lens-3.8.7.3: Lenses, Folds and Traversals

Portability | Rank2Types
Stability | provisional
Maintainer | Edward Kmett <ekmett@gmail.com>
Safe Haskell | None

Control.Lens.Level

Description

This module provides combinators for breadth-first searching within arbitrary traversals.

Synopsis

- data Level i a
- levels :: ATraversal s t a b -> IndexedTraversal Int s t (Level () a) (Level () b)
- ilevels :: AnIndexedTraversal i s t a b -> IndexedTraversal Int s t (Level i a) (Level j b)

# Documentation

data Level i a

This data type represents a path-compressed copy of one level of a source data structure. We can safely use path-compression because we know the depth of the tree.

Path compression is performed by viewing a `Level` as a PATRICIA trie of the paths into the structure to leaves at a given depth, similar in many ways to a `IntMap`, but unlike a regular PATRICIA trie we do not need to store the mask bits merely the depth of the fork.

One invariant of this structure is that underneath a `Two` node you will not find any `Zero` nodes, so `Zero` can only occur at the root.

Instances

TraversableWithIndex i (Level i) |
FoldableWithIndex i (Level i) |
FunctorWithIndex i (Level i) |
Functor (Level i) |
Foldable (Level i) |
Traversable (Level i) |
(Eq i, Eq a) => Eq (Level i a) |
(Ord i, Ord a) => Ord (Level i a) |
(Read i, Read a) => Read (Level i a) |
(Show i, Show a) => Show (Level i a) |

levels :: ATraversal s t a b -> IndexedTraversal Int s t (Level () a) (Level () b)

This provides a breadth-first `Traversal` of the individual `levels` of any other `Traversal` via iterative deepening depth-first search. The levels are returned to you in a compressed format.

This can permit us to extract the `levels` directly:

    >>> ["hello","world"]^..levels (traverse.traverse)
    [Zero,Zero,One () 'h',Two 0 (One () 'e') (One () 'w'),Two 0 (One () 'l') (One () 'o'),Two 0 (One () 'l') (One () 'r'),Two 0 (One () 'o') (One () 'l'),One () 'd']

But we can also traverse them in turn:

    >>> ["hello","world"]^..levels (traverse.traverse).traverse
    "hewlolrold"

We can use this to traverse to a fixed depth in the tree of (`<*>`) used in the `Traversal`:

    >>> ["hello","world"] & taking 4 (levels (traverse.traverse)).traverse %~ toUpper
    ["HEllo","World"]

Or we can use it to traverse the first `n` elements in found in that `Traversal` regardless of the depth at which they were found.

    >>> ["hello","world"] & taking 4 (levels (traverse.traverse).traverse) %~ toUpper
    ["HELlo","World"]

The resulting `Traversal` of the `levels` which is indexed by the depth of each `Level`.

    >>> ["dog","cat"]^@..levels (traverse.traverse) <. traverse
    [(2,'d'),(3,'o'),(3,'c'),(4,'g'),(4,'a'),(5,'t')]

Note: Internally this is implemented by using an illegal `Applicative`, as it extracts information in an order that violates the `Applicative` laws.

ilevels :: AnIndexedTraversal i s t a b -> IndexedTraversal Int s t (Level i a) (Level j b)

This provides a breadth-first `Traversal` of the individual levels of any other `Traversal` via iterative deepening depth-first search. The levels are returned to you in a compressed format.

This is similar to `levels`, but retains the index of the original `IndexedTraversal`, so you can access it when traversing the levels later on.

    >>> ["dog","cat"]^@..ilevels (traversed<.>traversed).itraversed
    [((0,0),'d'),((0,1),'o'),((1,0),'c'),((0,2),'g'),((1,1),'a'),((1,2),'t')]

The resulting `Traversal` of the levels which is indexed by the depth of each `Level`.

    >>> ["dog","cat"]^@..ilevels (traversed<.>traversed)<.>itraversed
    [((2,(0,0)),'d'),((3,(0,1)),'o'),((3,(1,0)),'c'),((4,(0,2)),'g'),((4,(1,1)),'a'),((5,(1,2)),'t')]

Note: Internally this is implemented by using an illegal `Applicative`, as it extracts information in an order that violates the `Applicative` laws.