Pandora.Paradigm.Schemes.T_U

Documentation

newtype T_U ct cu p t u a

Constructors

T_U (p (t a) (u a))

Instances

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

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)) := (:*:))

(Bivariant p, Contravariant t, Contravariant u) => Contravariant ((t >:.:< u) := p)

Defined in Pandora.Paradigm.Schemes.T_U

Methods

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

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

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

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

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

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

(>$$<) :: Contravariant u0 => (a -> b) -> ((((t >:.:< u) := p) :. u0) := a) -> (((t >:.:< u) := p) :. u0) := b

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

(>$$$$<) :: (Contravariant u0, Contravariant v, Contravariant w) => (a -> b) -> ((((t >:.:< u) := p) :. (u0 :. (v :. w))) := a) -> (((t >:.:< u) := p) :. (u0 :. (v :. w))) := b

(>&&<) :: Contravariant u0 => ((((t >:.:< u) := p) :. u0) := a) -> (a -> b) -> (((t >:.:< u) := p) :. u0) := b

(>&&&<) :: (Contravariant u0, Contravariant v) => ((((t >:.:< u) := p) :. (u0 :. v)) := b) -> (a -> b) -> (((t >:.:< u) := p) :. (u0 :. v)) := a

(>&&&&<) :: (Contravariant u0, Contravariant v, Contravariant w) => ((((t >:.:< u) := p) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((t >:.:< u) := p) :. (u0 :. (v :. w))) := b

(Divariant p, Contravariant t, Covariant u) => Covariant ((t >:.:> u) := p)

Defined in Pandora.Paradigm.Schemes.T_U

Methods

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

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

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

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

void :: ((t >:.:> u) := p) a -> ((t >:.:> u) := p) ()

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

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

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

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

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

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

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

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

(Bivariant p, Covariant t, Covariant u) => Covariant ((t <:.:> u) := p)

Defined in Pandora.Paradigm.Schemes.T_U

Methods

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

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

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

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

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

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

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

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

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

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

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

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

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

Interpreted (T_U ct cu p t u)

Defined in Pandora.Paradigm.Schemes.T_U

Associated Types

type Primary (T_U ct cu p t u) a

Methods

run :: T_U ct cu p t u a -> Primary (T_U ct cu p t u) a

unite :: Primary (T_U ct cu p t u) a -> T_U ct cu p t u a

(||=) :: (Primary (T_U ct cu p t u) a -> Primary (T_U ct cu p t u) b) -> T_U ct cu p t u a -> T_U ct cu p t u b

(=||) :: (T_U ct cu p t u a -> T_U ct cu p t u b) -> Primary (T_U ct cu p t u) a -> Primary (T_U ct cu p t u) b

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 Primary (T_U ct cu p t u) a

Defined in Pandora.Paradigm.Schemes.T_U

type Primary (T_U ct cu p t u) a = p (t a) (u a)

type (<:.:>) t u p = T_U Covariant Covariant p t u infixr 2

type (>:.:>) t u p = T_U Contravariant Covariant p t u infixr 2

type (<:.:<) t u p = T_U Covariant Contravariant p t u infixr 2

type (>:.:<) t u p = T_U Contravariant Contravariant p t u infixr 2