* Focus

An experiment with lenses.

#+BEGIN_QUOTE
A lens is a value that composes a getter and a setter function to produce a bidirectional view into a data structure. This definition is intentionally broad—lenses are a very general concept, and they can be applied to almost any kind of value that encapsulates data.
  -- [[https:docs.racket-lang.org/lens/lens-intro.html][Racket 'lens' documentation]] 
#+END_QUOTE 

** Usage

To construct a lens:

#+BEGIN_SRC elixir
  # A lens for the key `:name`
  Focus.Lens.makeLens(:name)

  # A lens for the key `"name"`
  Focus.Lens.makeLens("name")

  # A lens for the second item in a list/tuple:
  Focus.Lens.makeLens(1)
#+END_SRC

Each lens provides both a getter and a setter for the accessor it was created for.

Lenses can be used to access and/or modify structured data:

#+BEGIN_SRC elixir
  # Extract a value from a simple map:

  person = %{name: "Homer"}
  nameLens = Focus.Lens.makeLens(:name)

  Focus.Lens.view!(nameLens, person) == "Homer"
  # true

  Focus.Lens.set(nameLens, person, "Bart")
  # %{name: "Bart"}

  Focus.Lens.over(nameLens, person, &String.upcase/1)
  # %{name: "HOMER"}
#+END_SRC

Their real utility comes in operating on nested data. Lenses can be created by composing other lenses in order to traverse a data structure:

#+BEGIN_SRC elixir
  person = %{
    name: "Homer",
    address: %{
      locale: %{
        number: 742,
        street: "Evergreen Terrace",
        city: "Springfield",
      },
      state: "???"
    }
  }

  # To access the street, we can compose the lenses that lead there from the top level.
  # Lenses can be composed with Focus.Lens.compose/2, or the infix (~>) operator.

  address = Focus.Lens.makeLens(:address)
  locale =  Focus.Lens.makeLens(:locale)
  street =  Focus.Lens.makeLens(:street)

  address
  ~> locale
  ~> street
  |> Focus.Lens.view!(person)
  # "Evergreen Terrace"

  address
  ~> locale
  ~> street
  |> Focus.Lens.set(person, "Fake Street")
  # person = %{
  #   name: "Homer",
  #   address: %{
  #     locale: %{
  #       number: 742,
  #       street: "Fake Street",
  #       city: "Springfield",
  #     },
  #     state: "???"
  #   }
  # }
#+END_SRC

** Functions 
  + Focus.Lens.makeLens/1
  + Focus.Lens.compose/2 (~>)
  + Focus.Lens.view!/2
  + Focus.Lens.view/2
  + Focus.Lens.set/3
  + Focus.Lens.over/3
  + Focus.Lens.apply_list/2
** Installation

If [[https://hex.pm/docs/publish][available in Hex]], the package can be installed as:

  1. Add `focus` to your list of dependencies in `mix.exs`:

    ```elixir
    def deps do
      [{:focus, "~> 0.1.0"}]
    end
    ```

  2. Ensure `focus` is started before your application:

    ```elixir
    def application do
      [applications: [:focus]]
    end
    ```

** References
+ [[https://www.schoolofhaskell.com/user/tel/a-little-lens-starter-tutorial][A Little Lens Starter Tutorial]]
+ [[https://www21.in.tum.de/teaching/fp/SS15/papers/17.pdf][Lenses in Functional Programming]]
+ [[https://hackage.haskell.org/package/lens-tutorial-1.0.2/docs/Control-Lens-Tutorial.html][Control.Lens Tutorial]]