -> Store s a -> b

(|---) :: (a -> State s b) -> Store s a -> b

(|--) :: (a -> State s b) -> Store s a -> b

(--------|) :: (Store s a -> b) -> a -> State s b

(-------|) :: (Store s a -> b) -> a -> State s b

(------|) :: (Store s a -> b) -> a -> State s b

(-----|) :: (Store s a -> b) -> a -> State s b

(----|) :: (Store s a -> b) -> a -> State s b

(---|) :: (Store s a -> b) -> a -> State s b

(--|) :: (Store s a -> b) -> a -> State s b

Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Equipment e) (Provision e)

Defined in Pandora.Paradigm.Inventory

Methods

(-|) :: (Equipment e a -> b) -> a -> Provision e b

(|-) :: (a -> Provision e b) -> Equipment e a -> b

(|--------) :: (a -> Provision e b) -> Equipment e a -> b

(|-------) :: (a -> Provision e b) -> Equipment e a -> b

(|------) :: (a -> Provision e b) -> Equipment e a -> b

(|-----) :: (a -> Provision e b) -> Equipment e a -> b

(|----) :: (a -> Provision e b) -> Equipment e a -> b

(|---) :: (a -> Provision e b) -> Equipment e a -> b

(|--) :: (a -> Provision e b) -> Equipment e a -> b

(--------|) :: (Equipment e a -> b) -> a -> Provision e b

(-------|) :: (Equipment e a -> b) -> a -> Provision e b

(------|) :: (Equipment e a -> b) -> a -> Provision e b

(-----|) :: (Equipment e a -> b) -> a -> Provision e b

(----|) :: (Equipment e a -> b) -> a -> Provision e b

(---|) :: (Equipment e a -> b) -> a -> Provision e b

(--|) :: (Equipment e a -> b) -> a -> Provision e b

Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Accumulator e) (Imprint e)

Defined in Pandora.Paradigm.Inventory

Methods

(-|) :: (Accumulator e a -> b) -> a -> Imprint e b

(|-) :: (a -> Imprint e b) -> Accumulator e a -> b

(|--------) :: (a -> Imprint e b) -> Accumulator e a -> b

(|-------) :: (a -> Imprint e b) -> Accumulator e a -> b

(|------) :: (a -> Imprint e b) -> Accumulator e a -> b

(|-----) :: (a -> Imprint e b) -> Accumulator e a -> b

(|----) :: (a -> Imprint e b) -> Accumulator e a -> b

(|---) :: (a -> Imprint e b) -> Accumulator e a -> b

(|--) :: (a -> Imprint e b) -> Accumulator e a -> b

(--------|) :: (Accumulator e a -> b) -> a -> Imprint e b

(-------|) :: (Accumulator e a -> b) -> a -> Imprint e b

(------|) :: (Accumulator e a -> b) -> a -> Imprint e b

(-----|) :: (Accumulator e a -> b) -> a -> Imprint e b

(----|) :: (Accumulator e a -> b) -> a -> Imprint e b

(---|) :: (Accumulator e a -> b) -> a -> Imprint e b

(--|) :: (Accumulator e a -> b) -> a -> Imprint e b

Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((:*:) s) ((->) s :: Type -> Type)

Defined in Pandora.Paradigm.Algebraic.Functor

Methods

(-|) :: ((s :*: a) -> b) -> a -> (s -> b)

(|-) :: (a -> (s -> b)) -> (s :*: a) -> b

(|--------) :: (a -> (s -> b)) -> (s :*: a) -> b

(|-------) :: (a -> (s -> b)) -> (s :*: a) -> b

(|------) :: (a -> (s -> b)) -> (s :*: a) -> b

(|-----) :: (a -> (s -> b)) -> (s :*: a) -> b

(|----) :: (a -> (s -> b)) -> (s :*: a) -> b

(|---) :: (a -> (s -> b)) -> (s :*: a) -> b

(|--) :: (a -> (s -> b)) -> (s :*: a) -> b

(--------|) :: ((s :*: a) -> b) -> a -> (s -> b)

(-------|) :: ((s :*: a) -> b) -> a -> (s -> b)

(------|) :: ((s :*: a) -> b) -> a -> (s -> b)

(-----|) :: ((s :*: a) -> b) -> a -> (s -> b)

(----|) :: ((s :*: a) -> b) -> a -> (s -> b)

(---|) :: ((s :*: a) -> b) -> a -> (s -> b)

(--|) :: ((s :*: a) -> b) -> a -> (s -> b)

Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Flip (:*:) s) ((->) s :: Type -> Type)

Defined in Pandora.Paradigm.Primary

Methods

(-|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(|-) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|--------) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|-------) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|------) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|-----) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|----) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|---) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|--) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(--------|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(-------|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(------|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(-----|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(----|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(---|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(--|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t <.:> v), Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (w <:.> u), Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) v u, Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t w) => Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t <.:> v) (w <:.> u)

Defined in Pandora.Paradigm.Schemes

Methods

(-|) :: ((t <.:> v) a -> b) -> a -> (w <:.> u) b

(|-) :: (a -> (w <:.> u) b) -> (t <.:> v) a -> b

(|--------) :: (a -> (w <:.> u) b) -> (t <.:> v) a -> b

(|-------) :: (a -> (w <:.> u) b) -> (t <.:> v) a -> b

(|------) :: (a -> (w <:.> u) b) -> (t <.:> v) a -> b

(|-----) :: (a -> (w <:.> u) b) -> (t <.:> v) a -> b

(|----) :: (a -> (w <:.> u) b) -> (t <.:> v) a -> b

(|---) :: (a -> (w <:.> u) b) -> (t <.:> v) a -> b

(|--) :: (a -> (w <:.> u) b) -> (t <.:> v) a -> b

(--------|) :: ((t <.:> v) a -> b) -> a -> (w <:.> u) b

(-------|) :: ((t <.:> v) a -> b) -> a -> (w <:.> u) b

(------|) :: ((t <.:> v) a -> b) -> a -> (w <:.> u) b

(-----|) :: ((t <.:> v) a -> b) -> a -> (w <:.> u) b

(----|) :: ((t <.:> v) a -> b) -> a -> (w <:.> u) b

(---|) :: ((t <.:> v) a -> b) -> a -> (w <:.> u) b

(--|) :: ((t <.:> v) a -> b) -> a -> (w <:.> u) b

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t <.:> v), Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (w <.:> u), Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t u, Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) v w) => Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t <.:> v) (w <.:> u)

Defined in Pandora.Paradigm.Schemes

Methods

(-|) :: ((t <.:> v) a -> b) -> a -> (w <.:> u) b

(|-) :: (a -> (w <.:> u) b) -> (t <.:> v) a -> b

(|--------) :: (a -> (w <.:> u) b) -> (t <.:> v) a -> b

(|-------) :: (a -> (w <.:> u) b) -> (t <.:> v) a -> b

(|------) :: (a -> (w <.:> u) b) -> (t <.:> v) a -> b

(|-----) :: (a -> (w <.:> u) b) -> (t <.:> v) a -> b

(|----) :: (a -> (w <.:> u) b) -> (t <.:> v) a -> b

(|---) :: (a -> (w <.:> u) b) -> (t <.:> v) a -> b

(|--) :: (a -> (w <.:> u) b) -> (t <.:> v) a -> b

(--------|) :: ((t <.:> v) a -> b) -> a -> (w <.:> u) b

(-------|) :: ((t <.:> v) a -> b) -> a -> (w <.:> u) b

(------|) :: ((t <.:> v) a -> b) -> a -> (w <.:> u) b

(-----|) :: ((t <.:> v) a -> b) -> a -> (w <.:> u) b

(----|) :: ((t <.:> v) a -> b) -> a -> (w <.:> u) b

(---|) :: ((t <.:> v) a -> b) -> a -> (w <.:> u) b

(--|) :: ((t <.:> v) a -> b) -> a -> (w <.:> u) b

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (v <:.> t), Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (w <.:> u), Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t u, Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) v w) => Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (v <:.> t) (w <.:> u)

Defined in Pandora.Paradigm.Schemes

Methods

(-|) :: ((v <:.> t) a -> b) -> a -> (w <.:> u) b

(|-) :: (a -> (w <.:> u) b) -> (v <:.> t) a -> b

(|--------) :: (a -> (w <.:> u) b) -> (v <:.> t) a -> b

(|-------) :: (a -> (w <.:> u) b) -> (v <:.> t) a -> b

(|------) :: (a -> (w <.:> u) b) -> (v <:.> t) a -> b

(|-----) :: (a -> (w <.:> u) b) -> (v <:.> t) a -> b

(|----) :: (a -> (w <.:> u) b) -> (v <:.> t) a -> b

(|---) :: (a -> (w <.:> u) b) -> (v <:.> t) a -> b

(|--) :: (a -> (w <.:> u) b) -> (v <:.> t) a -> b

(--------|) :: ((v <:.> t) a -> b) -> a -> (w <.:> u) b

(-------|) :: ((v <:.> t) a -> b) -> a -> (w <.:> u) b

(------|) :: ((v <:.> t) a -> b) -> a -> (w <.:> u) b

(-----|) :: ((v <:.> t) a -> b) -> a -> (w <.:> u) b

(----|) :: ((v <:.> t) a -> b) -> a -> (w <.:> u) b

(---|) :: ((v <:.> t) a -> b) -> a -> (w <.:> u) b

(--|) :: ((v <:.> t) a -> b) -> a -> (w <.:> u) b

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (v <:.> t), Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (u <:.> w), Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t u, Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) v w) => Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (v <:.> t) (u <:.> w)

Defined in Pandora.Paradigm.Schemes

Methods

(-|) :: ((v <:.> t) a -> b) -> a -> (u <:.> w) b

(|-) :: (a -> (u <:.> w) b) -> (v <:.> t) a -> b

(|--------) :: (a -> (u <:.> w) b) -> (v <:.> t) a -> b

(|-------) :: (a -> (u <:.> w) b) -> (v <:.> t) a -> b

(|------) :: (a -> (u <:.> w) b) -> (v <:.> t) a -> b

(|-----) :: (a -> (u <:.> w) b) -> (v <:.> t) a -> b

(|----) :: (a -> (u <:.> w) b) -> (v <:.> t) a -> b

(|---) :: (a -> (u <:.> w) b) -> (v <:.> t) a -> b

(|--) :: (a -> (u <:.> w) b) -> (v <:.> t) a -> b

(--------|) :: ((v <:.> t) a -> b) -> a -> (u <:.> w) b

(-------|) :: ((v <:.> t) a -> b) -> a -> (u <:.> w) b

(------|) :: ((v <:.> t) a -> b) -> a -> (u <:.> w) b

(-----|) :: ((v <:.> t) a -> b) -> a -> (u <:.> w) b

(----|) :: ((v <:.> t) a -> b) -> a -> (u <:.> w) b

(---|) :: ((v <:.> t) a -> b) -> a -> (u <:.> w) b

(--|) :: ((v <:.> t) a -> b) -> a -> (u <:.> w) b

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((t <:<.>:> u) t'), Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((v <:<.>:> w) v'), Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t w, Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t' v', Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t v, Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u v, Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) v' t') => Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((t <:<.>:> u) t') ((v <:<.>:> w) v')

Defined in Pandora.Paradigm.Schemes

Methods

(-|) :: ((t <:<.>:> u) t' a -> b) -> a -> (v <:<.>:> w) v' b

(|-) :: (a -> (v <:<.>:> w) v' b) -> (t <:<.>:> u) t' a -> b

(|--------) :: (a -> (v <:<.>:> w) v' b) -> (t <:<.>:> u) t' a -> b

(|-------) :: (a -> (v <:<.>:> w) v' b) -> (t <:<.>:> u) t' a -> b

(|------) :: (a -> (v <:<.>:> w) v' b) -> (t <:<.>:> u) t' a -> b

(|-----) :: (a -> (v <:<.>:> w) v' b) -> (t <:<.>:> u) t' a -> b

(|----) :: (a -> (v <:<.>:> w) v' b) -> (t <:<.>:> u) t' a -> b

(|---) :: (a -> (v <:<.>:> w) v' b) -> (t <:<.>:> u) t' a -> b

(|--) :: (a -> (v <:<.>:> w) v' b) -> (t <:<.>:> u) t' a -> b

(--------|) :: ((t <:<.>:> u) t' a -> b) -> a -> (v <:<.>:> w) v' b

(-------|) :: ((t <:<.>:> u) t' a -> b) -> a -> (v <:<.>:> w) v' b

(------|) :: ((t <:<.>:> u) t' a -> b) -> a -> (v <:<.>:> w) v' b

(-----|) :: ((t <:<.>:> u) t' a -> b) -> a -> (v <:<.>:> w) v' b

(----|) :: ((t <:<.>:> u) t' a -> b) -> a -> (v <:<.>:> w) v' b

(---|) :: ((t <:<.>:> u) t' a -> b) -> a -> (v <:<.>:> w) v' b

(--|) :: ((t <:<.>:> u) t' a -> b) -> a -> (v <:<.>:> w) v' b