Pandora.Paradigm.Schemes.TU

Documentation

newtype TU ct cu t u a

Constructors

TU ((t :. u) := a)

Instances

Stack List

Defined in Pandora.Paradigm.Structure.Some.List

Measurable 'Length List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Measural 'Length List a

Methods

measurement :: Tagged 'Length (List a) -> Measural 'Length List a

Measurable 'Heighth Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Measural 'Heighth Binary a

Methods

measurement :: Tagged 'Heighth (Binary a) -> Measural 'Heighth Binary a

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Monoidal (<--) ((->) :: Type -> Type -> Type) (:*:) (:*:) t, Monoidal (<--) ((->) :: Type -> Type -> Type) (:*:) (:*:) u) => Monoidal (<--) ((->) :: Type -> Type -> Type) (:*:) (:*:) (t <:.> u)

Defined in Pandora.Paradigm.Schemes.TU

Methods

unit :: Proxy (:*:) -> (Unit (:*:) -> a) <-- (t <:.> u) a

Monotonic a ((t :. Construction t) := a) => Monotonic a ((t <:.> Construction t) := a)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

reduce :: (a -> r -> r) -> r -> ((t <:.> Construction t) := a) -> r

resolve :: (a -> r) -> r -> ((t <:.> Construction t) := a) -> r

Semigroup (List a)

Defined in Pandora.Paradigm.Structure.Some.List

Methods

(+) :: List a -> List a -> List a

Monoid (List a)

Defined in Pandora.Paradigm.Structure.Some.List

Methods

zero :: List a

Setoid a => Setoid (List a)

Defined in Pandora.Paradigm.Structure.Some.List

Methods

(==) :: List a -> List a -> Boolean

(!=) :: List a -> List a -> Boolean

Nullable List

Defined in Pandora.Paradigm.Structure.Some.List

Methods

null :: forall (a :: k). (Predicate :. List) := a

Nullable Rose

Defined in Pandora.Paradigm.Structure.Some.Rose

Methods

null :: forall (a :: k). (Predicate :. Rose) := a

Nullable Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

Methods

null :: forall (a :: k). (Predicate :. Binary) := a

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) u) => Semimonoidal (<--) (:*:) (:*:) (t <:.> u :: Type -> Type)

Defined in Pandora.Paradigm.Schemes.TU

Methods

multiply :: forall (a :: k) (b :: k). ((t <:.> u) a :*: (t <:.> u) b) <-- (t <:.> u) (a :*: b)

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 ('Delete ('All :: a -> Occurrence a) :: Morph (a -> Occurrence a)) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Delete 'All) List :: Type -> Type

Methods

morphing :: (Tagged ('Delete 'All) <:.> List) ~> Morphing ('Delete 'All) List

Morphable ('Delete ('First :: a -> Occurrence a) :: Morph (a -> Occurrence a)) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Delete 'First) List :: Type -> Type

Methods

morphing :: (Tagged ('Delete 'First) <:.> List) ~> Morphing ('Delete 'First) List

Morphable ('Find ('Element :: a -> Morph a) :: Morph (a -> Morph a)) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Find 'Element) List :: Type -> Type

Methods

morphing :: (Tagged ('Find 'Element) <:.> List) ~> Morphing ('Find 'Element) List

Morphable ('Into (o ds)) (Construction Wye) => Morphable ('Into (o ds) :: Morph a) Binary

Defined in Pandora.Paradigm.Structure

Associated Types

type Morphing ('Into (o ds)) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Into (o ds)) <:.> Binary) ~> Morphing ('Into (o ds)) Binary

Morphable ('Rotate ('Right ('Zig :: a -> Splay a)) :: Morph (Wye (a -> Splay a))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

Associated Types

type Morphing ('Rotate ('Right 'Zig)) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Right 'Zig)) <:.> Binary) ~> Morphing ('Rotate ('Right 'Zig)) Binary

Morphable ('Rotate ('Left ('Zig :: a -> Splay a)) :: Morph (Wye (a -> Splay a))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

Associated Types

type Morphing ('Rotate ('Left 'Zig)) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Left 'Zig)) <:.> Binary) ~> Morphing ('Rotate ('Left 'Zig)) Binary

Morphable ('Rotate ('Right ('Zig ('Zag :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

Associated Types

type Morphing ('Rotate ('Right ('Zig 'Zag))) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Right ('Zig 'Zag))) <:.> Binary) ~> Morphing ('Rotate ('Right ('Zig 'Zag))) Binary

Morphable ('Rotate ('Left ('Zig ('Zag :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

Associated Types

type Morphing ('Rotate ('Left ('Zig 'Zag))) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Left ('Zig 'Zag))) <:.> Binary) ~> Morphing ('Rotate ('Left ('Zig 'Zag))) Binary

Morphable ('Rotate ('Right ('Zig ('Zig :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

Associated Types

type Morphing ('Rotate ('Right ('Zig 'Zig))) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Right ('Zig 'Zig))) <:.> Binary) ~> Morphing ('Rotate ('Right ('Zig 'Zig))) Binary

Morphable ('Rotate ('Left ('Zig ('Zig :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

Associated Types

type Morphing ('Rotate ('Left ('Zig 'Zig))) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Left ('Zig 'Zig))) <:.> Binary) ~> Morphing ('Rotate ('Left ('Zig 'Zig))) Binary

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, Semimonoidal ((->) :: Type -> Type -> Type) (:*:) (:+:) t) => Semimonoidal ((->) :: Type -> Type -> Type) (:*:) (:+:) (t <:.> u :: Type -> Type)

Defined in Pandora.Paradigm.Schemes.TU

Methods

multiply :: forall (a :: k) (b :: k). ((t <:.> u) a :*: (t <:.> u) b) -> (t <:.> u) (a :+: b)

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Semimonoidal ((->) :: Type -> Type -> Type) (:*:) (:*:) t, Semimonoidal ((->) :: Type -> Type -> Type) (:*:) (:*:) u) => Semimonoidal ((->) :: Type -> Type -> Type) (:*:) (:*:) (t <:.> u :: Type -> Type)

Defined in Pandora.Paradigm.Schemes.TU

Methods

multiply :: forall (a :: k) (b :: k). ((t <:.> u) a :*: (t <:.> u) b) -> (t <:.> u) (a :*: b)

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

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

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

Methods

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

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into List) (Construction Maybe) :: Type -> Type

Methods

morphing :: (Tagged ('Into List) <:.> Construction Maybe) ~> Morphing ('Into List) (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 ('Into List) (Vector r)

Defined in Pandora.Paradigm.Primary.Linear.Vector

Associated Types

type Morphing ('Into List) (Vector r) :: Type -> Type

Methods

morphing :: (Tagged ('Into List) <:.> Vector r) ~> Morphing ('Into List) (Vector r)

Morphable ('Into Binary) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Into Binary) (Construction Wye) :: Type -> Type

Methods

morphing :: (Tagged ('Into Binary) <:.> Construction Wye) ~> Morphing ('Into Binary) (Construction Wye)

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) := (:*:)))

Setoid key => Morphable ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed List key)

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Lookup 'Key) (Prefixed List key) :: Type -> Type

Methods

morphing :: (Tagged ('Lookup 'Key) <:.> Prefixed List key) ~> Morphing ('Lookup 'Key) (Prefixed List key)

Setoid k => Morphable ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Rose k)

Defined in Pandora.Paradigm.Structure.Some.Rose

Associated Types

type Morphing ('Lookup 'Key) (Prefixed Rose k) :: Type -> Type

Methods

morphing :: (Tagged ('Lookup 'Key) <:.> Prefixed Rose k) ~> Morphing ('Lookup 'Key) (Prefixed Rose k)

Chain k => Morphable ('Vary ('Element :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Binary k)

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Vary 'Element) (Prefixed Binary k) :: Type -> Type

Methods

morphing :: (Tagged ('Vary 'Element) <:.> Prefixed Binary k) ~> Morphing ('Vary 'Element) (Prefixed Binary k)

Chain k => Morphable ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Binary k)

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Lookup 'Key) (Prefixed Binary k) :: Type -> Type

Methods

morphing :: (Tagged ('Lookup 'Key) <:.> Prefixed Binary k) ~> Morphing ('Lookup 'Key) (Prefixed Binary k)

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)) := (:*:))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Hoistable (TU Covariant Covariant t :: (Type -> Type) -> Type -> Type)

Defined in Pandora.Paradigm.Schemes.TU

Methods

(/|\) :: forall (u :: Type -> Type) (v :: Type -> Type). Covariant (->) (->) u => (u ~> v) -> TU Covariant Covariant t u ~> TU Covariant Covariant t v

hoist :: forall (u :: Type -> Type) (v :: Type -> Type). Covariant (->) (->) u => (u ~> v) -> TU Covariant Covariant t u ~> TU Covariant Covariant t v

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

Defined in Pandora.Paradigm.Structure.Some.List

Methods

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

Morphable ('Pop :: a -> Morph a) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing 'Pop List :: Type -> Type

Methods

morphing :: (Tagged 'Pop <:.> List) ~> Morphing 'Pop List

Morphable ('Push :: a -> Morph a) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing 'Push List :: Type -> Type

Methods

morphing :: (Tagged 'Push <:.> List) ~> Morphing 'Push List

Morphable ('Insert :: a -> Morph a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing 'Insert Binary :: Type -> Type

Methods

morphing :: (Tagged 'Insert <:.> Binary) ~> Morphing 'Insert Binary

Substructure ('Tail :: a -> Segment a) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Available 'Tail List :: Type -> Type

type Substance 'Tail List :: Type -> Type

Methods

substructure :: ((Tagged 'Tail <:.> List) #=@ Substance 'Tail List) := Available 'Tail List

sub :: (List #=@ Substance 'Tail List) := Available 'Tail List

Substructure ('Root :: a -> Segment a) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Available 'Root List :: Type -> Type

type Substance 'Root List :: Type -> Type

Methods

substructure :: ((Tagged 'Root <:.> List) #=@ Substance 'Root List) := Available 'Root List

sub :: (List #=@ Substance 'Root List) := Available 'Root List

Substructure ('Right :: a -> Wye a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Available 'Right Binary :: Type -> Type

type Substance 'Right Binary :: Type -> Type

Methods

substructure :: ((Tagged 'Right <:.> Binary) #=@ Substance 'Right Binary) := Available 'Right Binary

sub :: (Binary #=@ Substance 'Right Binary) := Available 'Right Binary

Substructure ('Left :: a -> Wye a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Available 'Left Binary :: Type -> Type

type Substance 'Left Binary :: Type -> Type

Methods

substructure :: ((Tagged 'Left <:.> Binary) #=@ Substance 'Left Binary) := Available 'Left Binary

sub :: (Binary #=@ Substance 'Left Binary) := Available 'Left Binary

Substructure ('Tail :: a -> Segment a) (Construction List)

Defined in Pandora.Paradigm.Structure.Some.Rose

Associated Types

type Available 'Tail (Construction List) :: Type -> Type

type Substance 'Tail (Construction List) :: Type -> Type

Methods

substructure :: ((Tagged 'Tail <:.> Construction List) #=@ Substance 'Tail (Construction List)) := Available 'Tail (Construction List)

sub :: (Construction List #=@ Substance 'Tail (Construction List)) := Available 'Tail (Construction List)

Substructure ('Root :: a -> Segment a) (Construction List)

Defined in Pandora.Paradigm.Structure.Some.Rose

Associated Types

type Available 'Root (Construction List) :: Type -> Type

type Substance 'Root (Construction List) :: Type -> Type

Methods

substructure :: ((Tagged 'Root <:.> Construction List) #=@ Substance 'Root (Construction List)) := Available 'Root (Construction List)

sub :: (Construction List #=@ Substance 'Root (Construction List)) := Available 'Root (Construction List)

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, Monoidal ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (:*:) (:+:) t) => Monoidal ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (:*:) (:+:) (t <:.> u)

Defined in Pandora.Paradigm.Schemes.TU

Methods

unit :: Proxy (:*:) -> (Unit (:+:) -> a) -> (t <:.> u) a

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, Semimonoidal ((->) :: Type -> Type -> Type) (:*:) (:*:) u, Monoidal ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (:*:) (:*:) t, Monoidal ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (:*:) (:*:) u) => Monoidal ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (:*:) (:*:) (t <:.> u)

Defined in Pandora.Paradigm.Schemes.TU

Methods

unit :: Proxy (:*:) -> (Unit (:*:) -> a) -> (t <:.> u) a

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

Defined in Pandora.Paradigm.Structure.Some.List

Methods

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

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u) => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t <:.> u)

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

(Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u) => Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t <:.> u)

Defined in Pandora.Paradigm.Schemes.TU

Methods

(<<-) :: (Covariant (->) (->) u0, Monoidal (->) (->) (:*:) (:*:) u0) => (a -> u0 b) -> (t <:.> u) a -> u0 ((t <:.> u) b)

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t <.:> v), Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (w <:.> u), Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) v u, Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t w) => Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t <.:> v) (w <:.> u)

Defined in Pandora.Paradigm.Schemes

Methods

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

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

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (v <:.> t), Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (w <.:> u), Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t u, Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) v w) => Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (v <:.> t) (w <.:> u)

Defined in Pandora.Paradigm.Schemes

Methods

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

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

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (v <:.> t), Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (u <:.> w), Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t u, Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) v w) => Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (v <:.> t) (u <:.> w)

Defined in Pandora.Paradigm.Schemes

Methods

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

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

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

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

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

(Bindable ((->) :: Type -> Type -> Type) t, Distributive ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, Bindable ((->) :: Type -> Type -> Type) u) => Bindable ((->) :: Type -> Type -> Type) (t <:.> u)

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

Monoidal ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (:*:) (:*:) t => Liftable ((->) :: Type -> Type -> Type) (TU Covariant Covariant t :: (Type -> Type) -> Type -> Type)

Defined in Pandora.Paradigm.Schemes.TU

Methods

lift :: Covariant (->) (->) u => u a -> TU Covariant Covariant t u a

Monoidal (<--) ((->) :: Type -> Type -> Type) (:*:) (:*:) t => Lowerable ((->) :: Type -> Type -> Type) (TU Covariant Covariant t :: (Type -> Type) -> Type -> Type)

Defined in Pandora.Paradigm.Schemes.TU

Methods

lower :: Covariant (->) (->) u => TU Covariant Covariant t u a -> u a

Interpreted (TU ct cu t u)

Defined in Pandora.Paradigm.Schemes.TU

Associated Types

type Primary (TU ct cu t u) a

Methods

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

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

(||=) :: Interpreted u0 => (Primary (TU ct cu t u) a -> Primary u0 b) -> TU ct cu t u a -> u0 b

(=||) :: Interpreted u0 => (TU ct cu t u a -> u0 b) -> Primary (TU ct cu t u) a -> Primary u0 b

(<$||=) :: (Covariant (->) (->) j, Interpreted u0) => (Primary (TU ct cu t u) a -> Primary u0 b) -> (j := TU ct cu t u a) -> j := u0 b

(<$$||=) :: (Covariant (->) (->) j, Covariant (->) (->) k, Interpreted u0) => (Primary (TU ct cu t u) a -> Primary u0 b) -> ((j :. k) := TU ct cu t u a) -> (j :. k) := u0 b

(<$$$||=) :: (Covariant (->) (->) j, Covariant (->) (->) k, Covariant (->) (->) l, Interpreted u0) => (Primary (TU ct cu t u) a -> Primary u0 b) -> ((j :. (k :. l)) := TU ct cu t u a) -> (j :. (k :. l)) := u0 b

(<$$$$||=) :: (Covariant (->) (->) j, Covariant (->) (->) k, Covariant (->) (->) l, Covariant (->) (->) m, Interpreted u0) => (Primary (TU ct cu t u) a -> Primary u0 b) -> ((j :. (k :. (l :. m))) := TU ct cu t u a) -> (j :. (k :. (l :. m))) := u0 b

(=||$>) :: (Covariant (->) (->) j, Interpreted u0) => (TU ct cu t u a -> u0 b) -> (j := Primary (TU ct cu t u) a) -> j := Primary u0 b

(=||$$>) :: (Covariant (->) (->) j, Covariant (->) (->) k, Interpreted u0) => (TU ct cu t u a -> u0 b) -> ((j :. k) := Primary (TU ct cu t u) a) -> (j :. k) := Primary u0 b

(=||$$$>) :: (Covariant (->) (->) j, Covariant (->) (->) k, Covariant (->) (->) l, Interpreted u0) => (TU ct cu t u a -> u0 b) -> ((j :. (k :. l)) := Primary (TU ct cu t u) a) -> (j :. (k :. l)) := Primary u0 b

(=||$$$$>) :: (Covariant (->) (->) j, Covariant (->) (->) k, Covariant (->) (->) l, Covariant (->) (->) m, Interpreted u0) => (TU ct cu t u a -> u0 b) -> ((j :. (k :. (l :. m))) := Primary (TU ct cu t u) a) -> (j :. (k :. (l :. m))) := Primary u0 b

type Nonempty List

Defined in Pandora.Paradigm.Structure.Some.List

type Nonempty List = Construction Maybe

type Nonempty Rose

Defined in Pandora.Paradigm.Structure.Some.Rose

type Nonempty Rose = Construction List

type Nonempty Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

type Nonempty Binary = Construction Wye

type Combinative List

Defined in Pandora.Paradigm.Structure.Some.List

type Combinative List = Comprehension Maybe

type Measural 'Length List a

Defined in Pandora.Paradigm.Structure.Some.List

type Measural 'Length List a = Numerator

type Measural 'Heighth Binary a

Defined in Pandora.Paradigm.Structure.Some.Binary

type Measural 'Heighth Binary a = Numerator

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

Defined in Pandora.Paradigm.Structure.Some.List

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

type Morphing ('Delete ('All :: a -> Occurrence a) :: Morph (a -> Occurrence a)) List

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Delete ('All :: a -> Occurrence a) :: Morph (a -> Occurrence a)) List = (Predicate <:.:> List) := ((->) :: Type -> Type -> Type)

type Morphing ('Delete ('First :: a -> Occurrence a) :: Morph (a -> Occurrence a)) List

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Delete ('First :: a -> Occurrence a) :: Morph (a -> Occurrence a)) List = (Predicate <:.:> List) := ((->) :: Type -> Type -> Type)

type Morphing ('Find ('Element :: a -> Morph a) :: Morph (a -> Morph a)) List

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Find ('Element :: a -> Morph a) :: Morph (a -> Morph a)) List = (Predicate <:.:> Maybe) := ((->) :: Type -> Type -> Type)

type Morphing ('Into (o ds) :: Morph a) Binary

Defined in Pandora.Paradigm.Structure

type Morphing ('Into (o ds) :: Morph a) Binary = Maybe <:.> Morphing ('Into (o ds)) (Construction Wye)

type Morphing ('Rotate ('Right ('Zig :: a -> Splay a)) :: Morph (Wye (a -> Splay a))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

type Morphing ('Rotate ('Right ('Zig :: a -> Splay a)) :: Morph (Wye (a -> Splay a))) Binary = Binary

type Morphing ('Rotate ('Left ('Zig :: a -> Splay a)) :: Morph (Wye (a -> Splay a))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

type Morphing ('Rotate ('Left ('Zig :: a -> Splay a)) :: Morph (Wye (a -> Splay a))) Binary = Binary

type Morphing ('Rotate ('Right ('Zig ('Zag :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

type Morphing ('Rotate ('Right ('Zig ('Zag :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary = Binary

type Morphing ('Rotate ('Left ('Zig ('Zag :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

type Morphing ('Rotate ('Left ('Zig ('Zag :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary = Binary

type Morphing ('Rotate ('Right ('Zig ('Zig :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

type Morphing ('Rotate ('Right ('Zig ('Zig :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary = Binary

type Morphing ('Rotate ('Left ('Zig ('Zig :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

type Morphing ('Rotate ('Left ('Zig ('Zig :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary = Binary

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

Defined in Pandora.Paradigm.Structure.Some.List

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

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

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

Defined in Pandora.Paradigm.Structure.Some.List

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

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

type Morphing ('Into List) (Construction Maybe)

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into List) (Construction Maybe) = List

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 ('Into List) (Vector r)

Defined in Pandora.Paradigm.Primary.Linear.Vector

type Morphing ('Into List) (Vector r) = List

type Morphing ('Into Binary) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Into Binary) (Construction Wye) = Binary

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

type Morphing ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed List key)

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed List key) = ((->) key :: Type -> Type) <:.> Maybe

type Morphing ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Rose k)

Defined in Pandora.Paradigm.Structure.Some.Rose

type Morphing ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Rose k) = ((->) (Nonempty List k) :: Type -> Type) <:.> Maybe

type Morphing ('Vary ('Element :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Binary k)

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Vary ('Element :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Binary k) = (((:*:) k <:.> Identity) <:.:> Prefixed Binary k) := ((->) :: Type -> Type -> Type)

type Morphing ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Binary k)

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Binary k) = ((->) k :: Type -> Type) <:.> Maybe

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 Zipper List (('Left :: a1 -> Wye a1) ::: ('Right :: a2 -> Wye a2) :: k -> k' -> Type)

Defined in Pandora.Paradigm.Structure.Some.List

type Zipper List (('Left :: a1 -> Wye a1) ::: ('Right :: a2 -> Wye a2) :: k -> k' -> Type) = Tap ((List <:.:> List) := (:*:))

type Morphing ('Pop :: a -> Morph a) List

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Pop :: a -> Morph a) List = List

type Morphing ('Push :: a -> Morph a) List

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Push :: a -> Morph a) List = (Identity <:.:> List) := ((->) :: Type -> Type -> Type)

type Morphing ('Insert :: a -> Morph a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Insert :: a -> Morph a) Binary = (((Identity <:.:> Comparison) := (:*:)) <:.:> Binary) := ((->) :: Type -> Type -> Type)

type Available ('Tail :: a -> Segment a) List

Defined in Pandora.Paradigm.Structure.Some.List

type Available ('Tail :: a -> Segment a) List = Identity

type Available ('Root :: a -> Segment a) List

Defined in Pandora.Paradigm.Structure.Some.List

type Available ('Root :: a -> Segment a) List = Maybe

type Available ('Right :: a -> Wye a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

type Available ('Right :: a -> Wye a) Binary = Maybe

type Available ('Left :: a -> Wye a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

type Available ('Left :: a -> Wye a) Binary = Maybe

type Substance ('Tail :: a -> Segment a) List

Defined in Pandora.Paradigm.Structure.Some.List

type Substance ('Tail :: a -> Segment a) List = List

type Substance ('Root :: a -> Segment a) List

Defined in Pandora.Paradigm.Structure.Some.List

type Substance ('Root :: a -> Segment a) List = Identity

type Substance ('Right :: a -> Wye a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

type Substance ('Right :: a -> Wye a) Binary = Construction Wye

type Substance ('Left :: a -> Wye a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

type Substance ('Left :: a -> Wye a) Binary = Construction Wye

type Available ('Tail :: a -> Segment a) (Construction List)

Defined in Pandora.Paradigm.Structure.Some.Rose

type Available ('Tail :: a -> Segment a) (Construction List) = Identity

type Available ('Root :: a -> Segment a) (Construction List)

Defined in Pandora.Paradigm.Structure.Some.Rose

type Available ('Root :: a -> Segment a) (Construction List) = Identity

type Substance ('Tail :: a -> Segment a) (Construction List)

Defined in Pandora.Paradigm.Structure.Some.Rose

type Substance ('Tail :: a -> Segment a) (Construction List) = List <:.> Construction List

type Substance ('Root :: a -> Segment a) (Construction List)

Defined in Pandora.Paradigm.Structure.Some.Rose

type Substance ('Root :: a -> Segment a) (Construction List) = Identity

type Primary (TU ct cu t u) a

Defined in Pandora.Paradigm.Schemes.TU

type Primary (TU ct cu t u) a = (t :. u) := a

type (<:.>) = TU Covariant Covariant infixr 3

type (>:.>) = TU Contravariant Covariant infixr 3

type (<:.<) = TU Covariant Contravariant infixr 3

type (>:.<) = TU Contravariant Contravariant infixr 3