While trying to understand State monad and use of Lens with it, I arrived at a surprisingly trivial definition of a lens for a simple counter:
self :: ASetter s s s s
self = ($)
incrementUsingLens :: State Int ()
incrementUsingLens = self %= (+1)
Since
type ASetter s t a b = (a -> Identity b) -> s -> Identity t
In my case is just
type ASetter s s s s = (s -> Identity s) -> s -> Identity s
Is this is indeed a correct definition for a lens into a state variable? I'm worried that I might be missing some laws or other assumptions.
lens calls this do-nothing optic simple. Note that simple is an Equality, and Equality is at the very bottom of the optics hierarchy, which means you can use it not only as a do-nothing setter, but also as a do-nothing lens, prism, etc.
I'm worried that I might be missing some laws or other assumptions.
The setter laws say that, for a foo setter, over foo should follow the functor laws:
over foo id = id
over foo (g . f) = over foo g . over foo f
If you try this with simple/id, you will find the laws hold trivially. The same goes for the other optic laws.