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Edward Kmett’s lens package. “JQuery for Haskell values”.

import Control.Lens

If you want to import the lens functions qualified, but the lens operators unqualified, then

import qualified Control.Lens
import           Control.Lens.Operators

Using Lenses

Control.Lens.Setter over setter f s setter %~ f $ s modify pure value
set setter b s setter .~ b $ s set pure value
setter %= f modify MonadState
setter .= b set MonadState
Control.Lens.Getter s ^. getter get pure value
view getter get MonadReader
use getter get MonadState


setter :: Setter s t a b
getter :: Getter s   a
s :: s
b :: b
f :: a -> b

Many other similar functions and operators are available.

Composing Lenses

Use . and pretend you're using a more mainstream language: outerLens . innerLens.

s = [Data.Map.singleton "bob" 7,
     Data.Map.fromList [("alice", 5), ("kerry", 8)],
     Data.Map.singleton "harry" 6]
t = element 1 . at "kerry" .~ Just 42 $ s
-- t = [Data.Map.singleton "bob" 7,
--      Data.Map.fromList [("alice", 5), ("kerry", 42)],
--      Data.Map.singleton "harry" 6]

Types (stab stab stabbity stab stab stab)

Mostly of the form

type Something s t a b = forall f. {- some constraint on f -} => (a -> f b) -> (s -> f t)

with a simple "primed" form

type Something' s a = Something s s a a

These allow us to

  • focus on an inner value of type a... within an outer value of type s; and perhaps
  • provide (a) new inner value(s) of type b... to produce a new outer value of type t

The simple types therefore describe lenses that produce new values without changing the types.

Setter s t a b set or modify value
Getter s a get value
Traversal s t a b focus on one, none or many values; can be used as a Setter;can be used as a Getter if a is a Monoid
Lens s t a b can be used as a Getter/Setter/Traversal/etc

Many other lens types are available. You can use a value of a more general type where a value of a more specific type is required. Some values are presented in this document with a more specific and less esoteric type than the more general and less common type they really have.

Predefined Lenses

Control.Lens.At at :: Ord k => k -> Lens' (Map k v) (Maybe v) Just v -> value is present; Nothing -> value is absent
at :: (Eq k, Hashable k) => k -> Lens' (HashMap k v) (Maybe v)
at :: Int -> Lens' (IntMap v) (Maybe v)
Control.Lens.Traversal element :: Int -> Traversable f => Traversal' (f v) v get/set/modify nth element of a container; no effect if no nth element

Many other predefined lenses are available.

Generating Lenses For Your Own Record Types

{-# LANGUAGE TemplateHaskell #-}
import Control.Lens.TH
data Foo a = Foo {_bar :: Int,
                  _baz :: a,
                  quux :: String}
$(makeLenses ''Foo)         -- creates `bar :: Lens' (Foo a) Int` and `baz :: Lens (Foo a) (Foo b) a b
$(makeLensesFor [("_bar", "bar"), ("_baz", "baz")] ''Foo)   -- the same

Many other TH lens functions are available providing varying amounts of control.