Using lenses

[Tyson Whitehead]

The thing that really clicked lenses for me was reading through some of Twan van Laarhoven's slides where he presented an isomorphic definition of lenses.  Googling reveals he actually has a very nice blog entry about this now.

  http://twanvl.nl/blog/haskell/isomorphism-lenses

To strip out the essential element.  A lens is

  -- Isomorphisms/bijections between type @a@ and @b@
  data Iso a b = Iso { fw :: a -> b, bw :: b -> a }

  -- Lenses with a data wrapper, in practice you might want to unpack the Iso type
  data Lens a b = forall r. Lens (Iso a (b,r))

That is, a lense is two functions

  1 - fw : data -> (element, residue data)  [ this takes apart the data ]

  2 - bw : (element, residue data) -> data  [ this puts it back together ]

such that they are an isomorphism (i.e., if you take it apart and then put it back together you get the same thing).

  fw . bw = bw . fw = id

This made sense to me pretty much as soon as I encountered it.  This was certainly not the case with the other.

Cheers!  -Tyson

PS:  I would really encourage looking at the blog post.  It is a relatively easy read and well worth it.