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Lenses

Lenses is an erlang porting of haskell library Lens

lens

just include servial functions currently, the rest will be added later.

Lens

type Lens s t a b = forall f. Functor f => (a -> f b) -> (s -> f t)
lens:lens(s -> a, s -> b -> t) -> Lens s t a b

Lens = lens:lens(fun({_, A}) -> A end, fun({C, _}, B) ->  {C, B} end),
?assertEqual(world, getter:view(Lens, {hello, world})),
?assertEqual({hello, another_world}, setter:set(Lens, another_world, {hello, world})).

Traversal

type Traversal s t a b = forall f. Applicative f => (a -> f b) -> (s -> f t)
traversal:traverse() -> forall t. Traversable t => Traversal (t a) (t b) a b

Traversal = traversal:traverse(),
?assertEqual([2, 4], setter:over(Traversal, fun(A) -> A + 1 end, As)).

ISO

type Iso s t a b = forall p f. (Profunctor p, Functor f) => p a (f b) -> p s (f t) 
iso:iso(s -> a, b -> t) -> Iso s t a b

Iso = iso:iso(fun(A) -> identity:run_identity(A) end, fun(A) -> identity:identity(A) end),
?assertEqual(3, getter:view(Iso, {identity, 3})),
?assertEqual({identity, 1}, setter:set(Iso, 1, {identity, 3})),

Prism

type Prism s t a b = forall p f. (Choice p, Applicative f) => p a (f b) -> p s (f t)
prism:prism(b -> t, s -> Either t a) -> Prism s t a b

-include_lib("erlando/include/op.hrl").
Prism = prism:prism(fun(A) -> {cat, A} end, fun({cat, A}) -> {right, A}; (Other) -> {left, Other} end),
Traverse = traversa:traverse(),
Compose = Traverse /'.'/ Prism,
CatsAndDogs = [{cat, kitty}, {dog, snoopy}, {cat, coffee}],
?assertEqual([kitty, coffee], fold:to_list_of(Compose, CatsAndDogs)),
?assertEqual([{cat, {my, kitty}}, {dog, snoopy}, {cat, {my, coffee}}],
              setter:over(Compose, fun(Cat) -> {my, Cat} end, CatsAndDogs)).

Getter

type Getting r s a = (a -> Const r a) -> (s -> Const r s)
type Getter s a = forall r. Getting r s a
getter:view(Getting a s a, s) -> a

Fold

fold:to_list_of(Getting [a] s a, s) -> a

Setter

type Setter s t a b = (a -> Identity b) -> (s -> Identity t)
setter:over(Setter s t a b, a -> b, s) -> t

TypeClass & Instances

  • function (->) is an instance of Profunctor
  • Const r is an instance of Functor
  • Identity is an Instance of Functor
  • Choice is Profucntor
  • Applicative is Functor
  • Lens is Getter
  • Lens is Traversal
  • Traversal is Setter
  • Traversal is Fold
  • Iso is Lens
  • Iso is Prism
  • Prism is Traversal
  • Getter is Fold

Compose

Lenses could be compose by . because

(p a (f b) -> p s (f t)) -> (p x (f y) -> p a (f b)) -> (p x (f y) -> p s (f t))

MakeLenses

-compile({parse_transform, make_lenses}).
-record(state, {hello, world}).
-make_lenses([state, #{module => state}]).

generates

state:hello/0
state:world/0

which represents lenses of #state.hello, #state.world