A 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 l s. We can also update (or put or set) the value using over (or set).

For example, given the following definitions:

>>> 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"}

A Lens is in particular a Getter and a Setter, therefore you can specialise types to obtain:

view :: Lens s t a b -> s -> a

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

view (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
  

See Data.Tuple.Optics for Lenses for tuples.

The van Laarhoven encoding of lenses is isomorphic to the profunctor encoding used internally by optics, but converting back and forth may have a performance penalty.