Pandora.Pattern.Functor.Traversable

Documentation

class Covariant t => Traversable t where

Let f :: (Applicative t, Applicative g) => t a -> u a
Let p :: (Pointable t, Pointable g) => t a -> u a

When providing a new instance, you should ensure it satisfies the four laws:
* Naturality of traversing: g . traverse f ≡ traverse (g . f)
* Naturality of sequencing: f . sequence = sequence . comap f
* Preserving point: p (point x) ≡ point x
* Preserving apply: f (x <*> y) ≡ f x <*> f y

Minimal complete definition

(->>)

Methods

(->>) :: (Pointable u, Applicative u) => t a -> (a -> u b) -> (u :. t) > b infixl 5

Infix version of traverse

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

Prefix version of ->>

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

The dual of distribute

(->>>) :: (Pointable u, Applicative u, Traversable v) => ((v :. t) > a) -> (a -> u b) -> (u :. (v :. t)) > b infixl 5

Infix versions of traverse with various nesting levels

(->>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w) => ((w :. (v :. t)) > a) -> (a -> u b) -> (u :. (w :. (v :. t))) > b infixl 5

(->>>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w, Traversable j) => ((j :. (w :. (v :. t))) > a) -> (a -> u b) -> (u :. (j :. (w :. (v :. t)))) > b infixl 5

Instances

Traversable Wye

Defined in Pandora.Paradigm.Basis.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

Traversable Edges

Defined in Pandora.Paradigm.Basis.Edges

Methods

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

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

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

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

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

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

Traversable Graph

Defined in Pandora.Paradigm.Structure.Graph

Methods

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

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

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

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

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

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

Traversable Maybe

Defined in Pandora.Paradigm.Basis.Maybe

Methods

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

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

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

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

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

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

Traversable Stack

Defined in Pandora.Paradigm.Structure.Stack

Methods

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

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

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

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

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

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

Traversable Identity

Defined in Pandora.Paradigm.Basis.Identity

Methods

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

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

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

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

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

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

Traversable (Variation e)

Defined in Pandora.Paradigm.Basis.Variation

Methods

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

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

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

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

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

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

Traversable t => Traversable (Jet t)

Defined in Pandora.Paradigm.Basis.Jet

Methods

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

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

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

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

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

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

Traversable t => Traversable (Free t)

Defined in Pandora.Paradigm.Basis.Free

Methods

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

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

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

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

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

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

Traversable (Validation e)

Defined in Pandora.Paradigm.Basis.Validation

Methods

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

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

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

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

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

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

Traversable t => Traversable (Twister t)

Defined in Pandora.Paradigm.Basis.Twister

Methods

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

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

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

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

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

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

Traversable (Product a)

Defined in Pandora.Paradigm.Basis.Product

Methods

(->>) :: (Pointable u, Applicative u) => Product a a0 -> (a0 -> u b) -> (u :. Product a) > b

traverse :: (Pointable u, Applicative u) => (a0 -> u b) -> Product a a0 -> (u :. Product a) > b

sequence :: (Pointable u, Applicative u) => (Product a :. u) a0 -> (u :. Product a) > a0

(->>>) :: (Pointable u, Applicative u, Traversable v) => ((v :. Product a) > a0) -> (a0 -> u b) -> (u :. (v :. Product a)) > b

(->>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w) => ((w :. (v :. Product a)) > a0) -> (a0 -> u b) -> (u :. (w :. (v :. Product a))) > b

(->>>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w, Traversable j) => ((j :. (w :. (v :. Product a))) > a0) -> (a0 -> u b) -> (u :. (j :. (w :. (v :. Product a)))) > b

Traversable t => Traversable (Jack t)

Defined in Pandora.Paradigm.Basis.Jack

Methods

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

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

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

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

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

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

Traversable (Conclusion e)

Defined in Pandora.Paradigm.Basis.Conclusion

Methods

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

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

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

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

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

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

Traversable (Tagged tag)

Defined in Pandora.Paradigm.Basis.Tagged

Methods

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

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

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

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

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

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

Traversable (Constant a :: Type -> Type)

Defined in Pandora.Paradigm.Basis.Constant

Methods

(->>) :: (Pointable u, Applicative u) => Constant a a0 -> (a0 -> u b) -> (u :. Constant a) > b

traverse :: (Pointable u, Applicative u) => (a0 -> u b) -> Constant a a0 -> (u :. Constant a) > b

sequence :: (Pointable u, Applicative u) => (Constant a :. u) a0 -> (u :. Constant a) > a0

(->>>) :: (Pointable u, Applicative u, Traversable v) => ((v :. Constant a) > a0) -> (a0 -> u b) -> (u :. (v :. Constant a)) > b

(->>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w) => ((w :. (v :. Constant a)) > a0) -> (a0 -> u b) -> (u :. (w :. (v :. Constant a))) > b

(->>>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w, Traversable j) => ((j :. (w :. (v :. Constant a))) > a0) -> (a0 -> u b) -> (u :. (j :. (w :. (v :. Constant a)))) > b