One of most commonly-asked questions about this package is whether it provides lenses for working with Map . It does, but their uses are perhaps obscured by their genericity. This module exists to provide documentation for them.

Map is an instance of At , so we have a lenses on values at keys:

>>> Map.fromList [(1, "world")] ^.at 1
Just "world"

>>> at 1 .~ Just "world" $ Map.empty
fromList [(1,"world")]

>>> at 0 ?~ "hello" $ Map.empty
fromList [(0,"hello")]

We can traverse, fold over, and map over key-value pairs in a Map , thanks to its TraversableWithIndex , FoldableWithIndex , and FunctorWithIndex instances.

>>> imap const $ Map.fromList [(1, "Venus")]
fromList [(1,1)]

>>> ifoldMap (\i _ -> Sum i) $ Map.fromList [(2, "Earth"), (3, "Mars")]
Sum {getSum = 5}

>>> itraverse_ (curry print) $ Map.fromList [(4, "Jupiter")]
(4,"Jupiter")

>>> itoList $ Map.fromList [(5, "Saturn")]
[(5,"Saturn")]

A related class, Ixed , allows us to use ix to traverse a value at a particular key.

>>> ix 2 %~ ("New " ++) $ Map.fromList [(2, "Earth")]
fromList [(2,"New Earth")]

>>> preview (ix 8) $ Map.empty
Nothing

Additionally, Map has TraverseMin and TraverseMax instances, which let us traverse over the value at the least and greatest keys, respectively.

>>> preview traverseMin $ Map.fromList [(5, "Saturn"), (6, "Uranus")]
Just "Saturn"

>>> preview traverseMax $ Map.fromList [(5, "Saturn"), (6, "Uranus")]
Just "Uranus"