Pandora.Paradigm.Primary

Documentation

module Pandora.Paradigm.Primary.Object

module Pandora.Paradigm.Primary.Functor

module Pandora.Paradigm.Primary.Transformer

module Pandora.Paradigm.Primary.Linear

Orphan instances

Category (Flip ((->) :: Type -> Type -> Type))

Methods

identity :: Flip (->) a a

(.) :: Flip (->) b c -> Flip (->) a b -> Flip (->) a c

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

(#) :: Flip (->) (Flip (->) a b) (Flip (->) 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) := (:*:))

Contravariant (Flip ((->) :: Type -> Type -> Type) r)

Methods

(>$<) :: (a -> b) -> Flip (->) r b -> Flip (->) r a

contramap :: (a -> b) -> Flip (->) r b -> Flip (->) r a

(>$) :: b -> Flip (->) r b -> Flip (->) r a

($<) :: Flip (->) r b -> b -> Flip (->) r a

full :: Flip (->) r () -> Flip (->) r a

(>&<) :: Flip (->) r b -> (a -> b) -> Flip (->) r a

(>$$<) :: Contravariant u => (a -> b) -> ((Flip (->) r :. u) := a) -> (Flip (->) r :. u) := b

(>$$$<) :: (Contravariant u, Contravariant v) => (a -> b) -> ((Flip (->) r :. (u :. v)) := b) -> (Flip (->) r :. (u :. v)) := a

(>$$$$<) :: (Contravariant u, Contravariant v, Contravariant w) => (a -> b) -> ((Flip (->) r :. (u :. (v :. w))) := a) -> (Flip (->) r :. (u :. (v :. w))) := b

(>&&<) :: Contravariant u => ((Flip (->) r :. u) := a) -> (a -> b) -> (Flip (->) r :. u) := b

(>&&&<) :: (Contravariant u, Contravariant v) => ((Flip (->) r :. (u :. v)) := b) -> (a -> b) -> (Flip (->) r :. (u :. v)) := a

(>&&&&<) :: (Contravariant u, Contravariant v, Contravariant w) => ((Flip (->) r :. (u :. (v :. w))) := a) -> (a -> b) -> (Flip (->) r :. (u :. (v :. w))) := b

Covariant (Flip (:*:) a)

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

(.#..) :: (Flip (:*:) a ~ v a0, Category v) => v c d -> ((v a0 :. v b) := c) -> (v a0 :. v b) := d

(.#...) :: (Flip (:*:) a ~ v a0, Flip (:*:) a ~ v b, Category v, Covariant (v a0), Covariant (v b)) => v d e -> ((v a0 :. (v b :. v c)) := d) -> (v a0 :. (v b :. v c)) := e

(.#....) :: (Flip (:*:) a ~ v a0, Flip (:*:) a ~ v b, Flip (:*:) a ~ v c, Category v, Covariant (v a0), Covariant (v b), Covariant (v c)) => v e f -> ((v a0 :. (v b :. (v c :. v d))) := e) -> (v a0 :. (v b :. (v c :. v d))) := f

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

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

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

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

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

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

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

Associated Types

type Available 'Right Wye :: Type -> Type

type Substance 'Right Wye :: Type -> Type

Methods

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

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

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

Associated Types

type Available 'Left Wye :: Type -> Type

type Substance 'Left Wye :: Type -> Type

Methods

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

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

Extractable (Flip (:*:) a) ((->) :: Type -> Type -> Type)

Methods

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

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

Methods

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

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

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

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

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

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

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

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

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

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

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