Pandora.Pattern.Functor.Contravariant

Documentation

class (Category source, Category target) => Contravariant source target t where

When providing a new instance, you should ensure it satisfies:
* Identity morphism: (identity >-|-) ≡ identity
* Interpreted of morphisms: (f >-|-) . (g >-|-) ≡ (g . f >-|-)

Minimal complete definition

(>-|-)

Methods

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

(>-|-|-) :: (Contravariant source (Betwixt source target) u, Contravariant (Betwixt source target) target t) => source a b -> target (t (u a)) (t (u b)) infixl 3

Instances

(Category m, Covariant m m t) => Contravariant m (Flip m) t

Defined in Pandora.Pattern.Morphism.Flip

Methods

(>-|-) :: m a b -> Flip m (t b) (t a)

(>-|-|-) :: (Contravariant m (Betwixt m (Flip m)) u, Contravariant (Betwixt m (Flip m)) (Flip m) t) => m a b -> Flip m (t (u a)) (t (u b))

(Category m, Covariant m m t) => Contravariant (Flip m) m t

Defined in Pandora.Pattern.Morphism.Flip

Methods

(>-|-) :: Flip m a b -> m (t b) (t a)

(>-|-|-) :: (Contravariant (Flip m) (Betwixt (Flip m) m) u, Contravariant (Betwixt (Flip m) m) m t) => Flip m a b -> m (t (u a)) (t (u b))

Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Predicate

Defined in Pandora.Paradigm.Primary.Functor.Predicate

Methods

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

(>-|-|-) :: (Contravariant (->) (Betwixt (->) (->)) u, Contravariant (Betwixt (->) (->)) (->) Predicate) => (a -> b) -> Predicate (u a) -> Predicate (u b)

Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((<--) a)

Defined in Pandora.Paradigm.Primary.Algebraic.Exponential

Methods

(>-|-) :: (a0 -> b) -> (a <-- b) -> (a <-- a0)

(>-|-|-) :: (Contravariant (->) (Betwixt (->) (->)) u, Contravariant (Betwixt (->) (->)) (->) ((<--) a)) => (a0 -> b) -> (a <-- u a0) -> (a <-- u b)

Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Proxy :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Proxy

Methods

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

(>-|-|-) :: (Contravariant (->) (Betwixt (->) (->)) u, Contravariant (Betwixt (->) (->)) (->) Proxy) => (a -> b) -> Proxy (u a) -> Proxy (u b)

Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Convergence r)

Defined in Pandora.Paradigm.Primary.Functor.Convergence

Methods

(>-|-) :: (a -> b) -> Convergence r b -> Convergence r a

(>-|-|-) :: (Contravariant (->) (Betwixt (->) (->)) u, Contravariant (Betwixt (->) (->)) (->) (Convergence r)) => (a -> b) -> Convergence r (u a) -> Convergence r (u b)

Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Flip Provision a)

Defined in Pandora.Paradigm.Inventory.Some.Provision

Methods

(>-|-) :: (a0 -> b) -> Flip Provision a b -> Flip Provision a a0

(>-|-|-) :: (Contravariant (->) (Betwixt (->) (->)) u, Contravariant (Betwixt (->) (->)) (->) (Flip Provision a)) => (a0 -> b) -> Flip Provision a (u a0) -> Flip Provision a (u b)

Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Flip Imprint a)

Defined in Pandora.Paradigm.Inventory.Some.Imprint

Methods

(>-|-) :: (a0 -> b) -> Flip Imprint a b -> Flip Imprint a a0

(>-|-|-) :: (Contravariant (->) (Betwixt (->) (->)) u, Contravariant (Betwixt (->) (->)) (->) (Flip Imprint a)) => (a0 -> b) -> Flip Imprint a (u a0) -> Flip Imprint a (u b)

Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Constant a :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Constant

Methods

(>-|-) :: (a0 -> b) -> Constant a b -> Constant a a0

(>-|-|-) :: (Contravariant (->) (Betwixt (->) (->)) u, Contravariant (Betwixt (->) (->)) (->) (Constant a)) => (a0 -> b) -> Constant a (u a0) -> Constant a (u b)

Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Backwards t)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

(>-|-) :: (a -> b) -> Backwards t b -> Backwards t a

(>-|-|-) :: (Contravariant (->) (Betwixt (->) (->)) u, Contravariant (Betwixt (->) (->)) (->) (Backwards t)) => (a -> b) -> Backwards t (u a) -> Backwards t (u b)

Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Reverse t)

Defined in Pandora.Paradigm.Primary.Transformer.Reverse

Methods

(>-|-) :: (a -> b) -> Reverse t b -> Reverse t a

(>-|-|-) :: (Contravariant (->) (Betwixt (->) (->)) u, Contravariant (Betwixt (->) (->)) (->) (Reverse t)) => (a -> b) -> Reverse t (u a) -> Reverse t (u b)

(Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, forall a. Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (p (t a)), Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, forall b. Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Flip p (u b))) => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((t >:.:> u) := p)

Defined in Pandora.Paradigm.Schemes.T_U

Methods

(<-|-) :: (a -> b) -> ((t >:.:> u) := p) a -> ((t >:.:> u) := p) b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u0, Covariant (Betwixt (->) (->)) (->) ((t >:.:> u) := p)) => (a -> b) -> ((t >:.:> u) := p) (u0 a) -> ((t >:.:> u) := p) (u0 b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u0, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) ((t >:.:> u) := p)) => (a -> b) -> ((t >:.:> u) := p) (u0 (v a)) -> ((t >:.:> u) := p) (u0 (v b))

Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Kan ('Left :: Type -> Wye Type) t u b)

Defined in Pandora.Paradigm.Primary.Transformer.Kan

Methods

(>-|-) :: (a -> b0) -> Kan 'Left t u b b0 -> Kan 'Left t u b a

(>-|-|-) :: (Contravariant (->) (Betwixt (->) (->)) u0, Contravariant (Betwixt (->) (->)) (->) (Kan 'Left t u b)) => (a -> b0) -> Kan 'Left t u b (u0 a) -> Kan 'Left t u b (u0 b0)

(>$<) :: Contravariant source target t => source a b -> target (t b) (t a) infixl 4

(>$$<) :: (Contravariant source target t, Contravariant source (Betwixt source target) u, Contravariant (Betwixt source target) target t) => source a b -> target (t (u a)) (t (u b)) infixl 3