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

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

Semimonoidal t (:*:) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) => Semimonoidal (Backwards t) (:*:) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

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

Extractable t ((->) :: Type -> Type -> Type) => Extractable (Backwards t) ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

extract :: Backwards t a -> a

Pointable t ((->) :: Type -> Type -> Type) => Pointable (Backwards t) ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

point :: a -> Backwards t a

Covariant_ t ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) => Covariant_ (Backwards t) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

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

Distributive t ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) => Distributive (Backwards t) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

(-<<) :: Covariant_ u (->) (->) => (a -> Backwards t b) -> u a -> Backwards t (u b)

Traversable t ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) => Traversable (Backwards t) ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

(<<-) :: (Covariant_ u (->) (->), Pointable u (->), Semimonoidal u (:*:) (->) (->)) => (a -> u b) -> Backwards t a -> u (Backwards t b)

type Primary (Backwards t) a

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

type Primary (Backwards t) a = t a