What is the difference between ix and element in the Lens library of Haskell

Question

In Haskell's lens library, ix and element both take an Int an can be used e.g. to read or write a list element at some index, like this

ghci> [1..10] ^? ix 4
Just 5
ghci> [1..10] & ix 4 .~ 1
[1,2,3,4,1,6,7,8,9,10]

and similarly:

ghci> [1..10] ^? element 4
Just 5
ghci> [1..10] & element 4 .~ 1
[1,2,3,4,1,6,7,8,9,10]

What is the difference between element and ix?

Answer 1

With ix you can index not only by number, but by e.g. key in the Maps. The element index in Traverse order.

λ> let m = Map.fromList [("foo", 'f'), ("bar", 'b')]
λ> m ^? ix "foo"
Just 'f'

λ> m ^? element 0 -- Map is ordered container!
Just 'b'

The difference is even more obvious with e.g. IntMap

λ> let im = IntMap.fromList [(1, "one"), (2, "two")]
λ> im ^? ix 1
Just "one"
λ> im ^? element 1
Just "two"