haskell - How to write an instance of Control.Lens.AT -

i have data structure can understood analogous data.map in maps keys of 1 type values of another. write instance of control.lens.at type cannot ever seem satisfy requirements.

given struct k v lookup, insert, update, , delete, must make instance @ (struct k v) work?

the at method should return indexed lens given index gets input structure , behaves this:

• on getting, if key not present, return nothing, otherwise return value @ key in structure.
• on setting, if new value nothing, remove key structure, otherwise set (or create if it's not there) value in just.
• the index key given at.

this leads following code requirements:

instance @ (struct k v)   @ key = ilens getter setter     getter = (key, lookup key)           setter s nothing = delete key s           setter s (just newvalue) = insert key newvalue s 

i use lens construct lens ilens construct indexed lens getter , setter. assume functions have 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 key when it's there 

you still have define ixvalue , index type family instances:

type instance ixvalue (struct k v) = v -- (struct k v) contains values of type v type instance index (struct k v) = k   -- (struct k v) has keys of type k. 

edit: actually, @ must return indexed lens, not lens. confused order of arguments setter.