Focus

An experiment with functional optics[fn:1].

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. – Racket ‘lens’ documentation

Usage

To construct a lens:

# A lens for the key :name
Focus.Lens.make_lens(:name)

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

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

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:

# Extract a value from a simple map:

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

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

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.make_lens(:address)
locale =  Focus.Lens.make_lens(:locale)
street =  Focus.Lens.make_lens(: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: "???"
#   }
# }

Functions

Lens creation

• Focus.Lens.make_lens/1

Lens application

• Focus.Lens.view!/2
• Focus.Lens.view/2
• Focus.Lens.set/3
• Focus.Lens.over/3
• Focus.Lens.apply_list/2

Lens composition

• Focus.Lens.compose/2, (~>)
• Focus.Lens.alongside/2

Installation

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

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

2. Ensure focus is started before your application:

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

References

• A Little Lens Starter Tutorial
• Lenses in Functional Programming
• Control.Lens Tutorial

Footnotes

[fn:1] This library currently combines Lenses, Prisms, and Traversals in its implementation of Lens.