Lens is a generalised or first-class *field*.

If we have a value s :: S, and a l :: Lens' S A, we can get the "field value" of type A using view. We can also update (or put or set) the value using over (or set).

>>> data Human = Human { _name :: String, _location :: String } deriving Show
>>> let human = Human "Bob" "London"

We can make a Lens for _name field:

>>> let name = lens _name $ \s x -> s { _name = x }

Which we can use as a Getter

>>> view name human
"Bob"

or a Setter

>>> set name "Robert" human
Human {_name = "Robert", _location = "London"}

Lens is a Setter and a Getter, therefore you can

view1 :: Lens i s t a b -> s -> a
set   :: Lens i s t a b -> b -> s -> t
over  :: Lens i s t a b -> (a -> b) -> s -> t

view1 (lens f g)   s = f s
set   (lens f g) a s = g s a

• GetPut: You get back what you put in:

  view l (set l v s) = v
  

• PutGet: Putting back what you got doesn’t change anything:

  set l (view l s) s = s
  

• PutPut: Setting twice is the same as setting once:

  set l v' (set l v s) = set l v' s