Data.Generics.Traversable

All of the functions below work only on «interesting» subterms. It is up to the instance writer to decide which subterms are interesting and which subterms should count as immediate. This can also depend on the context c.

The context, denoted c, is a constraint (of kind * -> Constraint) that provides additional facilities to work with the data. In most cases, the context cannot be inferred automatically. You need to provide it using the type application syntax:

gmap @Show f x
everywhere @Typeable f x

etc.

For more information, see:

Scrap your boilerplate with class

https://www.microsoft.com/en-us/research/publication/scrap-your-boilerplate-with-class/

Generalizing generic fold

http://ro-che.info/articles/2013-03-11-generalizing-gfoldl

Open recursion combinators

class GTraversable c a where

Methods

gtraverse :: Applicative f => (forall d. c d => d -> f d) -> a -> f a

Applicative traversal over (a subset of) immediate subterms. This is a generic version of traverse.

The supplied function is applied only to the «interesting» subterms.

Other subterms are lifted using pure, and the whole structure is folded back using <*>.

gtraverse has a default implementation const pure, which works for types without interesting subterms (in particular, atomic types).

gmap :: forall c a. GTraversable c a => (forall d. c d => d -> d) -> a -> a

Generic map over the immediate subterms

gmapM :: forall c m a. (Monad m, GTraversable c a) => (forall d. c d => d -> m d) -> a -> m a

Generic monadic map over the immediate subterms

gfoldMap :: forall c r a. (Monoid r, GTraversable c a) => (forall d. c d => d -> r) -> a -> r

Generic monoidal fold over the immediate subterms (cf. foldMap)

gfoldr :: forall c a r. GTraversable c a => (forall d. c d => d -> r -> r) -> r -> a -> r

Generic right fold over the immediate subterms

gfoldl' :: forall c a r. GTraversable c a => (forall d. c d => r -> d -> r) -> r -> a -> r

Generic strict left fold over the immediate subterms

Closed recursion combinators

class (GTraversable (Rec c) a, c a) => Rec c a

Rec enables "deep traversals".

It is satisfied automatically when its superclass constraints are satisfied — you are not supposed to declare new instances of this class.

Instances

(GTraversable (Rec c) a, c a) => Rec c a

everywhere :: forall c a. Rec c a => (forall d. Rec c d => d -> d) -> a -> a

Apply a transformation everywhere in bottom-up manner

everywhere' :: forall c a. Rec c a => (forall d. Rec c d => d -> d) -> a -> a

Apply a transformation everywhere in top-down manner

everywhereM :: forall c m a. (Monad m, Rec c a) => (forall d. Rec c d => d -> m d) -> a -> m a

Monadic variation on everywhere

everything :: forall c r a. Rec c a => (r -> r -> r) -> (forall d. Rec c d => d -> r) -> a -> r

Strict left fold over all elements, top-down