Control.Lens.Level

lens-4.15.1: Lenses, Folds and Traversals

Copyright | (C) 2012-16 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | Edward Kmett <ekmett@gmail.com>
Stability | provisional
Portability | Rank2Types
Safe Haskell | None
Language | Haskell98

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) # |
Methods itraverse :: Applicative f => (i -> a -> f b) -> Level i a -> f (Level i b) # itraversed :: (Indexable i p, Applicative f) => p a (f b) -> Level i a -> f (Level i b) #
FoldableWithIndex i (Level i) # |
Methods ifoldMap :: Monoid m => (i -> a -> m) -> Level i a -> m # ifolded :: (Indexable i p, Contravariant f, Applicative f) => p a (f a) -> Level i a -> f (Level i a) # ifoldr :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl :: (i -> b -> a -> b) -> b -> Level i a -> b # ifoldr' :: (i -> a -> b -> b) -> b -> Level i a -> b # ifoldl' :: (i -> b -> a -> b) -> b -> Level i a -> b #
FunctorWithIndex i (Level i) # |
Methods imap :: (i -> a -> b) -> Level i a -> Level i b # imapped :: (Indexable i p, Settable f) => p a (f b) -> Level i a -> f (Level i b) #
Functor (Level i) # |
Methods fmap :: (a -> b) -> Level i a -> Level i b # (<$) :: a -> Level i b -> Level i a #
Foldable (Level i) # |
Methods fold :: Monoid m => Level i m -> m # foldMap :: Monoid m => (a -> m) -> Level i a -> m # foldr :: (a -> b -> b) -> b -> Level i a -> b # foldr' :: (a -> b -> b) -> b -> Level i a -> b # foldl :: (b -> a -> b) -> b -> Level i a -> b # foldl' :: (b -> a -> b) -> b -> Level i a -> b # foldr1 :: (a -> a -> a) -> Level i a -> a # foldl1 :: (a -> a -> a) -> Level i a -> a # toList :: Level i a -> [a] # null :: Level i a -> Bool # length :: Level i a -> Int # elem :: Eq a => a -> Level i a -> Bool # maximum :: Ord a => Level i a -> a # minimum :: Ord a => Level i a -> a # sum :: Num a => Level i a -> a # product :: Num a => Level i a -> a #
Traversable (Level i) # |
Methods traverse :: Applicative f => (a -> f b) -> Level i a -> f (Level i b) # sequenceA :: Applicative f => Level i (f a) -> f (Level i a) # mapM :: Monad m => (a -> m b) -> Level i a -> m (Level i b) # sequence :: Monad m => Level i (m a) -> m (Level i a) #
(Eq i, Eq a) => Eq (Level i a) # |
Methods (==) :: Level i a -> Level i a -> Bool # (/=) :: Level i a -> Level i a -> Bool #
(Ord i, Ord a) => Ord (Level i a) # |
Methods compare :: Level i a -> Level i a -> Ordering # (<) :: Level i a -> Level i a -> Bool # (<=) :: Level i a -> Level i a -> Bool # (>) :: Level i a -> Level i a -> Bool # (>=) :: Level i a -> Level i a -> Bool # max :: Level i a -> Level i a -> Level i a # min :: Level i a -> Level i a -> Level i a #
(Read i, Read a) => Read (Level i a) # |
Methods readsPrec :: Int -> ReadS (Level i a) # readList :: ReadS [Level i a] # readPrec :: ReadPrec (Level i a) # readListPrec :: ReadPrec [Level i a] #
(Show i, Show a) => Show (Level i a) # |
Methods showsPrec :: Int -> Level i a -> ShowS # show :: Level i a -> String # showList :: [Level i a] -> ShowS #

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.