Pandora.Pattern.Functor.Contravariant

Documentation

class Contravariant (t :: * -> *) where

When providing a new instance, you should ensure it satisfies the two laws:
* Identity morphism: contramap identity ≡ identity
* Composition of morphisms: contramap f . contramap g ≡ contramap (g . f)

Minimal complete definition

(>$<)

Methods

(>$<) :: (a -> b) -> t b -> t a infixl 4

Infix version of contramap

contramap :: (a -> b) -> t b -> t a

Prefix version of >$<

(>$) :: b -> t b -> t a infixl 4

Replace all locations in the output with the same value

($<) :: t b -> b -> t a infixl 4

Flipped version of >$

full :: t () -> t a

Fill the input of evaluation

(>$$$<) :: (Contravariant u, Contravariant v) => (a -> b) -> t (u (v b)) -> t (u (v a))

Infix versions of contramap with various nesting levels

(>&<) :: t b -> (a -> b) -> t a

Flipped infix version of contramap

Instances

Contravariant Predicate

Defined in Pandora.Paradigm.Basis.Predicate

Methods

(>$<) :: (a -> b) -> Predicate b -> Predicate a

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

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

($<) :: Predicate b -> b -> Predicate a

full :: Predicate () -> Predicate a

(>$$$<) :: (Contravariant u, Contravariant v) => (a -> b) -> Predicate (u (v b)) -> Predicate (u (v a))

(>&<) :: Predicate b -> (a -> b) -> Predicate a

Contravariant (Proxy :: Type -> Type)

Defined in Pandora.Paradigm.Basis.Proxy

Methods

(>$<) :: (a -> b) -> Proxy b -> Proxy a

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

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

($<) :: Proxy b -> b -> Proxy a

full :: Proxy () -> Proxy a

(>$$$<) :: (Contravariant u, Contravariant v) => (a -> b) -> Proxy (u (v b)) -> Proxy (u (v a))

(>&<) :: Proxy b -> (a -> b) -> Proxy a

Contravariant (Constant a :: Type -> Type)

Defined in Pandora.Paradigm.Basis.Constant

Methods

(>$<) :: (a0 -> b) -> Constant a b -> Constant a a0

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

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

($<) :: Constant a b -> b -> Constant a a0

full :: Constant a () -> Constant a a0

(>$$$<) :: (Contravariant u, Contravariant v) => (a0 -> b) -> Constant a (u (v b)) -> Constant a (u (v a0))

(>&<) :: Constant a b -> (a0 -> b) -> Constant a a0

Contravariant (Lan t u b)

Defined in Pandora.Paradigm.Junction.Kan

Methods

(>$<) :: (a -> b0) -> Lan t u b b0 -> Lan t u b a

contramap :: (a -> b0) -> Lan t u b b0 -> Lan t u b a

(>$) :: b0 -> Lan t u b b0 -> Lan t u b a

($<) :: Lan t u b b0 -> b0 -> Lan t u b a

full :: Lan t u b () -> Lan t u b a

(>$$$<) :: (Contravariant u0, Contravariant v) => (a -> b0) -> Lan t u b (u0 (v b0)) -> Lan t u b (u0 (v a))

(>&<) :: Lan t u b b0 -> (a -> b0) -> Lan t u b a

(Covariant t, Contravariant u) => Contravariant (U Co Contra t u)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> U Co Contra t u b -> U Co Contra t u a

contramap :: (a -> b) -> U Co Contra t u b -> U Co Contra t u a

(>$) :: b -> U Co Contra t u b -> U Co Contra t u a

($<) :: U Co Contra t u b -> b -> U Co Contra t u a

full :: U Co Contra t u () -> U Co Contra t u a

(>$$$<) :: (Contravariant u0, Contravariant v) => (a -> b) -> U Co Contra t u (u0 (v b)) -> U Co Contra t u (u0 (v a))

(>&<) :: U Co Contra t u b -> (a -> b) -> U Co Contra t u a

(Contravariant t, Covariant u) => Contravariant (U Contra Co t u)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> U Contra Co t u b -> U Contra Co t u a

contramap :: (a -> b) -> U Contra Co t u b -> U Contra Co t u a

(>$) :: b -> U Contra Co t u b -> U Contra Co t u a

($<) :: U Contra Co t u b -> b -> U Contra Co t u a

full :: U Contra Co t u () -> U Contra Co t u a

(>$$$<) :: (Contravariant u0, Contravariant v) => (a -> b) -> U Contra Co t u (u0 (v b)) -> U Contra Co t u (u0 (v a))

(>&<) :: U Contra Co t u b -> (a -> b) -> U Contra Co t u a

(Covariant t, Covariant u, Contravariant v) => Contravariant (UU Co Co Contra t u v)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> UU Co Co Contra t u v b -> UU Co Co Contra t u v a

contramap :: (a -> b) -> UU Co Co Contra t u v b -> UU Co Co Contra t u v a

(>$) :: b -> UU Co Co Contra t u v b -> UU Co Co Contra t u v a

($<) :: UU Co Co Contra t u v b -> b -> UU Co Co Contra t u v a

full :: UU Co Co Contra t u v () -> UU Co Co Contra t u v a

(>$$$<) :: (Contravariant u0, Contravariant v0) => (a -> b) -> UU Co Co Contra t u v (u0 (v0 b)) -> UU Co Co Contra t u v (u0 (v0 a))

(>&<) :: UU Co Co Contra t u v b -> (a -> b) -> UU Co Co Contra t u v a

(Covariant t, Contravariant u, Covariant v) => Contravariant (UU Co Contra Co t u v)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> UU Co Contra Co t u v b -> UU Co Contra Co t u v a

contramap :: (a -> b) -> UU Co Contra Co t u v b -> UU Co Contra Co t u v a

(>$) :: b -> UU Co Contra Co t u v b -> UU Co Contra Co t u v a

($<) :: UU Co Contra Co t u v b -> b -> UU Co Contra Co t u v a

full :: UU Co Contra Co t u v () -> UU Co Contra Co t u v a

(>$$$<) :: (Contravariant u0, Contravariant v0) => (a -> b) -> UU Co Contra Co t u v (u0 (v0 b)) -> UU Co Contra Co t u v (u0 (v0 a))

(>&<) :: UU Co Contra Co t u v b -> (a -> b) -> UU Co Contra Co t u v a

(Contravariant t, Covariant u, Covariant v) => Contravariant (UU Contra Co Co t u v)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> UU Contra Co Co t u v b -> UU Contra Co Co t u v a

contramap :: (a -> b) -> UU Contra Co Co t u v b -> UU Contra Co Co t u v a

(>$) :: b -> UU Contra Co Co t u v b -> UU Contra Co Co t u v a

($<) :: UU Contra Co Co t u v b -> b -> UU Contra Co Co t u v a

full :: UU Contra Co Co t u v () -> UU Contra Co Co t u v a

(>$$$<) :: (Contravariant u0, Contravariant v0) => (a -> b) -> UU Contra Co Co t u v (u0 (v0 b)) -> UU Contra Co Co t u v (u0 (v0 a))

(>&<) :: UU Contra Co Co t u v b -> (a -> b) -> UU Contra Co Co t u v a

(Contravariant t, Contravariant u, Contravariant v) => Contravariant (UU Contra Contra Contra t u v)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> UU Contra Contra Contra t u v b -> UU Contra Contra Contra t u v a

contramap :: (a -> b) -> UU Contra Contra Contra t u v b -> UU Contra Contra Contra t u v a

(>$) :: b -> UU Contra Contra Contra t u v b -> UU Contra Contra Contra t u v a

($<) :: UU Contra Contra Contra t u v b -> b -> UU Contra Contra Contra t u v a

full :: UU Contra Contra Contra t u v () -> UU Contra Contra Contra t u v a

(>$$$<) :: (Contravariant u0, Contravariant v0) => (a -> b) -> UU Contra Contra Contra t u v (u0 (v0 b)) -> UU Contra Contra Contra t u v (u0 (v0 a))

(>&<) :: UU Contra Contra Contra t u v b -> (a -> b) -> UU Contra Contra Contra t u v a

(Covariant t, Covariant u, Covariant v, Contravariant w) => Contravariant (UUU Co Co Co Contra t u v w)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> UUU Co Co Co Contra t u v w b -> UUU Co Co Co Contra t u v w a

contramap :: (a -> b) -> UUU Co Co Co Contra t u v w b -> UUU Co Co Co Contra t u v w a

(>$) :: b -> UUU Co Co Co Contra t u v w b -> UUU Co Co Co Contra t u v w a

($<) :: UUU Co Co Co Contra t u v w b -> b -> UUU Co Co Co Contra t u v w a

full :: UUU Co Co Co Contra t u v w () -> UUU Co Co Co Contra t u v w a

(>$$$<) :: (Contravariant u0, Contravariant v0) => (a -> b) -> UUU Co Co Co Contra t u v w (u0 (v0 b)) -> UUU Co Co Co Contra t u v w (u0 (v0 a))

(>&<) :: UUU Co Co Co Contra t u v w b -> (a -> b) -> UUU Co Co Co Contra t u v w a

(Covariant t, Covariant u, Contravariant v, Covariant w) => Contravariant (UUU Co Co Contra Co t u v w)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> UUU Co Co Contra Co t u v w b -> UUU Co Co Contra Co t u v w a

contramap :: (a -> b) -> UUU Co Co Contra Co t u v w b -> UUU Co Co Contra Co t u v w a

(>$) :: b -> UUU Co Co Contra Co t u v w b -> UUU Co Co Contra Co t u v w a

($<) :: UUU Co Co Contra Co t u v w b -> b -> UUU Co Co Contra Co t u v w a

full :: UUU Co Co Contra Co t u v w () -> UUU Co Co Contra Co t u v w a

(>$$$<) :: (Contravariant u0, Contravariant v0) => (a -> b) -> UUU Co Co Contra Co t u v w (u0 (v0 b)) -> UUU Co Co Contra Co t u v w (u0 (v0 a))

(>&<) :: UUU Co Co Contra Co t u v w b -> (a -> b) -> UUU Co Co Contra Co t u v w a

(Covariant t, Contravariant u, Covariant v, Covariant w) => Contravariant (UUU Co Contra Co Co t u v w)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> UUU Co Contra Co Co t u v w b -> UUU Co Contra Co Co t u v w a

contramap :: (a -> b) -> UUU Co Contra Co Co t u v w b -> UUU Co Contra Co Co t u v w a

(>$) :: b -> UUU Co Contra Co Co t u v w b -> UUU Co Contra Co Co t u v w a

($<) :: UUU Co Contra Co Co t u v w b -> b -> UUU Co Contra Co Co t u v w a

full :: UUU Co Contra Co Co t u v w () -> UUU Co Contra Co Co t u v w a

(>$$$<) :: (Contravariant u0, Contravariant v0) => (a -> b) -> UUU Co Contra Co Co t u v w (u0 (v0 b)) -> UUU Co Contra Co Co t u v w (u0 (v0 a))

(>&<) :: UUU Co Contra Co Co t u v w b -> (a -> b) -> UUU Co Contra Co Co t u v w a

(Covariant t, Contravariant u, Contravariant v, Contravariant w) => Contravariant (UUU Co Contra Contra Contra t u v w)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> UUU Co Contra Contra Contra t u v w b -> UUU Co Contra Contra Contra t u v w a

contramap :: (a -> b) -> UUU Co Contra Contra Contra t u v w b -> UUU Co Contra Contra Contra t u v w a

(>$) :: b -> UUU Co Contra Contra Contra t u v w b -> UUU Co Contra Contra Contra t u v w a

($<) :: UUU Co Contra Contra Contra t u v w b -> b -> UUU Co Contra Contra Contra t u v w a

full :: UUU Co Contra Contra Contra t u v w () -> UUU Co Contra Contra Contra t u v w a

(>$$$<) :: (Contravariant u0, Contravariant v0) => (a -> b) -> UUU Co Contra Contra Contra t u v w (u0 (v0 b)) -> UUU Co Contra Contra Contra t u v w (u0 (v0 a))

(>&<) :: UUU Co Contra Contra Contra t u v w b -> (a -> b) -> UUU Co Contra Contra Contra t u v w a

(Contravariant t, Covariant u, Covariant v, Covariant w) => Contravariant (UUU Contra Co Co Co t u v w)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> UUU Contra Co Co Co t u v w b -> UUU Contra Co Co Co t u v w a

contramap :: (a -> b) -> UUU Contra Co Co Co t u v w b -> UUU Contra Co Co Co t u v w a

(>$) :: b -> UUU Contra Co Co Co t u v w b -> UUU Contra Co Co Co t u v w a

($<) :: UUU Contra Co Co Co t u v w b -> b -> UUU Contra Co Co Co t u v w a

full :: UUU Contra Co Co Co t u v w () -> UUU Contra Co Co Co t u v w a

(>$$$<) :: (Contravariant u0, Contravariant v0) => (a -> b) -> UUU Contra Co Co Co t u v w (u0 (v0 b)) -> UUU Contra Co Co Co t u v w (u0 (v0 a))

(>&<) :: UUU Contra Co Co Co t u v w b -> (a -> b) -> UUU Contra Co Co Co t u v w a

(Contravariant t, Covariant u, Contravariant v, Contravariant w) => Contravariant (UUU Contra Co Contra Contra t u v w)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> UUU Contra Co Contra Contra t u v w b -> UUU Contra Co Contra Contra t u v w a

contramap :: (a -> b) -> UUU Contra Co Contra Contra t u v w b -> UUU Contra Co Contra Contra t u v w a

(>$) :: b -> UUU Contra Co Contra Contra t u v w b -> UUU Contra Co Contra Contra t u v w a

($<) :: UUU Contra Co Contra Contra t u v w b -> b -> UUU Contra Co Contra Contra t u v w a

full :: UUU Contra Co Contra Contra t u v w () -> UUU Contra Co Contra Contra t u v w a

(>$$$<) :: (Contravariant u0, Contravariant v0) => (a -> b) -> UUU Contra Co Contra Contra t u v w (u0 (v0 b)) -> UUU Contra Co Contra Contra t u v w (u0 (v0 a))

(>&<) :: UUU Contra Co Contra Contra t u v w b -> (a -> b) -> UUU Contra Co Contra Contra t u v w a

(Contravariant t, Contravariant u, Covariant v, Contravariant w) => Contravariant (UUU Contra Contra Co Contra t u v w)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> UUU Contra Contra Co Contra t u v w b -> UUU Contra Contra Co Contra t u v w a

contramap :: (a -> b) -> UUU Contra Contra Co Contra t u v w b -> UUU Contra Contra Co Contra t u v w a

(>$) :: b -> UUU Contra Contra Co Contra t u v w b -> UUU Contra Contra Co Contra t u v w a

($<) :: UUU Contra Contra Co Contra t u v w b -> b -> UUU Contra Contra Co Contra t u v w a

full :: UUU Contra Contra Co Contra t u v w () -> UUU Contra Contra Co Contra t u v w a

(>$$$<) :: (Contravariant u0, Contravariant v0) => (a -> b) -> UUU Contra Contra Co Contra t u v w (u0 (v0 b)) -> UUU Contra Contra Co Contra t u v w (u0 (v0 a))

(>&<) :: UUU Contra Contra Co Contra t u v w b -> (a -> b) -> UUU Contra Contra Co Contra t u v w a

(Contravariant t, Contravariant u, Contravariant v, Covariant w) => Contravariant (UUU Contra Contra Contra Co t u v w)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(>$<) :: (a -> b) -> UUU Contra Contra Contra Co t u v w b -> UUU Contra Contra Contra Co t u v w a

contramap :: (a -> b) -> UUU Contra Contra Contra Co t u v w b -> UUU Contra Contra Contra Co t u v w a

(>$) :: b -> UUU Contra Contra Contra Co t u v w b -> UUU Contra Contra Contra Co t u v w a

($<) :: UUU Contra Contra Contra Co t u v w b -> b -> UUU Contra Contra Contra Co t u v w a

full :: UUU Contra Contra Contra Co t u v w () -> UUU Contra Contra Contra Co t u v w a

(>$$$<) :: (Contravariant u0, Contravariant v0) => (a -> b) -> UUU Contra Contra Contra Co t u v w (u0 (v0 b)) -> UUU Contra Contra Contra Co t u v w (u0 (v0 a))

(>&<) :: UUU Contra Contra Contra Co t u v w b -> (a -> b) -> UUU Contra Contra Contra Co t u v w a