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:
* Exactly morphism: (identity >-|-) ≡ identity
* Interpreted of morphisms: (f >-|-) . (g >-|-) ≡ (g . f >-|-)

Minimal complete definition

(>-|-)

Methods

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

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

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

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

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

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

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

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

(>-|-|-) :: (Contravariant source (Betwixt source target) u, Contravariant (Betwixt source target) target t) => source a b -> target (t (u a)) (t (u b)) infixl 4

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)

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

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

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

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

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

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

(>-|--------) :: 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)

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

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

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

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

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

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

(>-|--------) :: 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

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

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

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

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

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

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

(>-|--------) :: (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.Algebraic.Exponential

Methods

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

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

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

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

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

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

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

(>-|--------) :: (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

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

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

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

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

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

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

(>-|--------) :: (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

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

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

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

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

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

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

(>-|--------) :: (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

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

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

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

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

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

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

(>-|--------) :: (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

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

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

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

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

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

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

(>-|--------) :: (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

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

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

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

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

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

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

(>-|--------) :: (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

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

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

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

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

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

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

(>-|--------) :: (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

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

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

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

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

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

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

(>-|--------) :: (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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(>-|--------) :: (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)

(>$$<) :: (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))