Module `Lens`

Functional lenses.

Based on F# implementation in FSharpx (see src/FSharpx.Core/Lens.fs for the original implementation)

see http://bugsquash.blogspot.com/2011/11/lenses-in-f.html
Lenses in F#

see http://stackoverflow.com/questions/8179485/updating-nested-immutable-data-structures
Stackoverflow question about Updating nested immutable data structures

see http://stackoverflow.com/questions/5767129/lenses-fclabels-data-accessor-which-library-for-structure-access-and-mutatio
Haskell libraries for structure access and mutation

see http://www.youtube.com/watch?v=efv0SQNde5Q
Functional lenses for Scala by Edward Kmett on YouTube

see http://patternsinfp.wordpress.com/2011/01/31/lenses-are-the-coalgebras-for-the-costate-comonad/
Lenses are the coalgebras for the costate comonad by Jeremy Gibbons

type ('a, 'b) t = {

get : 'a -> 'b;
(*
Functional getter
*)
set : 'b -> 'a -> 'a;
(*
Functional setter
*)

}

Lens type definition

val modify : ('a, 'b) t -> ('b -> 'b) -> 'a -> 'a

Updates a value through a lens

Combinators

val compose : ('a, 'b) t -> ('c, 'a) t -> ('c, 'b) t

Sequentially composes two lenses

val pair : ('a, 'b) t -> ('c, 'd) t -> ('a * 'c, 'b * 'd) t

Pairs two lenses

val pair3 : 
  ('a, 'b) t ->
  ('c, 'd) t ->
  ('e, 'f) t ->
  ('a * 'c * 'e, 'b * 'd * 'f) t

Pairs three lenses

val cond : ('a -> bool) -> ('a, 'b) t -> ('a, 'b) t -> ('a, 'b) t

Selects a lens checking a predicate.

cond pred lensTrue lensFalse: pred is applied to source. If true, lensTrue is selected. If false, lensFalse is selected.

State monad integration

val get_state : ('a, 'b) t -> 'a -> 'b * 'a

Gets a value from the state monad.

val put_state : ('a, 'b) t -> 'b -> 'a -> unit * 'a

Puts a value in the state monad.

val modify_state : ('a, 'b) t -> ('b -> 'b) -> 'a -> unit * 'a

Modifies a value in the state monad.

Stock lenses

val ignore : ('a, unit) t

Trivial lens

val id : ('a, 'a) t

Identity lens

val first : ('a * 'b, 'a) t

Gets/sets the first element in a pair

val second : ('a * 'b, 'b) t

Gets/sets the second element in a pair

val head : ('a list, 'a) t

Gets/sets the first element in a list

val tail : ('a list, 'a list) t

Gets/sets the tail of a list

val for_hash : 'a -> (('a, 'b) Hashtbl.t, 'b option) t

Lens for a particular key in a hashtable

val for_assoc : 'a -> (('a * 'b) list, 'b option) t

Lens for a particular key in an associative list

val for_array : int -> ('a array, 'a) t

Lens for a particular position in an array

val for_list : int -> ('a list, 'a) t

Lens for a particular position in a list

val option_get : ('a option, 'a) t

Lens for extracting the value from an option type (same as Option.get)

List combinators

val list_map : ('a, 'b) t -> ('a list, 'b list) t

Creates a lens that maps the given lens in a list

Isomorphism

val xmap : ('a -> 'b) -> ('b -> 'a) -> ('c, 'a) t -> ('c, 'b) t

Applies an isomorphism to the value viewed through a lens

module Infix : sig ... end

Infix operators

module StateInfix : sig ... end

Infix operators for the state monad

package lens