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 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 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

(Traversable (t u), Traversable u) => Traversable (Y t u)

Defined in Pandora.Paradigm.Junction.Transformer

Methods

(->>) :: (Pointable u0, Applicative u0) => Y t u a -> (a -> u0 b) -> (u0 :.: Y t u) b

traverse :: (Pointable u0, Applicative u0) => (a -> u0 b) -> Y t u a -> (u0 :.: Y t u) b

sequence :: (Pointable u0, Applicative u0) => (Y t u :.: u0) a -> (u0 :.: Y t u) a

(->>>) :: (Pointable u0, Applicative u0, Traversable v) => (v :.: Y t u) a -> (a -> u0 b) -> (u0 :.: (v :.: Y t u)) b

(->>>>) :: (Pointable u0, Applicative u0, Traversable v, Traversable w) => (w :.: (v :.: Y t u)) a -> (a -> u0 b) -> (u0 :.: (w :.: (v :.: Y t u))) b

(->>>>>) :: (Pointable u0, Applicative u0, Traversable v, Traversable w, Traversable j) => (j :.: (w :.: (v :.: Y t u))) a -> (a -> u0 b) -> (u0 :.: (j :.: (w :.: (v :.: Y t u)))) b

(Traversable t, Traversable u) => Traversable (T t u)

Defined in Pandora.Paradigm.Junction.Transformer

Methods

(->>) :: (Pointable u0, Applicative u0) => T t u a -> (a -> u0 b) -> (u0 :.: T t u) b

traverse :: (Pointable u0, Applicative u0) => (a -> u0 b) -> T t u a -> (u0 :.: T t u) b

sequence :: (Pointable u0, Applicative u0) => (T t u :.: u0) a -> (u0 :.: T t u) a

(->>>) :: (Pointable u0, Applicative u0, Traversable v) => (v :.: T t u) a -> (a -> u0 b) -> (u0 :.: (v :.: T t u)) b

(->>>>) :: (Pointable u0, Applicative u0, Traversable v, Traversable w) => (w :.: (v :.: T t u)) a -> (a -> u0 b) -> (u0 :.: (w :.: (v :.: T t u))) b

(->>>>>) :: (Pointable u0, Applicative u0, Traversable v, Traversable w, Traversable j) => (j :.: (w :.: (v :.: T t u))) a -> (a -> u0 b) -> (u0 :.: (j :.: (w :.: (v :.: T t u)))) b

(Traversable t, Traversable u) => Traversable (U Co Co t u)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(->>) :: (Pointable u0, Applicative u0) => U Co Co t u a -> (a -> u0 b) -> (u0 :.: U Co Co t u) b

traverse :: (Pointable u0, Applicative u0) => (a -> u0 b) -> U Co Co t u a -> (u0 :.: U Co Co t u) b

sequence :: (Pointable u0, Applicative u0) => (U Co Co t u :.: u0) a -> (u0 :.: U Co Co t u) a

(->>>) :: (Pointable u0, Applicative u0, Traversable v) => (v :.: U Co Co t u) a -> (a -> u0 b) -> (u0 :.: (v :.: U Co Co t u)) b

(->>>>) :: (Pointable u0, Applicative u0, Traversable v, Traversable w) => (w :.: (v :.: U Co Co t u)) a -> (a -> u0 b) -> (u0 :.: (w :.: (v :.: U Co Co t u))) b

(->>>>>) :: (Pointable u0, Applicative u0, Traversable v, Traversable w, Traversable j) => (j :.: (w :.: (v :.: U Co Co t u))) a -> (a -> u0 b) -> (u0 :.: (j :.: (w :.: (v :.: U Co Co t u)))) b

(Traversable t, Traversable u, Traversable v) => Traversable (UU Co Co Co t u v)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(->>) :: (Pointable u0, Applicative u0) => UU Co Co Co t u v a -> (a -> u0 b) -> (u0 :.: UU Co Co Co t u v) b

traverse :: (Pointable u0, Applicative u0) => (a -> u0 b) -> UU Co Co Co t u v a -> (u0 :.: UU Co Co Co t u v) b

sequence :: (Pointable u0, Applicative u0) => (UU Co Co Co t u v :.: u0) a -> (u0 :.: UU Co Co Co t u v) a

(->>>) :: (Pointable u0, Applicative u0, Traversable v0) => (v0 :.: UU Co Co Co t u v) a -> (a -> u0 b) -> (u0 :.: (v0 :.: UU Co Co Co t u v)) b

(->>>>) :: (Pointable u0, Applicative u0, Traversable v0, Traversable w) => (w :.: (v0 :.: UU Co Co Co t u v)) a -> (a -> u0 b) -> (u0 :.: (w :.: (v0 :.: UU Co Co Co t u v))) b

(->>>>>) :: (Pointable u0, Applicative u0, Traversable v0, Traversable w, Traversable j) => (j :.: (w :.: (v0 :.: UU Co Co Co t u v))) a -> (a -> u0 b) -> (u0 :.: (j :.: (w :.: (v0 :.: UU Co Co Co t u v)))) b

(Traversable t, Traversable u, Traversable v, Traversable w) => Traversable (UUU Co Co Co Co t u v w)

Defined in Pandora.Paradigm.Junction.Composition

Methods

(->>) :: (Pointable u0, Applicative u0) => UUU Co Co Co Co t u v w a -> (a -> u0 b) -> (u0 :.: UUU Co Co Co Co t u v w) b

traverse :: (Pointable u0, Applicative u0) => (a -> u0 b) -> UUU Co Co Co Co t u v w a -> (u0 :.: UUU Co Co Co Co t u v w) b

sequence :: (Pointable u0, Applicative u0) => (UUU Co Co Co Co t u v w :.: u0) a -> (u0 :.: UUU Co Co Co Co t u v w) a

(->>>) :: (Pointable u0, Applicative u0, Traversable v0) => (v0 :.: UUU Co Co Co Co t u v w) a -> (a -> u0 b) -> (u0 :.: (v0 :.: UUU Co Co Co Co t u v w)) b

(->>>>) :: (Pointable u0, Applicative u0, Traversable v0, Traversable w0) => (w0 :.: (v0 :.: UUU Co Co Co Co t u v w)) a -> (a -> u0 b) -> (u0 :.: (w0 :.: (v0 :.: UUU Co Co Co Co t u v w))) b

(->>>>>) :: (Pointable u0, Applicative u0, Traversable v0, Traversable w0, Traversable j) => (j :.: (w0 :.: (v0 :.: UUU Co Co Co Co t u v w))) a -> (a -> u0 b) -> (u0 :.: (j :.: (w0 :.: (v0 :.: UUU Co Co Co Co t u v w)))) b