Control.Lens.Level

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

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 a, Eq i) => Eq (Level i a)

Methods

(==) :: Level i a -> Level i a -> Bool

(/=) :: Level i a -> Level i a -> Bool

(Ord a, Ord i) => 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 a, Read i) => 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 a, Show i) => Show (Level i a)

Methods

showsPrec :: Int -> Level i a -> ShowS

show :: Level i a -> String

showList :: [Level i a] -> ShowS

levels :: Applicative f => Traversing (->) f s t a b -> IndexedLensLike Int f s t (Level () a) (Level () b)

This provides a breadth-first Traversal or Fold of the individual levels of any other Traversal or Fold 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')]

levels :: Traversal s t a b      -> IndexedTraversal Int s t (Level () a) (Level () b)
levels :: Fold s a               -> IndexedFold Int s (Level () a)

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

ilevels :: Applicative f => Traversing (Indexed i) f s t a b -> IndexedLensLike Int f s t (Level i a) (Level j b)

This provides a breadth-first Traversal or Fold of the individual levels of any other Traversal or Fold 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')]

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

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