Many of the limitations associated with Haskell type classes can be solved very cleanly with lenses. This lens-driven programming is more explicit but significantly more general and (in my opinion) easier to use.
All of these examples will work with any -like library, but I will begin with the library to provide simpler types which better type inference and better type errors and then later transition to the library which has a larger set of utilities.
Case study #1 - bias
Let's begin with a simple example - the instance for :fmap (+ 1) (Right 2 ) = Right 3fmap (+ 1) (Left "Foo") = Left "Foo"
Some people object to this instance because it's biased to values. The only way we can use to transform values is to wrap in a .
These same people would probably like the library which provides an function that generalizes . Instead of using the type to infer what to transform we can explicitly specify what we wish to transform by supplying or :$ stack install lens-simple --resolver=lts-3.9$ stack ghci --resolver=lts-3.9>>> import Lens.Simple>>> over _Right (+ 1) (Right 2)Right 3>>> over _Right (+ 1) (Left "Foo")Left "Foo>>> over _Left (++ "!") (Right 2)Right 2>>> over _Left (++ "!") (Left "Foo")Left "Foo!"
The inferred types are exactly what we would expect:>>> :type over _Rightover _Right :: (b -> b') -> Either a b -> Either a b'>>> :type over _Leftover _Left :: (b -> b') -> Either b b1 -> Either b' b1
Same thing for tuples. only lets us transform the second value of a tuple, but lets us specify which one we want to transform:>>> over _1 (+ 1) (2, "Foo")(3,"Foo")>>> over _2 (++ "!") (2, "Foo")(2,"Foo!")
We can even transform of the values in the tuple if they share the same type:>>> over both (+ 1) (3, 4)(4,5)
Again, the inferred types are exactly what we expect:>>> :type over _2over _2 :: (b -> b') -> (a, b) -> (a, b')>>> :type over _1over _1 :: (b -> b') -> (b, b1) -> (b', b1)>>> :type over bothover both :: (b -> b') -> (b, b) -> (b', b')
Case study #2 - confusion
Many people have complained about the tuple instance for , which gives weird behavior like this in or later:>>> length (3, 4)1
We could eliminate all confusion by specifying what we intend to count at the term level instead of the type level:>>> lengthOf _2 (3, 4)1>>> lengthOf both (3, 4)2
This works for , too:>>> lengthOf _Right (Right 1)1>>> lengthOf _Right (Left "Foo")0>>> lengthOf _Left (Right 1)0>>> lengthOf _Left (Left "Foo")1
... and this trick is not limited to . We can improve any function by taking a lens instead of a type class constraint:>>> sumOf both (3, 4)7>>> mapMOf_ both print (3, 4)34 Case study #3 - Monomorphic containers
doesn't work on because is not a type constructor and has no type parameter that we can map over. Some people use the or packages to solve this problem, but I prefer to use lenses. These examples will require the library which has more batteries included.
For example, if I want to transform each character of a value I can use the optic:$ stack install lens --resolver=lts-3.9 # For `text` optics$ stach ghci --resolver=lts-3.9>>> import Control.Lens>>> import Data.Text.Lens>>> import qualified Data.Text as Text>>> let example = Text.pack "Hello, world!">>> over text succ example"Ifmmp-!xpsme/""
I can use the same optic to loop over each character:>>> mapMOf_ text print example'H''e''l''l''o'','' ''w''o''r''l''d''!'
There are also optics for s, too:>>> import Data.ByteString.Lens>>> import qualified Data.ByteString as ByteString>>> let example2 = ByteString.pack [0, 1, 2]>>> mapMOf_ bytes print example2012
The lens approach has one killer feature over and which is that you can be explicit about what exactly you want to map over. For example, suppose that I want to loop over the bitsof a instead of the bytes. Then I can just provide an optic that points to the bits and everyting "just works":>>> import Data.Bits.Lens>>> mapMOf_ (bytes . bits) print example2FalseFalseFalseFalseFalseFalseFalseFalseTrueFalseFalseFalseFalseFalseFalseFalseFalseTrueFalseFalseFalseFalseFalseFalse
The or packages do not let you specify what you want to loop over. Instead, the and type classes guess what you want the elements to be, and if they guess wrong then you are out of luck.Conclusion
Here are some more examples to illustrate how powerful and general the lens approach is over the type class approach.>>> lengthOf (bytes . bits) example224>>> sumOf (both . _1) ((2, 3), (4, 5))6>>> mapMOf_ (_Just . _Left) print (Just (Left 4))4>>> over (traverse . _Right) (+ 1) [Left "Foo", Right 4, Right 5][Left "Foo",Right 5,Right 6]
Once you get used to this style of programming you begin to prefer specifying things the term level instead of relying on type inference or wrangling with s.