Pandora.Pattern.Functor.Covariant

Documentation

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

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

Minimal complete definition

(<$>)

Methods

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

Infix version of comap

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

Prefix version of <$>

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

Replace all locations in the input with the same value

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

Flipped version of <$

void :: t a -> t ()

Discards the result of evaluation

loeb :: t (t a -> a) -> t a

Computing a value from a structure of values

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

Flipped infix version of comap

(<$$>) :: Covariant u => (a -> b) -> ((t :. u) := a) -> (t :. u) := b

Infix versions of comap with various nesting levels

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

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((t :. (u :. (v :. w))) := a) -> (t :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((t :. u) := a) -> (a -> b) -> (t :. u) := b

Infix flipped versions of comap with various nesting levels

(<&&&>) :: (Covariant u, Covariant v) => ((t :. (u :. v)) := a) -> (a -> b) -> (t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((t :. (u :. (v :. w))) := a) -> (a -> b) -> (t :. (u :. (v :. w))) := b

Instances

Covariant Wye

Defined in Pandora.Paradigm.Basis.Wye

Methods

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

comap :: (a -> b) -> Wye a -> Wye b

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

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

void :: Wye a -> Wye ()

loeb :: Wye (Wye a -> a) -> Wye a

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

(<$$>) :: Covariant u => (a -> b) -> ((Wye :. u) := a) -> (Wye :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Wye :. (u :. v)) := a) -> (Wye :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Wye :. (u :. (v :. w))) := a) -> (Wye :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Wye :. u) := a) -> (a -> b) -> (Wye :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Wye :. (u :. v)) := a) -> (a -> b) -> (Wye :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Wye :. (u :. (v :. w))) := a) -> (a -> b) -> (Wye :. (u :. (v :. w))) := b

Covariant Edges

Defined in Pandora.Paradigm.Basis.Edges

Methods

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

comap :: (a -> b) -> Edges a -> Edges b

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

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

void :: Edges a -> Edges ()

loeb :: Edges (Edges a -> a) -> Edges a

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

(<$$>) :: Covariant u => (a -> b) -> ((Edges :. u) := a) -> (Edges :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Edges :. (u :. v)) := a) -> (Edges :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Edges :. (u :. (v :. w))) := a) -> (Edges :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Edges :. u) := a) -> (a -> b) -> (Edges :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Edges :. (u :. v)) := a) -> (a -> b) -> (Edges :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Edges :. (u :. (v :. w))) := a) -> (a -> b) -> (Edges :. (u :. (v :. w))) := b

Covariant Graph

Defined in Pandora.Paradigm.Structure.Specific.Graph

Methods

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

comap :: (a -> b) -> Graph a -> Graph b

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

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

void :: Graph a -> Graph ()

loeb :: Graph (Graph a -> a) -> Graph a

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

(<$$>) :: Covariant u => (a -> b) -> ((Graph :. u) := a) -> (Graph :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Graph :. (u :. v)) := a) -> (Graph :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Graph :. (u :. (v :. w))) := a) -> (Graph :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Graph :. u) := a) -> (a -> b) -> (Graph :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Graph :. (u :. v)) := a) -> (a -> b) -> (Graph :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Graph :. (u :. (v :. w))) := a) -> (a -> b) -> (Graph :. (u :. (v :. w))) := b

Covariant Maybe

Defined in Pandora.Paradigm.Basis.Maybe

Methods

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

comap :: (a -> b) -> Maybe a -> Maybe b

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

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

void :: Maybe a -> Maybe ()

loeb :: Maybe (Maybe a -> a) -> Maybe a

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

(<$$>) :: Covariant u => (a -> b) -> ((Maybe :. u) := a) -> (Maybe :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Maybe :. (u :. v)) := a) -> (Maybe :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Maybe :. (u :. (v :. w))) := a) -> (Maybe :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Maybe :. u) := a) -> (a -> b) -> (Maybe :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Maybe :. (u :. v)) := a) -> (a -> b) -> (Maybe :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Maybe :. (u :. (v :. w))) := a) -> (a -> b) -> (Maybe :. (u :. (v :. w))) := b

Covariant Stack

Defined in Pandora.Paradigm.Structure.Specific.Stack

Methods

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

comap :: (a -> b) -> Stack a -> Stack b

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

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

void :: Stack a -> Stack ()

loeb :: Stack (Stack a -> a) -> Stack a

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

(<$$>) :: Covariant u => (a -> b) -> ((Stack :. u) := a) -> (Stack :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Stack :. (u :. v)) := a) -> (Stack :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Stack :. (u :. (v :. w))) := a) -> (Stack :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Stack :. u) := a) -> (a -> b) -> (Stack :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Stack :. (u :. v)) := a) -> (a -> b) -> (Stack :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Stack :. (u :. (v :. w))) := a) -> (a -> b) -> (Stack :. (u :. (v :. w))) := b

Covariant Identity

Defined in Pandora.Paradigm.Basis.Identity

Methods

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

comap :: (a -> b) -> Identity a -> Identity b

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

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

void :: Identity a -> Identity ()

loeb :: Identity (Identity a -> a) -> Identity a

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

(<$$>) :: Covariant u => (a -> b) -> ((Identity :. u) := a) -> (Identity :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Identity :. (u :. v)) := a) -> (Identity :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Identity :. (u :. (v :. w))) := a) -> (Identity :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Identity :. u) := a) -> (a -> b) -> (Identity :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Identity :. (u :. v)) := a) -> (a -> b) -> (Identity :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Identity :. (u :. (v :. w))) := a) -> (a -> b) -> (Identity :. (u :. (v :. w))) := b

Covariant (Environmental e)

Defined in Pandora.Paradigm.Inventory.Environmental

Methods

(<$>) :: (a -> b) -> Environmental e a -> Environmental e b

comap :: (a -> b) -> Environmental e a -> Environmental e b

(<$) :: a -> Environmental e b -> Environmental e a

($>) :: Environmental e a -> b -> Environmental e b

void :: Environmental e a -> Environmental e ()

loeb :: Environmental e (Environmental e a -> a) -> Environmental e a

(<&>) :: Environmental e a -> (a -> b) -> Environmental e b

(<$$>) :: Covariant u => (a -> b) -> ((Environmental e :. u) := a) -> (Environmental e :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Environmental e :. (u :. v)) := a) -> (Environmental e :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Environmental e :. (u :. (v :. w))) := a) -> (Environmental e :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Environmental e :. u) := a) -> (a -> b) -> (Environmental e :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Environmental e :. (u :. v)) := a) -> (a -> b) -> (Environmental e :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Environmental e :. (u :. (v :. w))) := a) -> (a -> b) -> (Environmental e :. (u :. (v :. w))) := b

Covariant (Yoneda t)

Defined in Pandora.Paradigm.Basis.Yoneda

Methods

(<$>) :: (a -> b) -> Yoneda t a -> Yoneda t b

comap :: (a -> b) -> Yoneda t a -> Yoneda t b

(<$) :: a -> Yoneda t b -> Yoneda t a

($>) :: Yoneda t a -> b -> Yoneda t b

void :: Yoneda t a -> Yoneda t ()

loeb :: Yoneda t (Yoneda t a -> a) -> Yoneda t a

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

(<$$>) :: Covariant u => (a -> b) -> ((Yoneda t :. u) := a) -> (Yoneda t :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Yoneda t :. (u :. v)) := a) -> (Yoneda t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Yoneda t :. (u :. (v :. w))) := a) -> (Yoneda t :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Yoneda t :. u) := a) -> (a -> b) -> (Yoneda t :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Yoneda t :. (u :. v)) := a) -> (a -> b) -> (Yoneda t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Yoneda t :. (u :. (v :. w))) := a) -> (a -> b) -> (Yoneda t :. (u :. (v :. w))) := b

Covariant (Proxy :: Type -> Type)

Defined in Pandora.Paradigm.Basis.Proxy

Methods

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

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

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

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

void :: Proxy a -> Proxy ()

loeb :: Proxy (Proxy a -> a) -> Proxy a

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

(<$$>) :: Covariant u => (a -> b) -> ((Proxy :. u) := a) -> (Proxy :. u) := b

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

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Proxy :. (u :. (v :. w))) := a) -> (Proxy :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Proxy :. u) := a) -> (a -> b) -> (Proxy :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Proxy :. (u :. v)) := a) -> (a -> b) -> (Proxy :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Proxy :. (u :. (v :. w))) := a) -> (a -> b) -> (Proxy :. (u :. (v :. w))) := b

Covariant (Variation e)

Defined in Pandora.Paradigm.Basis.Variation

Methods

(<$>) :: (a -> b) -> Variation e a -> Variation e b

comap :: (a -> b) -> Variation e a -> Variation e b

(<$) :: a -> Variation e b -> Variation e a

($>) :: Variation e a -> b -> Variation e b

void :: Variation e a -> Variation e ()

loeb :: Variation e (Variation e a -> a) -> Variation e a

(<&>) :: Variation e a -> (a -> b) -> Variation e b

(<$$>) :: Covariant u => (a -> b) -> ((Variation e :. u) := a) -> (Variation e :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Variation e :. (u :. v)) := a) -> (Variation e :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Variation e :. (u :. (v :. w))) := a) -> (Variation e :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Variation e :. u) := a) -> (a -> b) -> (Variation e :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Variation e :. (u :. v)) := a) -> (a -> b) -> (Variation e :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Variation e :. (u :. (v :. w))) := a) -> (a -> b) -> (Variation e :. (u :. (v :. w))) := b

Covariant t => Covariant (Jet t)

Defined in Pandora.Paradigm.Basis.Jet

Methods

(<$>) :: (a -> b) -> Jet t a -> Jet t b

comap :: (a -> b) -> Jet t a -> Jet t b

(<$) :: a -> Jet t b -> Jet t a

($>) :: Jet t a -> b -> Jet t b

void :: Jet t a -> Jet t ()

loeb :: Jet t (Jet t a -> a) -> Jet t a

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

(<$$>) :: Covariant u => (a -> b) -> ((Jet t :. u) := a) -> (Jet t :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Jet t :. (u :. v)) := a) -> (Jet t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Jet t :. (u :. (v :. w))) := a) -> (Jet t :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Jet t :. u) := a) -> (a -> b) -> (Jet t :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Jet t :. (u :. v)) := a) -> (a -> b) -> (Jet t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Jet t :. (u :. (v :. w))) := a) -> (a -> b) -> (Jet t :. (u :. (v :. w))) := b

Covariant t => Covariant (Free t)

Defined in Pandora.Paradigm.Basis.Free

Methods

(<$>) :: (a -> b) -> Free t a -> Free t b

comap :: (a -> b) -> Free t a -> Free t b

(<$) :: a -> Free t b -> Free t a

($>) :: Free t a -> b -> Free t b

void :: Free t a -> Free t ()

loeb :: Free t (Free t a -> a) -> Free t a

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

(<$$>) :: Covariant u => (a -> b) -> ((Free t :. u) := a) -> (Free t :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Free t :. (u :. v)) := a) -> (Free t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Free t :. (u :. (v :. w))) := a) -> (Free t :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Free t :. u) := a) -> (a -> b) -> (Free t :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Free t :. (u :. v)) := a) -> (a -> b) -> (Free t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Free t :. (u :. (v :. w))) := a) -> (a -> b) -> (Free t :. (u :. (v :. w))) := b

Covariant (Validation e)

Defined in Pandora.Paradigm.Basis.Validation

Methods

(<$>) :: (a -> b) -> Validation e a -> Validation e b

comap :: (a -> b) -> Validation e a -> Validation e b

(<$) :: a -> Validation e b -> Validation e a

($>) :: Validation e a -> b -> Validation e b

void :: Validation e a -> Validation e ()

loeb :: Validation e (Validation e a -> a) -> Validation e a

(<&>) :: Validation e a -> (a -> b) -> Validation e b

(<$$>) :: Covariant u => (a -> b) -> ((Validation e :. u) := a) -> (Validation e :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Validation e :. (u :. v)) := a) -> (Validation e :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Validation e :. (u :. (v :. w))) := a) -> (Validation e :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Validation e :. u) := a) -> (a -> b) -> (Validation e :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Validation e :. (u :. v)) := a) -> (a -> b) -> (Validation e :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Validation e :. (u :. (v :. w))) := a) -> (a -> b) -> (Validation e :. (u :. (v :. w))) := b

Covariant t => Covariant (Twister t)

Defined in Pandora.Paradigm.Basis.Twister

Methods

(<$>) :: (a -> b) -> Twister t a -> Twister t b

comap :: (a -> b) -> Twister t a -> Twister t b

(<$) :: a -> Twister t b -> Twister t a

($>) :: Twister t a -> b -> Twister t b

void :: Twister t a -> Twister t ()

loeb :: Twister t (Twister t a -> a) -> Twister t a

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

(<$$>) :: Covariant u => (a -> b) -> ((Twister t :. u) := a) -> (Twister t :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Twister t :. (u :. v)) := a) -> (Twister t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Twister t :. (u :. (v :. w))) := a) -> (Twister t :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Twister t :. u) := a) -> (a -> b) -> (Twister t :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Twister t :. (u :. v)) := a) -> (a -> b) -> (Twister t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Twister t :. (u :. (v :. w))) := a) -> (a -> b) -> (Twister t :. (u :. (v :. w))) := b

Covariant (Product a)

Defined in Pandora.Paradigm.Basis.Product

Methods

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

comap :: (a0 -> b) -> Product a a0 -> Product a b

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

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

void :: Product a a0 -> Product a ()

loeb :: Product a (Product a a0 -> a0) -> Product a a0

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

(<$$>) :: Covariant u => (a0 -> b) -> ((Product a :. u) := a0) -> (Product a :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a0 -> b) -> ((Product a :. (u :. v)) := a0) -> (Product a :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a0 -> b) -> ((Product a :. (u :. (v :. w))) := a0) -> (Product a :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Product a :. u) := a0) -> (a0 -> b) -> (Product a :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Product a :. (u :. v)) := a0) -> (a0 -> b) -> (Product a :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Product a :. (u :. (v :. w))) := a0) -> (a0 -> b) -> (Product a :. (u :. (v :. w))) := b

Covariant (Storage p)

Defined in Pandora.Paradigm.Inventory.Storage

Methods

(<$>) :: (a -> b) -> Storage p a -> Storage p b

comap :: (a -> b) -> Storage p a -> Storage p b

(<$) :: a -> Storage p b -> Storage p a

($>) :: Storage p a -> b -> Storage p b

void :: Storage p a -> Storage p ()

loeb :: Storage p (Storage p a -> a) -> Storage p a

(<&>) :: Storage p a -> (a -> b) -> Storage p b

(<$$>) :: Covariant u => (a -> b) -> ((Storage p :. u) := a) -> (Storage p :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Storage p :. (u :. v)) := a) -> (Storage p :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Storage p :. (u :. (v :. w))) := a) -> (Storage p :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Storage p :. u) := a) -> (a -> b) -> (Storage p :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Storage p :. (u :. v)) := a) -> (a -> b) -> (Storage p :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Storage p :. (u :. (v :. w))) := a) -> (a -> b) -> (Storage p :. (u :. (v :. w))) := b

Covariant (Stateful s)

Defined in Pandora.Paradigm.Inventory.Stateful

Methods

(<$>) :: (a -> b) -> Stateful s a -> Stateful s b

comap :: (a -> b) -> Stateful s a -> Stateful s b

(<$) :: a -> Stateful s b -> Stateful s a

($>) :: Stateful s a -> b -> Stateful s b

void :: Stateful s a -> Stateful s ()

loeb :: Stateful s (Stateful s a -> a) -> Stateful s a

(<&>) :: Stateful s a -> (a -> b) -> Stateful s b

(<$$>) :: Covariant u => (a -> b) -> ((Stateful s :. u) := a) -> (Stateful s :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Stateful s :. (u :. v)) := a) -> (Stateful s :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Stateful s :. (u :. (v :. w))) := a) -> (Stateful s :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Stateful s :. u) := a) -> (a -> b) -> (Stateful s :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Stateful s :. (u :. v)) := a) -> (a -> b) -> (Stateful s :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Stateful s :. (u :. (v :. w))) := a) -> (a -> b) -> (Stateful s :. (u :. (v :. w))) := b

Covariant t => Covariant (Jack t)

Defined in Pandora.Paradigm.Basis.Jack

Methods

(<$>) :: (a -> b) -> Jack t a -> Jack t b

comap :: (a -> b) -> Jack t a -> Jack t b

(<$) :: a -> Jack t b -> Jack t a

($>) :: Jack t a -> b -> Jack t b

void :: Jack t a -> Jack t ()

loeb :: Jack t (Jack t a -> a) -> Jack t a

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

(<$$>) :: Covariant u => (a -> b) -> ((Jack t :. u) := a) -> (Jack t :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Jack t :. (u :. v)) := a) -> (Jack t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Jack t :. (u :. (v :. w))) := a) -> (Jack t :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Jack t :. u) := a) -> (a -> b) -> (Jack t :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Jack t :. (u :. v)) := a) -> (a -> b) -> (Jack t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Jack t :. (u :. (v :. w))) := a) -> (a -> b) -> (Jack t :. (u :. (v :. w))) := b

Covariant (Conclusion e)

Defined in Pandora.Paradigm.Basis.Conclusion

Methods

(<$>) :: (a -> b) -> Conclusion e a -> Conclusion e b

comap :: (a -> b) -> Conclusion e a -> Conclusion e b

(<$) :: a -> Conclusion e b -> Conclusion e a

($>) :: Conclusion e a -> b -> Conclusion e b

void :: Conclusion e a -> Conclusion e ()

loeb :: Conclusion e (Conclusion e a -> a) -> Conclusion e a

(<&>) :: Conclusion e a -> (a -> b) -> Conclusion e b

(<$$>) :: Covariant u => (a -> b) -> ((Conclusion e :. u) := a) -> (Conclusion e :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Conclusion e :. (u :. v)) := a) -> (Conclusion e :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Conclusion e :. (u :. (v :. w))) := a) -> (Conclusion e :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Conclusion e :. u) := a) -> (a -> b) -> (Conclusion e :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Conclusion e :. (u :. v)) := a) -> (a -> b) -> (Conclusion e :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Conclusion e :. (u :. (v :. w))) := a) -> (a -> b) -> (Conclusion e :. (u :. (v :. w))) := b

Covariant (Tagged tag)

Defined in Pandora.Paradigm.Basis.Tagged

Methods

(<$>) :: (a -> b) -> Tagged tag a -> Tagged tag b

comap :: (a -> b) -> Tagged tag a -> Tagged tag b

(<$) :: a -> Tagged tag b -> Tagged tag a

($>) :: Tagged tag a -> b -> Tagged tag b

void :: Tagged tag a -> Tagged tag ()

loeb :: Tagged tag (Tagged tag a -> a) -> Tagged tag a

(<&>) :: Tagged tag a -> (a -> b) -> Tagged tag b

(<$$>) :: Covariant u => (a -> b) -> ((Tagged tag :. u) := a) -> (Tagged tag :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Tagged tag :. (u :. v)) := a) -> (Tagged tag :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Tagged tag :. (u :. (v :. w))) := a) -> (Tagged tag :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Tagged tag :. u) := a) -> (a -> b) -> (Tagged tag :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Tagged tag :. (u :. v)) := a) -> (a -> b) -> (Tagged tag :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Tagged tag :. (u :. (v :. w))) := a) -> (a -> b) -> (Tagged tag :. (u :. (v :. w))) := b

Covariant (Constant a :: Type -> Type)

Defined in Pandora.Paradigm.Basis.Constant

Methods

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

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

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

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

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

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

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

(<$$>) :: Covariant u => (a0 -> b) -> ((Constant a :. u) := a0) -> (Constant a :. u) := b

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

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a0 -> b) -> ((Constant a :. (u :. (v :. w))) := a0) -> (Constant a :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Constant a :. u) := a0) -> (a0 -> b) -> (Constant a :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Constant a :. (u :. v)) := a0) -> (a0 -> b) -> (Constant a :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Constant a :. (u :. (v :. w))) := a0) -> (a0 -> b) -> (Constant a :. (u :. (v :. w))) := b

Covariant ((->) a :: Type -> Type)

Defined in Pandora.Pattern.Functor.Covariant

Methods

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

comap :: (a0 -> b) -> (a -> a0) -> a -> b

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

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

void :: (a -> a0) -> a -> ()

loeb :: (a -> ((a -> a0) -> a0)) -> a -> a0

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

(<$$>) :: Covariant u => (a0 -> b) -> (((->) a :. u) := a0) -> ((->) a :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a0 -> b) -> (((->) a :. (u :. v)) := a0) -> ((->) a :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a0 -> b) -> (((->) a :. (u :. (v :. w))) := a0) -> ((->) a :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => (((->) a :. u) := a0) -> (a0 -> b) -> ((->) a :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => (((->) a :. (u :. v)) := a0) -> (a0 -> b) -> ((->) a :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => (((->) a :. (u :. (v :. w))) := a0) -> (a0 -> b) -> ((->) a :. (u :. (v :. w))) := b

Covariant (Ran t u b)

Defined in Pandora.Paradigm.Basis.Kan

Methods

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

comap :: (a -> b0) -> Ran t u b a -> Ran t u b b0

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

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

void :: Ran t u b a -> Ran t u b ()

loeb :: Ran t u b (Ran t u b a -> a) -> Ran t u b a

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

(<$$>) :: Covariant u0 => (a -> b0) -> ((Ran t u b :. u0) := a) -> (Ran t u b :. u0) := b0

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b0) -> ((Ran t u b :. (u0 :. v)) := a) -> (Ran t u b :. (u0 :. v)) := b0

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b0) -> ((Ran t u b :. (u0 :. (v :. w))) := a) -> (Ran t u b :. (u0 :. (v :. w))) := b0

(<&&>) :: Covariant u0 => ((Ran t u b :. u0) := a) -> (a -> b0) -> (Ran t u b :. u0) := b0

(<&&&>) :: (Covariant u0, Covariant v) => ((Ran t u b :. (u0 :. v)) := a) -> (a -> b0) -> (Ran t u b :. (u0 :. v)) := b0

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((Ran t u b :. (u0 :. (v :. w))) := a) -> (a -> b0) -> (Ran t u b :. (u0 :. (v :. w))) := b0

Covariant t => Covariant (Continuation r t)

Defined in Pandora.Paradigm.Basis.Continuation

Methods

(<$>) :: (a -> b) -> Continuation r t a -> Continuation r t b

comap :: (a -> b) -> Continuation r t a -> Continuation r t b

(<$) :: a -> Continuation r t b -> Continuation r t a

($>) :: Continuation r t a -> b -> Continuation r t b

void :: Continuation r t a -> Continuation r t ()

loeb :: Continuation r t (Continuation r t a -> a) -> Continuation r t a

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

(<$$>) :: Covariant u => (a -> b) -> ((Continuation r t :. u) := a) -> (Continuation r t :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Continuation r t :. (u :. v)) := a) -> (Continuation r t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Continuation r t :. (u :. (v :. w))) := a) -> (Continuation r t :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Continuation r t :. u) := a) -> (a -> b) -> (Continuation r t :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Continuation r t :. (u :. v)) := a) -> (a -> b) -> (Continuation r t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Continuation r t :. (u :. (v :. w))) := a) -> (a -> b) -> (Continuation r t :. (u :. (v :. w))) := b

Covariant u => Covariant (UT Co Co Maybe u)

Defined in Pandora.Paradigm.Basis.Maybe

Methods

(<$>) :: (a -> b) -> UT Co Co Maybe u a -> UT Co Co Maybe u b

comap :: (a -> b) -> UT Co Co Maybe u a -> UT Co Co Maybe u b

(<$) :: a -> UT Co Co Maybe u b -> UT Co Co Maybe u a

($>) :: UT Co Co Maybe u a -> b -> UT Co Co Maybe u b

void :: UT Co Co Maybe u a -> UT Co Co Maybe u ()

loeb :: UT Co Co Maybe u (UT Co Co Maybe u a -> a) -> UT Co Co Maybe u a

(<&>) :: UT Co Co Maybe u a -> (a -> b) -> UT Co Co Maybe u b

(<$$>) :: Covariant u0 => (a -> b) -> ((UT Co Co Maybe u :. u0) := a) -> (UT Co Co Maybe u :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((UT Co Co Maybe u :. (u0 :. v)) := a) -> (UT Co Co Maybe u :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((UT Co Co Maybe u :. (u0 :. (v :. w))) := a) -> (UT Co Co Maybe u :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((UT Co Co Maybe u :. u0) := a) -> (a -> b) -> (UT Co Co Maybe u :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => ((UT Co Co Maybe u :. (u0 :. v)) := a) -> (a -> b) -> (UT Co Co Maybe u :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((UT Co Co Maybe u :. (u0 :. (v :. w))) := a) -> (a -> b) -> (UT Co Co Maybe u :. (u0 :. (v :. w))) := b

Covariant u => Covariant (UT Co Co (Conclusion e) u)

Defined in Pandora.Paradigm.Basis.Conclusion

Methods

(<$>) :: (a -> b) -> UT Co Co (Conclusion e) u a -> UT Co Co (Conclusion e) u b

comap :: (a -> b) -> UT Co Co (Conclusion e) u a -> UT Co Co (Conclusion e) u b

(<$) :: a -> UT Co Co (Conclusion e) u b -> UT Co Co (Conclusion e) u a

($>) :: UT Co Co (Conclusion e) u a -> b -> UT Co Co (Conclusion e) u b

void :: UT Co Co (Conclusion e) u a -> UT Co Co (Conclusion e) u ()

loeb :: UT Co Co (Conclusion e) u (UT Co Co (Conclusion e) u a -> a) -> UT Co Co (Conclusion e) u a

(<&>) :: UT Co Co (Conclusion e) u a -> (a -> b) -> UT Co Co (Conclusion e) u b

(<$$>) :: Covariant u0 => (a -> b) -> ((UT Co Co (Conclusion e) u :. u0) := a) -> (UT Co Co (Conclusion e) u :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((UT Co Co (Conclusion e) u :. (u0 :. v)) := a) -> (UT Co Co (Conclusion e) u :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((UT Co Co (Conclusion e) u :. (u0 :. (v :. w))) := a) -> (UT Co Co (Conclusion e) u :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((UT Co Co (Conclusion e) u :. u0) := a) -> (a -> b) -> (UT Co Co (Conclusion e) u :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => ((UT Co Co (Conclusion e) u :. (u0 :. v)) := a) -> (a -> b) -> (UT Co Co (Conclusion e) u :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((UT Co Co (Conclusion e) u :. (u0 :. (v :. w))) := a) -> (a -> b) -> (UT Co Co (Conclusion e) u :. (u0 :. (v :. w))) := b

Covariant u => Covariant (TUV Co Co Co ((->) s :: Type -> Type) u ((:*:) s))

Defined in Pandora.Paradigm.Inventory.Stateful

Methods

(<$>) :: (a -> b) -> TUV Co Co Co ((->) s) u ((:*:) s) a -> TUV Co Co Co ((->) s) u ((:*:) s) b

comap :: (a -> b) -> TUV Co Co Co ((->) s) u ((:*:) s) a -> TUV Co Co Co ((->) s) u ((:*:) s) b

(<$) :: a -> TUV Co Co Co ((->) s) u ((:*:) s) b -> TUV Co Co Co ((->) s) u ((:*:) s) a

($>) :: TUV Co Co Co ((->) s) u ((:*:) s) a -> b -> TUV Co Co Co ((->) s) u ((:*:) s) b

void :: TUV Co Co Co ((->) s) u ((:*:) s) a -> TUV Co Co Co ((->) s) u ((:*:) s) ()

loeb :: TUV Co Co Co ((->) s) u ((:*:) s) (TUV Co Co Co ((->) s) u ((:*:) s) a -> a) -> TUV Co Co Co ((->) s) u ((:*:) s) a

(<&>) :: TUV Co Co Co ((->) s) u ((:*:) s) a -> (a -> b) -> TUV Co Co Co ((->) s) u ((:*:) s) b

(<$$>) :: Covariant u0 => (a -> b) -> ((TUV Co Co Co ((->) s) u ((:*:) s) :. u0) := a) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. v)) := a) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. (v :. w))) := a) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((TUV Co Co Co ((->) s) u ((:*:) s) :. u0) := a) -> (a -> b) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => ((TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. v)) := a) -> (a -> b) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (TUV Co Co Co ((->) s) u ((:*:) s) :. (u0 :. (v :. w))) := b