Pandora.Pattern.Functor.Traversable

Documentation

class Covariant source target t => Traversable source target t where

Let f :: (Applicative t, Applicative g) => t a -> u a
Let p :: (Monoidal u category category (:*:) (:*:), Monoidal u category category (:*:) (:*:)) => t a -> u a

When providing a new instance, you should ensure it satisfies:
* Numeratority of traversing: g . (f <<--) ≡ (g . f <<--)
* Numeratority of sequencing: f . (identity <<--)= (identity <<--) . (f <-|-)
* Preserving point: p (point x) ≡ point x
* Preserving apply: f (x <-*- y) ≡ f x <-*- f y

Methods

(<<-) :: (Covariant source target u, Monoidal (Straight source) (Straight target) (:*:) (:*:) u) => source a (u b) -> target (t a) (u (t b)) infixl 5

Instances

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Identity a -> u (Identity b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Edges

Defined in Pandora.Paradigm.Primary.Functor.Edges

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Edges a -> u (Edges b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Maybe

Defined in Pandora.Paradigm.Primary.Functor.Maybe

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Maybe a -> u (Maybe b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Biforked

Defined in Pandora.Paradigm.Structure.Some.Binary

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Biforked a -> u (Biforked b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((:*:) s)

Defined in Pandora.Paradigm.Primary.Algebraic

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> (s :*: a) -> u (s :*: b)

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

Defined in Pandora.Paradigm.Primary.Transformer.Jet

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Jet t a -> u (Jet t b)

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

Defined in Pandora.Paradigm.Primary.Transformer.Jack

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Jack t a -> u (Jack t b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Wedge e)

Defined in Pandora.Paradigm.Primary.Functor.Wedge

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Wedge e a -> u (Wedge e b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Validation e)

Defined in Pandora.Paradigm.Primary.Functor.Validation

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Validation e a -> u (Validation e b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (These e)

Defined in Pandora.Paradigm.Primary.Functor.These

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> These e a -> u (These e b)

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

Defined in Pandora.Paradigm.Primary.Transformer.Instruction

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Instruction t a -> u (Instruction t b)

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

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Construction t a -> u (Construction t b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Some.Binary

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Construction Wye a -> u (Construction Wye b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Conclusion e)

Defined in Pandora.Paradigm.Primary.Functor.Conclusion

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Conclusion e a -> u (Conclusion e b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t <:.> Construction t) => Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Comprehension t)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Comprehension t a -> u (Comprehension t b)

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

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Tap t a -> u (Tap t b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Tap ((t <:.:> t) := (:*:)) a -> u (Tap ((t <:.:> t) := (:*:)) b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Equipment e)

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Equipment e a -> u (Equipment e b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Tagged tag)

Defined in Pandora.Paradigm.Primary.Functor.Tagged

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Tagged tag a -> u (Tagged tag b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Schematic Monad t u) => Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t :> u)

Defined in Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic

Methods

(<<-) :: (Covariant (->) (->) u0, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u0) => (a -> u0 b) -> (t :> u) a -> u0 ((t :> u) b)

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

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Backwards t a -> u (Backwards t b)

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

Defined in Pandora.Paradigm.Primary.Transformer.Reverse

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Reverse t a -> u (Reverse t b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Schematic Comonad t u) => Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t :< u)

Defined in Pandora.Paradigm.Controlflow.Effect.Transformer.Comonadic

Methods

(<<-) :: (Covariant (->) (->) u0, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u0) => (a -> u0 b) -> (t :< u) a -> u0 ((t :< u) b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Prefixed t k)

Defined in Pandora.Paradigm.Structure.Modification.Prefixed

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Prefixed t k a -> u (Prefixed t k b)

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.List

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> ((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) a -> u (((Identity <:.:> ((List <:.:> List) := (:*:))) := (:*:)) b)

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

(<<-) :: (Covariant (->) (->) u0, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u0) => (a -> u0 b) -> (t <:.> u) a -> u0 ((t <:.> u) b)

(-<<-<<-) :: forall t u v category a b. (Traversable category category t, Covariant category category u, Monoidal (Straight category) (Straight category) (:*:) (:*:) u, Traversable category category v) => category a (u b) -> category (v (t a)) (u (v (t b))) infixl 5