Type family that takes a key-value container type and returns the type of keys (indices) into the container, for example Index (Map k a) ~ k. This is shared by Ixed, At and Contains.

Type family that takes a key-value container type and returns the type of values stored in the container, for example IxValue (Map k a) ~ a. This is shared by both Ixed and At.

Provides a simple AffineTraversal lets you traverse the value at a given key in a Map or element at an ordinal position in a list or Seq.

A definition of ix for types with an At instance. This is the default if you don't specify a definition for ix.

At provides a Lens that can be used to read, write or delete the value associated with a key in a Map-like container on an ad hoc basis.

An instance of At should satisfy:

ix k ≡ at k % _Just

Version of at strict in the value inside the Just constructor.

Example:

>>> (at () .~ Just (error "oops") $ Nothing) `seq` ()
()

>>> (at' () .~ Just (error "oops") $ Nothing) `seq` ()
*** Exception: oops
...

>>> view (at ()) (Just $ error "oops") `seq` ()
()

>>> view (at' ()) (Just $ error "oops") `seq` ()
*** Exception: oops
...

It also works as expected for other data structures:

>>> (at 1 .~ Just (error "oops") $ Map.empty) `seq` ()
()

>>> (at' 1 .~ Just (error "oops") $ Map.empty) `seq` ()
*** Exception: oops
...

Delete the value associated with a key in a Map-like container

sans k = at k .~ Nothing

This class provides a simple Lens that lets you view (and modify) information about whether or not a container contains a given Index. Instances are provided for Set-like containers only.