Lenses
Accessing part of a structure¶
Lenses are the way to access and update parts of data structures in a pure functional way. Here are some examples using the lens package:
repl example
> import Control.Lens
> tuple = (True, ('a', 'b'))
-- simple example: accessing the values inside a tuple
> tuple ^. _1 -- (1)!
True
> tuple ^. _2
('a','b')
> tuple ^. (_2 . _1) -- (2)!
'a'
-- updating parts of a data structure
> tuple & _1 .~ 3 -- (3) (4)
(3,('a','b'))
> tuple & (_2 . _1) .~ 3
(True,(3,'b'))
> tuple & (_2 . _1) %~ toUpper
(True,('A','b'))
_1is a lens. It "points" towards a part of a data structure, in this case, the first element of a tuple.^.means: get the thing pointed to by the lens.(_2 . _1)is a lens too! It points towards the 1st element of the 2nd element of a tuple.- Note:
tuple & _1 .~ 3is a new tuple - it hasn't mutated the old one. &is just like$but in reverse:x & f = f x.
Updating part of a structure¶
You can also use the lens library to access or update multiple (or optional) parts of a data structure:
repl example
import Control.Lens
-- access multiple fields
> tuple = ((4, True), (3, False))
> tuple ^.. both -- (1)!
[(4,True),(3,False)]
> tuple ^.. both . _2 -- (2)!
[True,False]
-- update multiple values
> tuple & both . _2 %~ not
((4,False),(3,True))
-- example of an optional lookup
> ls = [(True, 'a'), (False, 'b'), (True, 'c')]
> ls ^.. ix 2 -- (3) (4)
[(True,'c')]
> ls ^.. ix 4
[]
-- an example with a dictionary, or Map
> import qualified Data.Map as M
> dictionary = M.fromList [("John", (True, 3)), ("Sally", (False, 1))]
> dictionary ^.. ix "John"
[(True,3)]
> dictionary ^.. ix "Jim"
[]
> dictionary ^.. (ix "John" . _1)
[True]
> dictionary & (ix "John" . _2) %~ (+1)
fromList [("John",(True,4)),("Sally",(False,1))]
bothis a lens, or more precisely, aTraversal.- Like other lenses and traversals,
bothcan be composed, here with_2. ix nlooks up the element at the nth index of a structure.- Since
ix nmay fail ifnis out of bounds, it must be used with^..
Note
The lens package has two properties which make it unfriendly:
- A large set of packages it depends on.
- Sophisticated use of very abstract typeclasses, which results in hard-to-interpret error messages:
repl example
import Control.Lens
> tuple = (True, ('a', 'b'))
-- scary error message
> tuple ^. (_1 . _1)
"No instance for (Field1 Bool Bool () ())"
-- another scary error message
> tuple2 = (True, False)
> tuple2 ^. both
"No instance for (Monoid Bool) arising from a use of ‘both’"
In either case, the error messages refer to typeclass constraints that your program requires, but without understanding the internals of the lens library, it is hard to make sense of these.
The optics package aims to address these problems, with a different set of tradeoffs.
Gotcha
Haskell is immutable, so when we talk about changing a data structure, we mean producing a new data structure that has that change. For example, to change the third element of [1,2,3] to 4 is to produce a new list [1,2,4].
Custom data¶
You can write lenses for custom types, or generate them automatically with Template Haskell (a macro extension to Haskell):
{-# LANGUAGE TemplateHaskell #-}
import Control.Lens
data Point a
= Point { _x :: a, _y :: a }
makeLenses ''Point -- (1)!
example = Point {_x = 2, _y = 3}
xVal = example ^. x
yVal = example ^. y
main = print xVal
- This is the syntax for a Template Haskell macro, here
makeLenses, whichControl.Lensexports.
Useful examples¶
The lens library has an enormous range of useful tools, some of which are not easily discoverable. Here are some examples:
Set¶
repl example
> import qualified Data.Set as S
> numberSet = S.fromList [1,2,3,5]
> numberSet
fromList [1,2,3,5]
> numberSet ^. contains 3
True
> numberSet ^. contains 4
False
> numberSet & contains .~ 4
-- even update a set this way!
> numberSet & contains 4 .~ True
fromList [1,2,3,4,5]
> numberSet & contains 3 %~ not
fromList [1,2,5]
Coercions¶
coercedis a lens, which points towards theBoolinside aB.
JSON¶
Lenses are particularly useful for working with JSON data, and can automate almost any querying or updating task, even very complex ones.
Let's use this JSON as an example, saved in "data/file.json":
{
"firstName": "John",
"lastName": "Smith",
"isAlive": true,
"age": 27,
"address": {
"streetAddress": "21 2nd Street",
"city": "New York",
"state": "NY",
"postalCode": "10021-3100"
},
"phoneNumbers": [
{
"type": "home",
"number": "212 555-1234"
},
{
"type": "office",
"number": "646 555-4567"
}
],
"children": [
"Catherine",
"Thomas",
"Trevor"
],
"spouse": null
}
repl example
-- read into a string
> json <- readFile "data/file.json"
> json
"{\n \"firstName\": \"John\",\n \"lastName\": \"Smith\",\n \"isAlive\": true,\n \"age\": 27,\n \"address\": {\n \"streetAddress\": \"21 2nd Street\",\n \"city\": \"New York\",\n \"state\": \"NY\",\n \"postalCode\": \"10021-3100\"\n },\n \"phoneNumbers\": [\n {\n \"type\": \"home\",\n \"number\": \"212 555-1234\"\n },\n {\n \"type\": \"office\",\n \"number\": \"646 555-4567\"\n }\n ],\n \"children\": [\n \"Catherine\",\n \"Thomas\",\n \"Trevor\"\n ],\n \"spouse\": null\n }"
-- imports
> import Data.Aeson
> import Data.Aeson.Lens
> import Text.Pretty.Simple
> import Control.Lens
-- view the underlying JSON data structure as a Haskell value "inside" the string:
> pPrint $ json ^.. _Value -- (3)!
[ Object
( fromList
[
( "address"
, Object
( fromList
[
( "city"
, String "New York"
)
,
( "postalCode"
, String "10021-3100"
)
,
( "state"
, String "NY"
)
,
( "streetAddress"
, String "21 2nd Street"
)
]
)
)
...
> query (_Value . key "address" . key "city") -- (2)!
[ String "New York" ]
> query (_Value . key "children" . nth 2)
[ String "Trevor" ]
> query (_Value . key "children" . nth 1)
[ String "Thomas" ]
> query (_Value . key "spouse" . nth 1) -- (4)!
[]
> query (_Value . key "children" . values)
[ String "Catherine"
, String "Thomas"
, String "Trevor"
]
- This is a Haskell data structure (of type
ValuefromData.Aeson) which represents the JSON. - As usual, we can compose lenses
pPrintis a pretty printing function. The lens (or more precisely, the traversal) is_Value.- Since there is no list inside the entry for "spouse", this returns no results.
The most powerful use cases involve recursively searching the JSON, using a lens which (lazily) points to every JSON subpart in the JSON as a whole:
repl example
-- for all Strings in the JSON, show them
> pPrint $ json ^.. _Value . cosmos . _String
[ "New York"
, "10021-3100"
, "NY"
, "21 2nd Street"
, "Catherine"
, "Thomas"
, "Trevor"
, "John"
, "Smith"
, "212 555-1234"
, "home"
, "646 555-4567"
, "office"
]
-- for all Strings in the JSON underneath the key "address", show them:
> pPrint $ json ^.. _Value . key "address" . cosmos . _String
[ "New York"
, "10021-3100"
, "NY"
, "21 2nd Street"
]
-- for all arrays in the JSON that contain at least 3 elements, show the third:
> pPrint $ json ^.. _Value . cosmos . _Array . ix 2
[ String "Trevor" ]
One can similarly update the raw JSON string in a structured way with lenses:
repl example
-- modify the string corresponding to the address's city to be uppercase
> json & _JSON' @String @Value . key "address" . key "city" . _String %~ T.map toUpper
"{\"address\":{\"city\":\"NEW YORK\",\"postalCode\":\"10021-3100\",\"state\":\"NY\",\"streetAddress\":\"21 2nd Street\"},\"age\":27,\"children\":[\"Catherine\",\"Thomas\",\"Trevor\"],\"firstName\":\"John\",\"isAlive\":true,\"lastName\":\"Smith\",\"phoneNumbers\":[{\"number\":\"212 555-1234\",\"type\":\"home\"},{\"number\":\"646 555-4567\",\"type\":\"office\"}],\"spouse\":null}"
Last update:
February 10, 2023
Created: January 12, 2023
Created: January 12, 2023