Pandora.Paradigm.Primary.Functor.Wye

Documentation

data Wye a

Constructors

End

Left a

Right a

Both a a

Instances

Covariant Wye

Defined in Pandora.Paradigm.Primary.Functor.Wye

Methods

(<$>) :: (a -> b) -> Wye a -> Wye b

comap :: (a -> b) -> Wye a -> Wye b

(<$) :: a -> Wye b -> Wye a

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

void :: Wye a -> Wye ()

loeb :: Wye (a <-| Wye) -> Wye a

(<&>) :: Wye a -> (a -> b) -> Wye b

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

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

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

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

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

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

Traversable Wye

Defined in Pandora.Paradigm.Primary.Functor.Wye

Methods

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

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

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

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

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

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

Substructure (Left :: Type -> Wye Type) Binary

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Substructural Left Binary a :: Type

Methods

substructure :: Tagged Left (Binary a) :-. Substructural Left Binary a

Substructure (Right :: Type -> Wye Type) Binary

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Substructural Right Binary a :: Type

Methods

substructure :: Tagged Right (Binary a) :-. Substructural Right Binary a

(forall a. Chain a) => Focusable (Root :: Type -> Type) Binary

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Focusing Root Binary a :: Type

Methods

focusing :: Tagged Root (Binary a) :-. Focusing Root Binary a

Substructure (Left :: Type -> Wye Type) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Substructural Left (Construction Wye) a :: Type

Methods

substructure :: Tagged Left (Construction Wye a) :-. Substructural Left (Construction Wye) a

Substructure (Right :: Type -> Wye Type) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Substructural Right (Construction Wye) a :: Type

Methods

substructure :: Tagged Right (Construction Wye a) :-. Substructural Right (Construction Wye) a

Focusable (Root :: Type -> Type) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Focusing Root (Construction Wye) a :: Type

Methods

focusing :: Tagged Root (Construction Wye a) :-. Focusing Root (Construction Wye) a

Rotatable (Right (Zig :: a -> Splay a) :: Wye (a -> Splay a)) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Binary

Methods

rotation :: Tagged (Right Zig) (Construction Wye a0) -> Maybe (Construction Wye a0)

Rotatable (Left (Zig :: a -> Splay a) :: Wye (a -> Splay a)) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Binary

Methods

rotation :: Tagged (Left Zig) (Construction Wye a0) -> Maybe (Construction Wye a0)

Rotatable (Right (Zig (Zag :: a -> Splay a)) :: Wye (Splay (a -> Splay a))) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Binary

Methods

rotation :: Tagged (Right (Zig Zag)) (Construction Wye a0) -> Maybe (Construction Wye a0)

Rotatable (Left (Zig (Zag :: a -> Splay a)) :: Wye (Splay (a -> Splay a))) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Binary

Methods

rotation :: Tagged (Left (Zig Zag)) (Construction Wye a0) -> Maybe (Construction Wye a0)

Rotatable (Right (Zig (Zig :: a -> Splay a)) :: Wye (Splay (a -> Splay a))) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Binary

Methods

rotation :: Tagged (Right (Zig Zig)) (Construction Wye a0) -> Maybe (Construction Wye a0)

Rotatable (Left (Zig (Zig :: a -> Splay a)) :: Wye (Splay (a -> Splay a))) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Binary

Methods

rotation :: Tagged (Left (Zig Zig)) (Construction Wye a0) -> Maybe (Construction Wye a0)

Interpreted (Kan (Left :: Type -> Wye Type) t u b)

Defined in Pandora.Paradigm.Primary.Transformer.Kan

Associated Types

type Primary (Kan Left t u b) a :: Type

Methods

run :: Kan Left t u b a -> Primary (Kan Left t u b) a

Interpreted (Kan (Right :: Type -> Wye Type) t u b)

Defined in Pandora.Paradigm.Primary.Transformer.Kan

Associated Types

type Primary (Kan Right t u b) a :: Type

Methods

run :: Kan Right t u b a -> Primary (Kan Right t u b) a

Contravariant (Kan (Left :: Type -> Wye Type) t u b)

Defined in Pandora.Paradigm.Primary.Transformer.Kan

Methods

(>$<) :: (a -> b0) -> Kan Left t u b b0 -> Kan Left t u b a

contramap :: (a -> b0) -> Kan Left t u b b0 -> Kan Left t u b a

(>$) :: b0 -> Kan Left t u b b0 -> Kan Left t u b a

($<) :: Kan Left t u b b0 -> b0 -> Kan Left t u b a

full :: Kan Left t u b () -> Kan Left t u b a

(>&<) :: Kan Left t u b b0 -> (a -> b0) -> Kan Left t u b a

(>$$<) :: Contravariant u0 => (a -> b0) -> ((Kan Left t u b :. u0) := a) -> (Kan Left t u b :. u0) := b0

(>$$$<) :: (Contravariant u0, Contravariant v) => (a -> b0) -> ((Kan Left t u b :. (u0 :. v)) := b0) -> (Kan Left t u b :. (u0 :. v)) := a

(>$$$$<) :: (Contravariant u0, Contravariant v, Contravariant w) => (a -> b0) -> ((Kan Left t u b :. (u0 :. (v :. w))) := a) -> (Kan Left t u b :. (u0 :. (v :. w))) := b0

(>&&<) :: Contravariant u0 => ((Kan Left t u b :. u0) := a) -> (a -> b0) -> (Kan Left t u b :. u0) := b0

(>&&&<) :: (Contravariant u0, Contravariant v) => ((Kan Left t u b :. (u0 :. v)) := b0) -> (a -> b0) -> (Kan Left t u b :. (u0 :. v)) := a

(>&&&&<) :: (Contravariant u0, Contravariant v, Contravariant w) => ((Kan Left t u b :. (u0 :. (v :. w))) := a) -> (a -> b0) -> (Kan Left t u b :. (u0 :. (v :. w))) := b0

Covariant (Kan (Right :: Type -> Wye Type) t u b)

Defined in Pandora.Paradigm.Primary.Transformer.Kan

Methods

(<$>) :: (a -> b0) -> Kan Right t u b a -> Kan Right t u b b0

comap :: (a -> b0) -> Kan Right t u b a -> Kan Right t u b b0

(<$) :: a -> Kan Right t u b b0 -> Kan Right t u b a

($>) :: Kan Right t u b a -> b0 -> Kan Right t u b b0

void :: Kan Right t u b a -> Kan Right t u b ()

loeb :: Kan Right t u b (a <-| Kan Right t u b) -> Kan Right t u b a

(<&>) :: Kan Right t u b a -> (a -> b0) -> Kan Right t u b b0

(<$$>) :: Covariant u0 => (a -> b0) -> ((Kan Right t u b :. u0) := a) -> (Kan Right t u b :. u0) := b0

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b0) -> ((Kan Right t u b :. (u0 :. v)) := a) -> (Kan Right t u b :. (u0 :. v)) := b0

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b0) -> ((Kan Right t u b :. (u0 :. (v :. w))) := a) -> (Kan Right t u b :. (u0 :. (v :. w))) := b0

(<&&>) :: Covariant u0 => ((Kan Right t u b :. u0) := a) -> (a -> b0) -> (Kan Right t u b :. u0) := b0

(<&&&>) :: (Covariant u0, Covariant v) => ((Kan Right t u b :. (u0 :. v)) := a) -> (a -> b0) -> (Kan Right t u b :. (u0 :. v)) := b0

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((Kan Right t u b :. (u0 :. (v :. w))) := a) -> (a -> b0) -> (Kan Right t u b :. (u0 :. (v :. w))) := b0

type Nonempty Binary

Defined in Pandora.Paradigm.Structure.Binary

type Nonempty Binary = Construction Wye

data Kan (Left :: Type -> Wye Type) t u b a

Defined in Pandora.Paradigm.Primary.Transformer.Kan

data Kan (Left :: Type -> Wye Type) t u b a = Lan ((t b -> a) -> u b)

data Kan (Right :: Type -> Wye Type) t u b a

Defined in Pandora.Paradigm.Primary.Transformer.Kan

data Kan (Right :: Type -> Wye Type) t u b a = Ran ((a -> t b) -> u b)

type Substructural (Left :: Type -> Wye Type) Binary a

Defined in Pandora.Paradigm.Structure.Binary

type Substructural (Left :: Type -> Wye Type) Binary a = Binary a

type Substructural (Right :: Type -> Wye Type) Binary a

Defined in Pandora.Paradigm.Structure.Binary

type Substructural (Right :: Type -> Wye Type) Binary a = Binary a

type Focusing (Root :: Type -> Type) Binary a

Defined in Pandora.Paradigm.Structure.Binary

type Focusing (Root :: Type -> Type) Binary a = Maybe a

type Substructural (Left :: Type -> Wye Type) (Construction Wye) a

Defined in Pandora.Paradigm.Structure.Binary

type Substructural (Left :: Type -> Wye Type) (Construction Wye) a = (Maybe :. Construction Wye) := a

type Substructural (Right :: Type -> Wye Type) (Construction Wye) a

Defined in Pandora.Paradigm.Structure.Binary

type Substructural (Right :: Type -> Wye Type) (Construction Wye) a = (Maybe :. Construction Wye) := a

type Focusing (Root :: Type -> Type) (Construction Wye) a

Defined in Pandora.Paradigm.Structure.Binary

type Focusing (Root :: Type -> Type) (Construction Wye) a = a

type Primary (Kan (Left :: Type -> Wye Type) t u b) a

Defined in Pandora.Paradigm.Primary.Transformer.Kan

type Primary (Kan (Left :: Type -> Wye Type) t u b) a = (t b -> a) -> u b

type Primary (Kan (Right :: Type -> Wye Type) t u b) a

Defined in Pandora.Paradigm.Primary.Transformer.Kan

type Primary (Kan (Right :: Type -> Wye Type) t u b) a = (a -> t b) -> u b

wye :: r -> (a -> r) -> (a -> r) -> (a -> a -> r) -> Wye a -> r