How to write an instance of Control.Lens.AT

I have a data structure that can be understood as analogous to Data.Map in that it maps keys of one type to values of another. I would like to write an instance of Control.Lens.At for this type but I cannot ever seem to satisfy all the requirements.

Given Struct k v with lookup, insert, update, and delete, what must I do to make instance At (Struct k v) work?

Solution

The at method should return an indexed lens for a given index gets as input your structure and behaves like this:

On getting, if the key is not present, return Nothing, otherwise return the value at the key in the structure.
On setting, if new value is Nothing, remove the key from the structure, otherwise set it (or create it if it's not already there) to the value in the Just.
The index is just the key given to at.

This leads to the following code for your requirements:

instance At (Struct k v) where
  at key = ilens getter setter
    where getter = (key, lookup key)
          setter s Nothing = delete key s
          setter s (Just newValue) = insert key newValue s

I use ~~lens to construct a lens~~ ilens to construct an indexed lens from a getter and a setter. I also assume that your functions have the following types:

lookup :: k -> Struct k v -> Maybe v
delete :: k -> Struct k v -> Struct k v
insert :: k -> v -> Struct k v -> Struct k v
-- Insert should override the key when it's already there

You still have to define the IxValue and Index type family instances:

type instance IxValue (Struct k v) = v -- A (Struct k v) contains values of type v
type instance Index (Struct k v) = k   -- A (Struct k v) has keys of type k.

EDIT: Actually, at must return an indexed lens, not just a lens. I also confused the order of the arguments to the setter.