lens-4.17: Lenses, Folds and Traversals

Copyright (C) 2012-16 Edward Kmett BSD-style (see the file LICENSE) Edward Kmett provisional Rank2Types Safe Haskell98

Control.Lens.Level

Description

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

Synopsis

# Documentation

data Level i a Source #

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
 Source # Instance detailsDefined in Control.Lens.Indexed Methodsitraverse :: Applicative f => (i -> a -> f b) -> Level i a -> f (Level i b) Source #itraversed :: (Indexable i p, Applicative f) => p a (f b) -> Level i a -> f (Level i b) Source # Source # Instance detailsDefined in Control.Lens.Indexed MethodsifoldMap :: Monoid m => (i -> a -> m) -> Level i a -> m Source #ifolded :: (Indexable i p, Contravariant f, Applicative f) => p a (f a) -> Level i a -> f (Level i a) Source #ifoldr :: (i -> a -> b -> b) -> b -> Level i a -> b Source #ifoldl :: (i -> b -> a -> b) -> b -> Level i a -> b Source #ifoldr' :: (i -> a -> b -> b) -> b -> Level i a -> b Source #ifoldl' :: (i -> b -> a -> b) -> b -> Level i a -> b Source # Source # Instance detailsDefined in Control.Lens.Indexed Methodsimap :: (i -> a -> b) -> Level i a -> Level i b Source #imapped :: (Indexable i p, Settable f) => p a (f b) -> Level i a -> f (Level i b) Source # Functor (Level i) Source # Instance detailsDefined in Control.Lens.Internal.Level Methodsfmap :: (a -> b) -> Level i a -> Level i b #(<\$) :: a -> Level i b -> Level i a # Source # Instance detailsDefined in Control.Lens.Internal.Level Methodsfold :: 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 # Source # Instance detailsDefined in Control.Lens.Internal.Level Methodstraverse :: 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) Source # Instance detailsDefined in Control.Lens.Internal.Level Methods(==) :: Level i a -> Level i a -> Bool #(/=) :: Level i a -> Level i a -> Bool # (Ord i, Ord a) => Ord (Level i a) Source # Instance detailsDefined in Control.Lens.Internal.Level Methodscompare :: 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) Source # Instance detailsDefined in Control.Lens.Internal.Level MethodsreadsPrec :: 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) Source # Instance detailsDefined in Control.Lens.Internal.Level MethodsshowsPrec :: 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) Source #

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) Source #

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.