Pandora.Paradigm.Primary.Transformer.Backwards

Documentation

newtype Backwards t a

Constructors

Backwards (t a)

Instances

Liftable (Backwards :: (Type -> Type) -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

lift :: forall (u :: Type -> Type). Covariant u => u ~> Backwards u

Lowerable (Backwards :: (Type -> Type) -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

lower :: forall (u :: Type -> Type). Covariant u => Backwards u ~> u

Hoistable (Backwards :: (Type -> Type) -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

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

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

Contravariant t => Contravariant (Backwards t)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

(>$<) :: (a -> b) -> Backwards t b -> Backwards t a

contramap :: (a -> b) -> Backwards t b -> Backwards t a

(>$) :: b -> Backwards t b -> Backwards t a

($<) :: Backwards t b -> b -> Backwards t a

full :: Backwards t () -> Backwards t a

(>&<) :: Backwards t b -> (a -> b) -> Backwards t a

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

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

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

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

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

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

Covariant t => Covariant (Backwards t)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

(<$>) :: (a -> b) -> Backwards t a -> Backwards t b

comap :: (a -> b) -> Backwards t a -> Backwards t b

(<$) :: a -> Backwards t b -> Backwards t a

($>) :: Backwards t a -> b -> Backwards t b

void :: Backwards t a -> Backwards t ()

loeb :: Backwards t (a <:= Backwards t) -> Backwards t a

(<&>) :: Backwards t a -> (a -> b) -> Backwards t b

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

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

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

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

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

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

(.#..) :: (Backwards t ~ v a, Category v) => v c d -> ((v a :. v b) := c) -> (v a :. v b) := d

(.#...) :: (Backwards t ~ v a, Backwards t ~ v b, Category v, Covariant (v a), Covariant (v b)) => v d e -> ((v a :. (v b :. v c)) := d) -> (v a :. (v b :. v c)) := e

(.#....) :: (Backwards t ~ v a, Backwards t ~ v b, Backwards t ~ v c, Category v, Covariant (v a), Covariant (v b), Covariant (v c)) => v e f -> ((v a :. (v b :. (v c :. v d))) := e) -> (v a :. (v b :. (v c :. v d))) := f

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

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

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

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

($$$>) :: (Covariant u, Covariant v) => ((Backwards t :. (u :. v)) := a) -> b -> (Backwards t :. (u :. v)) := b

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

Applicative t => Applicative (Backwards t)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

(<*>) :: Backwards t (a -> b) -> Backwards t a -> Backwards t b

apply :: Backwards t (a -> b) -> Backwards t a -> Backwards t b

(*>) :: Backwards t a -> Backwards t b -> Backwards t b

(<*) :: Backwards t a -> Backwards t b -> Backwards t a

forever :: Backwards t a -> Backwards t b

(<%>) :: Backwards t a -> Backwards t (a -> b) -> Backwards t b

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

(<***>) :: (Applicative u, Applicative v) => ((Backwards t :. (u :. v)) := (a -> b)) -> ((Backwards t :. (u :. v)) := a) -> (Backwards t :. (u :. v)) := b

(<****>) :: (Applicative u, Applicative v, Applicative w) => ((Backwards t :. (u :. (v :. w))) := (a -> b)) -> ((Backwards t :. (u :. (v :. w))) := a) -> (Backwards t :. (u :. (v :. w))) := b

Distributive t => Distributive (Backwards t)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

(>>-) :: Covariant u => u a -> (a -> Backwards t b) -> (Backwards t :. u) := b

collect :: Covariant u => (a -> Backwards t b) -> u a -> (Backwards t :. u) := b

distribute :: Covariant u => ((u :. Backwards t) := a) -> (Backwards t :. u) := a

(>>>-) :: (Covariant u, Covariant v) => ((u :. v) := a) -> (a -> Backwards t b) -> (Backwards t :. (u :. v)) := b

(>>>>-) :: (Covariant u, Covariant v, Covariant w) => ((u :. (v :. w)) := a) -> (a -> Backwards t b) -> (Backwards t :. (u :. (v :. w))) := b

(>>>>>-) :: (Covariant u, Covariant v, Covariant w, Covariant j) => ((u :. (v :. (w :. j))) := a) -> (a -> Backwards t b) -> (Backwards t :. (u :. (v :. (w :. j)))) := b

Extractable t => Extractable (Backwards t)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

extract :: a <:= Backwards t

Pointable t => Pointable (Backwards t)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

point :: a :=> Backwards t

pass :: Backwards t ()

Traversable t => Traversable (Backwards t)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

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

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

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

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

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

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

Interpreted (Backwards t)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Associated Types

type Primary (Backwards t) a

Methods

run :: Backwards t a -> Primary (Backwards t) a

unite :: Primary (Backwards t) a -> Backwards t a

(||=) :: Interpreted u => (Primary (Backwards t) a -> Primary u b) -> Backwards t a -> u b

(=||) :: Interpreted u => (Backwards t a -> u b) -> Primary (Backwards t) a -> Primary u b

(<$||=) :: (Covariant j, Interpreted u) => (Primary (Backwards t) a -> Primary u b) -> (j := Backwards t a) -> j := u b

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

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

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

(=||$>) :: (Covariant j, Interpreted u) => (Backwards t a -> u b) -> (j := Primary (Backwards t) a) -> j := Primary u b

(=||$$>) :: (Covariant j, Covariant k, Interpreted u) => (Backwards t a -> u b) -> ((j :. k) := Primary (Backwards t) a) -> (j :. k) := Primary u b

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

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

type Primary (Backwards t) a

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

type Primary (Backwards t) a = t a