Pandora.Paradigm.Primary

Documentation

module Pandora.Paradigm.Primary.Algebraic

module Pandora.Paradigm.Primary.Object

module Pandora.Paradigm.Primary.Functor

module Pandora.Paradigm.Primary.Transformer

module Pandora.Paradigm.Primary.Linear

type family Simplification (t :: * -> *) (a :: *) where ...

Equations

Simplification Exactly a = a

Simplification (TU _ _ t u) a = (t :. u) > a

Simplification (UT _ _ t u) a = (u :. t) > a

Simplification (TUT _ _ _ t t' u) a = (t :. (u :. t')) > a

Simplification (T_U _ _ p t u) a = p (t a) (u a)

Simplification t a = t a

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

Orphan instances

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

Methods

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

Morphable ('Into (Flip Conclusion e) :: Morph (Type -> Type)) Maybe

Associated Types

type Morphing ('Into (Flip Conclusion e)) Maybe :: Type -> Type

Methods

morphing :: (Tagged ('Into (Flip Conclusion e)) <::> Maybe) ~> Morphing ('Into (Flip Conclusion e)) Maybe

Morphable ('Into (Conclusion e) :: Morph (Type -> Type)) Maybe

Associated Types

type Morphing ('Into (Conclusion e)) Maybe :: Type -> Type

Methods

morphing :: (Tagged ('Into (Conclusion e)) <::> Maybe) ~> Morphing ('Into (Conclusion e)) Maybe

Morphable ('Into ('Left Maybe)) Wye

Associated Types

type Morphing ('Into ('Left Maybe)) Wye :: Type -> Type

Methods

morphing :: (Tagged ('Into ('Left Maybe)) <::> Wye) ~> Morphing ('Into ('Left Maybe)) Wye

Morphable ('Into ('Right Maybe)) Wye

Associated Types

type Morphing ('Into ('Right Maybe)) Wye :: Type -> Type

Methods

morphing :: (Tagged ('Into ('Right Maybe)) <::> Wye) ~> Morphing ('Into ('Right Maybe)) Wye

Morphable ('Into Maybe) (Conclusion e)

Associated Types

type Morphing ('Into Maybe) (Conclusion e) :: Type -> Type

Methods

morphing :: (Tagged ('Into Maybe) <::> Conclusion e) ~> Morphing ('Into Maybe) (Conclusion e)

Morphable ('Into ('There Maybe :: Wedge e1 (Type -> Type)) :: Morph (Wedge e1 (Type -> Type))) (Wedge e2)

Associated Types

type Morphing ('Into ('There Maybe)) (Wedge e2) :: Type -> Type

Methods

morphing :: (Tagged ('Into ('There Maybe)) <::> Wedge e2) ~> Morphing ('Into ('There Maybe)) (Wedge e2)

Morphable ('Into ('This Maybe :: These e1 (Type -> Type)) :: Morph (These e1 (Type -> Type))) (These e2)

Associated Types

type Morphing ('Into ('This Maybe)) (These e2) :: Type -> Type

Methods

morphing :: (Tagged ('Into ('This Maybe)) <::> These e2) ~> Morphing ('Into ('This Maybe)) (These e2)

Morphable ('Into ('Here Maybe :: Wedge (Type -> Type) a1) :: Morph (Wedge (Type -> Type) a1)) (Flip Wedge a2)

Associated Types

type Morphing ('Into ('Here Maybe)) (Flip Wedge a2) :: Type -> Type

Methods

morphing :: (Tagged ('Into ('Here Maybe)) <::> Flip Wedge a2) ~> Morphing ('Into ('Here Maybe)) (Flip Wedge a2)

Morphable ('Into ('That Maybe :: These (Type -> Type) a1) :: Morph (These (Type -> Type) a1)) (Flip These a2)

Associated Types

type Morphing ('Into ('That Maybe)) (Flip These a2) :: Type -> Type

Methods

morphing :: (Tagged ('Into ('That Maybe)) <::> Flip These a2) ~> Morphing ('Into ('That Maybe)) (Flip These a2)

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

Associated Types

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

Methods

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

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

Associated Types

type Substance 'Right Wye :: Type -> Type

Methods

substructure :: (Tagged 'Right <:.> Wye) @>>> Substance 'Right Wye

sub :: Wye @>>> Substance 'Right Wye

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

Associated Types

type Substance 'Left Wye :: Type -> Type

Methods

substructure :: (Tagged 'Left <:.> Wye) @>>> Substance 'Left Wye

sub :: Wye @>>> Substance 'Left Wye

Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Flip (:*:) s) ((->) s :: Type -> Type)

Methods

(-|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(|-) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|--) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|---) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|----) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|-----) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|------) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|-------) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|--------) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(|---------) :: (a -> (s -> b)) -> Flip (:*:) s a -> b

(--|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(---|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(----|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(-----|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(------|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(-------|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(--------|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)

(---------|) :: (Flip (:*:) s a -> b) -> a -> (s -> b)