lens package:rio

lens creates a Lens from a getter and a setter. The resulting lens isn't the most effective one (because of having to traverse the structure twice when modifying), but it shouldn't matter much. A (partial) lens for list indexing:

ix :: Int -> Lens' [a] a
ix i = lens (!! i)                                   -- getter
(\s b -> take i s ++ b : drop (i+1) s)   -- setter

Usage:

>>> [1..9] ^. ix 3
4

>>> [1..9] & ix 3 %~ negate
[1,2,3,-4,5,6,7,8,9]

When getting, the setter is completely unused; when setting, the getter is unused. Both are used only when the value is being modified. For instance, here we define a lens for the 1st element of a list, but instead of a legitimate getter we use undefined. Then we use the resulting lens for setting and it works, which proves that the getter wasn't used:

>>> [1,2,3] & lens undefined (\s b -> b : tail s) .~ 10
[10,2,3]

Lens s t a b is the lowest common denominator of a setter and a getter, something that has the power of both; it has a Functor constraint, and since both Const and Identity are functors, it can be used whenever a getter or a setter is needed.

• a is the type of the value inside of structure
• b is the type of the replaced value
• s is the type of the whole structure
• t is the type of the structure after replacing a in it with b

Extra utilities from microlens. @since: 0.1.16.0

This is a type alias for monomorphic lenses which don't change the type of the container (or of the value inside).