Pandora.Paradigm.Primary.Functor.Product

Documentation

data Product s a

Constructors

s :*: a infixr 0

Instances

Bivariant Product

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(<->) :: (a -> b) -> (c -> d) -> Product a c -> Product b d

bimap :: (a -> b) -> (c -> d) -> Product a c -> Product b d

Monotonic a (Vector r a) => Monotonic a (Vector (a :*: r) a)

Defined in Pandora.Paradigm.Primary.Linear.Vector

Methods

reduce :: (a -> r0 -> r0) -> r0 -> Vector (a :*: r) a -> r0

resolve :: (a -> r0) -> r0 -> Vector (a :*: r) a -> r0

Monotonic s a => Monotonic s (s :*: a)

Defined in Pandora.Paradigm.Structure

Methods

reduce :: (s -> r -> r) -> r -> (s :*: a) -> r

resolve :: (s -> r) -> r -> (s :*: a) -> r

Accessible b a => Accessible b (s :*: a)

Defined in Pandora.Paradigm.Structure

Methods

access :: (s :*: a) :-. b

Accessible a (s :*: a)

Defined in Pandora.Paradigm.Structure

Methods

access :: (s :*: a) :-. a

Accessible s (s :*: a)

Defined in Pandora.Paradigm.Structure

Methods

access :: (s :*: a) :-. s

Vectorize a r => Vectorize a (a :*: r)

Defined in Pandora.Paradigm.Primary.Linear.Vector

Methods

vectorize :: (a :*: r) -> Vector (a :*: r) a

Covariant (Product s)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

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

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

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

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

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

loeb :: Product s (a <:= Product s) -> Product s a

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

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

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

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

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

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

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

Extendable (Product s)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(=>>) :: Product s a -> (Product s a -> b) -> Product s b

(<<=) :: (Product s a -> b) -> Product s a -> Product s b

extend :: (Product s a -> b) -> Product s a -> Product s b

duplicate :: Product s a -> (Product s :. Product s) := a

(=<=) :: (Product s b -> c) -> (Product s a -> b) -> Product s a -> c

(=>=) :: (Product s a -> b) -> (Product s b -> c) -> Product s a -> c

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

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

Extendable (Tap ((Stream <:.:> Stream) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.Stream

Methods

(=>>) :: Tap ((Stream <:.:> Stream) := (:*:)) a -> (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> Tap ((Stream <:.:> Stream) := (:*:)) b

(<<=) :: (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> Tap ((Stream <:.:> Stream) := (:*:)) a -> Tap ((Stream <:.:> Stream) := (:*:)) b

extend :: (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> Tap ((Stream <:.:> Stream) := (:*:)) a -> Tap ((Stream <:.:> Stream) := (:*:)) b

duplicate :: Tap ((Stream <:.:> Stream) := (:*:)) a -> (Tap ((Stream <:.:> Stream) := (:*:)) :. Tap ((Stream <:.:> Stream) := (:*:))) := a

(=<=) :: (Tap ((Stream <:.:> Stream) := (:*:)) b -> c) -> (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> Tap ((Stream <:.:> Stream) := (:*:)) a -> c

(=>=) :: (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> (Tap ((Stream <:.:> Stream) := (:*:)) b -> c) -> Tap ((Stream <:.:> Stream) := (:*:)) a -> c

($=>>) :: Covariant u => ((u :. Tap ((Stream <:.:> Stream) := (:*:))) := a) -> (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> (u :. Tap ((Stream <:.:> Stream) := (:*:))) := b

(<<=$) :: Covariant u => ((u :. Tap ((Stream <:.:> Stream) := (:*:))) := a) -> (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> (u :. Tap ((Stream <:.:> Stream) := (:*:))) := b

Extendable (Tap ((List <:.:> List) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Methods

(=>>) :: Tap ((List <:.:> List) := (:*:)) a -> (Tap ((List <:.:> List) := (:*:)) a -> b) -> Tap ((List <:.:> List) := (:*:)) b

(<<=) :: (Tap ((List <:.:> List) := (:*:)) a -> b) -> Tap ((List <:.:> List) := (:*:)) a -> Tap ((List <:.:> List) := (:*:)) b

extend :: (Tap ((List <:.:> List) := (:*:)) a -> b) -> Tap ((List <:.:> List) := (:*:)) a -> Tap ((List <:.:> List) := (:*:)) b

duplicate :: Tap ((List <:.:> List) := (:*:)) a -> (Tap ((List <:.:> List) := (:*:)) :. Tap ((List <:.:> List) := (:*:))) := a

(=<=) :: (Tap ((List <:.:> List) := (:*:)) b -> c) -> (Tap ((List <:.:> List) := (:*:)) a -> b) -> Tap ((List <:.:> List) := (:*:)) a -> c

(=>=) :: (Tap ((List <:.:> List) := (:*:)) a -> b) -> (Tap ((List <:.:> List) := (:*:)) b -> c) -> Tap ((List <:.:> List) := (:*:)) a -> c

($=>>) :: Covariant u => ((u :. Tap ((List <:.:> List) := (:*:))) := a) -> (Tap ((List <:.:> List) := (:*:)) a -> b) -> (u :. Tap ((List <:.:> List) := (:*:))) := b

(<<=$) :: Covariant u => ((u :. Tap ((List <:.:> List) := (:*:))) := a) -> (Tap ((List <:.:> List) := (:*:)) a -> b) -> (u :. Tap ((List <:.:> List) := (:*:))) := b

Extractable (Product a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

extract :: a0 <:= Product a

Comonad (Product s)

Defined in Pandora.Paradigm.Primary.Functor.Product

Traversable (Product s)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(->>) :: (Pointable u, Applicative u) => Product s a -> (a -> u b) -> (u :. Product s) := b

traverse :: (Pointable u, Applicative u) => (a -> u b) -> Product s a -> (u :. Product s) := b

sequence :: (Pointable u, Applicative u) => ((Product s :. u) := a) -> (u :. Product s) := a

(->>>) :: (Pointable u, Applicative u, Traversable v) => ((v :. Product s) := a) -> (a -> u b) -> (u :. (v :. Product s)) := b

(->>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w) => ((w :. (v :. Product s)) := a) -> (a -> u b) -> (u :. (w :. (v :. Product s))) := b

(->>>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w, Traversable j) => ((j :. (w :. (v :. Product s))) := a) -> (a -> u b) -> (u :. (j :. (w :. (v :. Product s)))) := b

Traversable (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Methods

(->>) :: (Pointable u, Applicative u) => Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)) a -> (a -> u b) -> (u :. Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := b

traverse :: (Pointable u, Applicative u) => (a -> u b) -> Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)) a -> (u :. Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := b

sequence :: (Pointable u, Applicative u) => ((Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)) :. u) := a) -> (u :. Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := a

(->>>) :: (Pointable u, Applicative u, Traversable v) => ((v :. Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) := a) -> (a -> u b) -> (u :. (v :. Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))) := b

(->>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w) => ((w :. (v :. Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))) := a) -> (a -> u b) -> (u :. (w :. (v :. Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))))) := b

(->>>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w, Traversable j) => ((j :. (w :. (v :. Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))))) := a) -> (a -> u b) -> (u :. (j :. (w :. (v :. Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))))) := b

Traversable (Tap ((List <:.:> List) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Methods

(->>) :: (Pointable u, Applicative u) => Tap ((List <:.:> List) := (:*:)) a -> (a -> u b) -> (u :. Tap ((List <:.:> List) := (:*:))) := b

traverse :: (Pointable u, Applicative u) => (a -> u b) -> Tap ((List <:.:> List) := (:*:)) a -> (u :. Tap ((List <:.:> List) := (:*:))) := b

sequence :: (Pointable u, Applicative u) => ((Tap ((List <:.:> List) := (:*:)) :. u) := a) -> (u :. Tap ((List <:.:> List) := (:*:))) := a

(->>>) :: (Pointable u, Applicative u, Traversable v) => ((v :. Tap ((List <:.:> List) := (:*:))) := a) -> (a -> u b) -> (u :. (v :. Tap ((List <:.:> List) := (:*:)))) := b

(->>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w) => ((w :. (v :. Tap ((List <:.:> List) := (:*:)))) := a) -> (a -> u b) -> (u :. (w :. (v :. Tap ((List <:.:> List) := (:*:))))) := b

(->>>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w, Traversable j) => ((j :. (w :. (v :. Tap ((List <:.:> List) := (:*:))))) := a) -> (a -> u b) -> (u :. (j :. (w :. (v :. Tap ((List <:.:> List) := (:*:)))))) := b

Focusable ('Left :: Type -> Wye Type) (Product s)

Defined in Pandora.Paradigm.Structure

Associated Types

type Focusing 'Left (Product s) a

Methods

focusing :: Tagged 'Left (Product s a) :-. Focusing 'Left (Product s) a

Focusable ('Right :: Type -> Wye Type) (Product s)

Defined in Pandora.Paradigm.Structure

Associated Types

type Focusing 'Right (Product s) a

Methods

focusing :: Tagged 'Right (Product s a) :-. Focusing 'Right (Product s) a

Focusable ('Head :: Type -> Location Type) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Focusing 'Head (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) a

Methods

focusing :: Tagged 'Head (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)) a) :-. Focusing 'Head (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) a

Focusable ('Head :: Type -> Location Type) (Tap ((List <:.:> List) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Focusing 'Head (Tap ((List <:.:> List) := (:*:))) a

Methods

focusing :: Tagged 'Head (Tap ((List <:.:> List) := (:*:)) a) :-. Focusing 'Head (Tap ((List <:.:> List) := (:*:))) a

Morphable ('Into (Tap ((List <:.:> List) := (:*:)))) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Tap ((List <:.:> List) := (:*:)))) List :: Type -> Type

Methods

morphing :: (Tagged ('Into (Tap ((List <:.:> List) := (:*:)))) <:.> List) ~> Morphing ('Into (Tap ((List <:.:> List) := (:*:)))) List

Morphable ('Into (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))) (Tap ((List <:.:> List) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))) (Tap ((List <:.:> List) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Into (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))) <:.> Tap ((List <:.:> List) := (:*:))) ~> Morphing ('Into (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))) (Tap ((List <:.:> List) := (:*:)))

Morphable ('Into (Tap ((List <:.:> List) := (:*:)))) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Tap ((List <:.:> List) := (:*:)))) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Into (Tap ((List <:.:> List) := (:*:)))) <:.> Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) ~> Morphing ('Into (Tap ((List <:.:> List) := (:*:)))) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Morphable ('Into (Tap ((List <:.:> List) := (:*:)))) (Construction Maybe)

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Tap ((List <:.:> List) := (:*:)))) (Construction Maybe) :: Type -> Type

Methods

morphing :: (Tagged ('Into (Tap ((List <:.:> List) := (:*:)))) <:.> Construction Maybe) ~> Morphing ('Into (Tap ((List <:.:> List) := (:*:)))) (Construction Maybe)

Morphable ('Into (Construction Maybe)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Construction Maybe)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Into (Construction Maybe)) <:.> Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) ~> Morphing ('Into (Construction Maybe)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Morphable ('Into List) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into List) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Into List) <:.> Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) ~> Morphing ('Into List) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Morphable ('Into List) (Tap ((List <:.:> List) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into List) (Tap ((List <:.:> List) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Into List) <:.> Tap ((List <:.:> List) := (:*:))) ~> Morphing ('Into List) (Tap ((List <:.:> List) := (:*:)))

Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.Stream

Associated Types

type Morphing ('Rotate 'Right) (Tap ((Stream <:.:> Stream) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Right) <:.> Tap ((Stream <:.:> Stream) := (:*:))) ~> Morphing ('Rotate 'Right) (Tap ((Stream <:.:> Stream) := (:*:)))

Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.Stream

Associated Types

type Morphing ('Rotate 'Left) (Tap ((Stream <:.:> Stream) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Left) <:.> Tap ((Stream <:.:> Stream) := (:*:))) ~> Morphing ('Rotate 'Left) (Tap ((Stream <:.:> Stream) := (:*:)))

Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Right) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Right) <:.> Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) ~> Morphing ('Rotate 'Right) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Left) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Left) <:.> Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) ~> Morphing ('Rotate 'Left) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((List <:.:> List) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Right) (Tap ((List <:.:> List) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Right) <:.> Tap ((List <:.:> List) := (:*:))) ~> Morphing ('Rotate 'Right) (Tap ((List <:.:> List) := (:*:)))

Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((List <:.:> List) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Left) (Tap ((List <:.:> List) := (:*:))) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Left) <:.> Tap ((List <:.:> List) := (:*:))) ~> Morphing ('Rotate 'Left) (Tap ((List <:.:> List) := (:*:)))

Morphable ('Into Wye) ((Maybe <:.:> Maybe) := (:*:))

Defined in Pandora.Paradigm.Primary

Associated Types

type Morphing ('Into Wye) ((Maybe <:.:> Maybe) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Into Wye) <:.> ((Maybe <:.:> Maybe) := (:*:))) ~> Morphing ('Into Wye) ((Maybe <:.:> Maybe) := (:*:))

Morphable ('Rotate ('Up :: a -> Vertical a) :: Morph (a -> Vertical a)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Rotate 'Up) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Up) <:.> ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))) ~> Morphing ('Rotate 'Up) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Morphable ('Rotate ('Down ('Right :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Rotate ('Down 'Right)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Down 'Right)) <:.> ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))) ~> Morphing ('Rotate ('Down 'Right)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Morphable ('Rotate ('Down ('Left :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Rotate ('Down 'Left)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Down 'Left)) <:.> ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))) ~> Morphing ('Rotate ('Down 'Left)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

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

Defined in Pandora.Paradigm.Primary.Functor

Methods

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

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

phi :: (Product s a -> b) -> a -> s -> b

psi :: (a -> s -> b) -> Product s a -> b

eta :: a -> ((->) s :. Product s) := a

epsilon :: ((Product s :. (->) s) := a) -> a

(-|$) :: Covariant v => v a -> (Product s a -> b) -> v (s -> b)

($|-) :: Covariant v => v (Product s a) -> (a -> s -> b) -> v b

($$|-) :: (Covariant v, Covariant w) => ((v :. (w :. Product s)) := a) -> (a -> s -> b) -> (v :. w) := b

($$$|-) :: (Covariant v, Covariant w, Covariant x) => ((v :. (w :. (x :. Product s))) := a) -> (a -> s -> b) -> (v :. (w :. x)) := b

($$$$|-) :: (Covariant v, Covariant w, Covariant x, Covariant y) => ((v :. (w :. (x :. (y :. Product s)))) := a) -> (a -> s -> b) -> (v :. (w :. (x :. y))) := b

Covariant (Flip (:*:) a)

Defined in Pandora.Paradigm.Primary

Methods

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

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

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

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

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

loeb :: Flip (:*:) a (a0 <:= Flip (:*:) a) -> Flip (:*:) a a0

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

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

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

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

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

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

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

Extractable (Flip (:*:) a)

Defined in Pandora.Paradigm.Primary

Methods

extract :: a0 <:= Flip (:*:) a

(Semigroup s, Semigroup a) => Semigroup (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(+) :: (s :*: a) -> (s :*: a) -> s :*: a

(Semigroup a, Semigroup r, Semigroup (a :*: r), Semigroup (Vector r a)) => Semigroup (Vector (a :*: r) a)

Defined in Pandora.Paradigm.Primary.Linear.Vector

Methods

(+) :: Vector (a :*: r) a -> Vector (a :*: r) a -> Vector (a :*: r) a

(Ringoid s, Ringoid a) => Ringoid (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

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

(Ringoid a, Ringoid r, Ringoid (a :*: r), Ringoid (Vector r a)) => Ringoid (Vector (a :*: r) a)

Defined in Pandora.Paradigm.Primary.Linear.Vector

Methods

(*) :: Vector (a :*: r) a -> Vector (a :*: r) a -> Vector (a :*: r) a

(Monoid s, Monoid a) => Monoid (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

zero :: s :*: a

(Monoid a, Monoid r, Monoid (a :*: r), Monoid (Vector r a)) => Monoid (Vector (a :*: r) a)

Defined in Pandora.Paradigm.Primary.Linear.Vector

Methods

zero :: Vector (a :*: r) a

(Quasiring s, Quasiring a) => Quasiring (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

one :: s :*: a

(Quasiring a, Quasiring r, Quasiring (a :*: r), Quasiring (Vector r a)) => Quasiring (Vector (a :*: r) a)

Defined in Pandora.Paradigm.Primary.Linear.Vector

Methods

one :: Vector (a :*: r) a

(Group s, Group a) => Group (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

invert :: (s :*: a) -> s :*: a

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

(Group a, Group r, Group (a :*: r), Group (Vector r a)) => Group (Vector (a :*: r) a)

Defined in Pandora.Paradigm.Primary.Linear.Vector

Methods

invert :: Vector (a :*: r) a -> Vector (a :*: r) a

(-) :: Vector (a :*: r) a -> Vector (a :*: r) a -> Vector (a :*: r) a

(Supremum s, Supremum a) => Supremum (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(\/) :: (s :*: a) -> (s :*: a) -> s :*: a

(Infimum s, Infimum a) => Infimum (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(/\) :: (s :*: a) -> (s :*: a) -> s :*: a

(Lattice s, Lattice a) => Lattice (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

(Setoid s, Setoid a) => Setoid (s :*: a)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(==) :: (s :*: a) -> (s :*: a) -> Boolean

(!=) :: (s :*: a) -> (s :*: a) -> Boolean

(Setoid a, Setoid (Vector r a)) => Setoid (Vector (a :*: r) a)

Defined in Pandora.Paradigm.Primary.Linear.Vector

Methods

(==) :: Vector (a :*: r) a -> Vector (a :*: r) a -> Boolean

(!=) :: Vector (a :*: r) a -> Vector (a :*: r) a -> Boolean

Substructure ('Right :: a -> Wye a) (Product s)

Defined in Pandora.Paradigm.Structure

Associated Types

type Substructural 'Right (Product s) :: Type -> Type

Methods

substructure :: (Tagged 'Right <:.> Product s) :~. Substructural 'Right (Product s)

sub :: Product s :~. Substructural 'Right (Product s)

(Semigroup e, Pointable u, Bindable u) => Bindable ((:*:) e <.:> u)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

(>>=) :: ((:*:) e <.:> u) a -> (a -> ((:*:) e <.:> u) b) -> ((:*:) e <.:> u) b

(=<<) :: (a -> ((:*:) e <.:> u) b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b

bind :: (a -> ((:*:) e <.:> u) b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b

join :: ((((:*:) e <.:> u) :. ((:*:) e <.:> u)) := a) -> ((:*:) e <.:> u) a

(>=>) :: (a -> ((:*:) e <.:> u) b) -> (b -> ((:*:) e <.:> u) c) -> a -> ((:*:) e <.:> u) c

(<=<) :: (b -> ((:*:) e <.:> u) c) -> (a -> ((:*:) e <.:> u) b) -> a -> ((:*:) e <.:> u) c

($>>=) :: Covariant u0 => ((u0 :. ((:*:) e <.:> u)) := a) -> (a -> ((:*:) e <.:> u) b) -> (u0 :. ((:*:) e <.:> u)) := b

(Semigroup e, Applicative u) => Applicative ((:*:) e <.:> u)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

(<*>) :: ((:*:) e <.:> u) (a -> b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b

apply :: ((:*:) e <.:> u) (a -> b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b

(*>) :: ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b -> ((:*:) e <.:> u) b

(<*) :: ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b -> ((:*:) e <.:> u) a

forever :: ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b

(<%>) :: ((:*:) e <.:> u) a -> ((:*:) e <.:> u) (a -> b) -> ((:*:) e <.:> u) b

(<**>) :: Applicative u0 => ((((:*:) e <.:> u) :. u0) := (a -> b)) -> ((((:*:) e <.:> u) :. u0) := a) -> (((:*:) e <.:> u) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => ((((:*:) e <.:> u) :. (u0 :. v)) := (a -> b)) -> ((((:*:) e <.:> u) :. (u0 :. v)) := a) -> (((:*:) e <.:> u) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => ((((:*:) e <.:> u) :. (u0 :. (v :. w))) := (a -> b)) -> ((((:*:) e <.:> u) :. (u0 :. (v :. w))) := a) -> (((:*:) e <.:> u) :. (u0 :. (v :. w))) := b

Extendable u => Extendable ((:*:) e <:.> u)

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

(=>>) :: ((:*:) e <:.> u) a -> (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) b

(<<=) :: (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) a -> ((:*:) e <:.> u) b

extend :: (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) a -> ((:*:) e <:.> u) b

duplicate :: ((:*:) e <:.> u) a -> (((:*:) e <:.> u) :. ((:*:) e <:.> u)) := a

(=<=) :: (((:*:) e <:.> u) b -> c) -> (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) a -> c

(=>=) :: (((:*:) e <:.> u) a -> b) -> (((:*:) e <:.> u) b -> c) -> ((:*:) e <:.> u) a -> c

($=>>) :: Covariant u0 => ((u0 :. ((:*:) e <:.> u)) := a) -> (((:*:) e <:.> u) a -> b) -> (u0 :. ((:*:) e <:.> u)) := b

(<<=$) :: Covariant u0 => ((u0 :. ((:*:) e <:.> u)) := a) -> (((:*:) e <:.> u) a -> b) -> (u0 :. ((:*:) e <:.> u)) := b

(Pointable u, Monoid e) => Pointable ((:*:) e <.:> u)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

point :: a :=> ((:*:) e <.:> u)

pass :: ((:*:) e <.:> u) ()

type Focusing ('Left :: Type -> Wye Type) (Product s) a

Defined in Pandora.Paradigm.Structure

type Focusing ('Left :: Type -> Wye Type) (Product s) a = s

type Focusing ('Right :: Type -> Wye Type) (Product s) a

Defined in Pandora.Paradigm.Structure

type Focusing ('Right :: Type -> Wye Type) (Product s) a = a

type Focusing ('Head :: Type -> Location Type) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) a

Defined in Pandora.Paradigm.Structure.Some.List

type Focusing ('Head :: Type -> Location Type) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) a = a

type Focusing ('Head :: Type -> Location Type) (Tap ((List <:.:> List) := (:*:))) a

Defined in Pandora.Paradigm.Structure.Some.List

type Focusing ('Head :: Type -> Location Type) (Tap ((List <:.:> List) := (:*:))) a = a

type Morphing ('Into (Tap ((List <:.:> List) := (:*:)))) List

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Tap ((List <:.:> List) := (:*:)))) List = Maybe <:.> Zipper List

type Morphing ('Into (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))) (Tap ((List <:.:> List) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))) (Tap ((List <:.:> List) := (:*:))) = Maybe <:.> Zipper (Construction Maybe)

type Morphing ('Into (Tap ((List <:.:> List) := (:*:)))) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Tap ((List <:.:> List) := (:*:)))) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) = Zipper List

type Morphing ('Into (Tap ((List <:.:> List) := (:*:)))) (Construction Maybe)

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Tap ((List <:.:> List) := (:*:)))) (Construction Maybe) = Zipper List

type Morphing ('Into (Construction Maybe)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Construction Maybe)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) = Construction Maybe

type Morphing ('Into List) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into List) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) = List

type Morphing ('Into List) (Tap ((List <:.:> List) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into List) (Tap ((List <:.:> List) := (:*:))) = List

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.Stream

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:))) = Tap ((Stream <:.:> Stream) := (:*:))

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.Stream

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:))) = Tap ((Stream <:.:> Stream) := (:*:))

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) = Maybe <:.> Zipper (Construction Maybe)

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) = Maybe <:.> Zipper (Construction Maybe)

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((List <:.:> List) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((List <:.:> List) := (:*:))) = Maybe <:.> Zipper List

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((List <:.:> List) := (:*:)))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((List <:.:> List) := (:*:))) = Maybe <:.> Zipper List

type Morphing ('Into Wye) ((Maybe <:.:> Maybe) := (:*:))

Defined in Pandora.Paradigm.Primary

type Morphing ('Into Wye) ((Maybe <:.:> Maybe) := (:*:)) = Wye

type Morphing ('Rotate ('Up :: a -> Vertical a) :: Morph (a -> Vertical a)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Rotate ('Up :: a -> Vertical a) :: Morph (a -> Vertical a)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) = Maybe <:.> ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

type Morphing ('Rotate ('Down ('Right :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Rotate ('Down ('Right :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) = Maybe <:.> ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

type Morphing ('Rotate ('Down ('Left :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Rotate ('Down ('Left :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) = Maybe <:.> ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:))

type Substructural ('Right :: a -> Wye a) (Product s)

Defined in Pandora.Paradigm.Structure

type Substructural ('Right :: a -> Wye a) (Product s) = Identity

type (:*:) = Product infixr 0

delta :: a -> a :*: a

swap :: (a :*: b) -> b :*: a

attached :: (a :*: b) -> a

twosome :: t a -> u a -> (<:.:>) t u (:*:) a