How to write an instance of Control.Lens.AT

Question

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?

Answer 1

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.