applicative (functional) bidirectional programming beyond composition chains https://bitbucket.org/kztk/app-lens
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A bidirectional transformation connects data in difference formats, maintaining consistency amid separate updates. The "lens" programming language---with Kmett's Haskell lens package being one of the most influentials---is a solution to this problem.
Many lens implementations (including Kmett's Haskell library) only support the point-free style of programming. Though concise at times, this style becomes less handy when programs get more complicated.
This module provides the infrastructure for programming complex
bidirectional transformations, by representing lenses as functions
that are subject to the normal applicative-style programming. For
example, let us consider the
unlines functions and to define a
lens version of it. In our framework we can program through pattern
matching and explicit recursion as in normal functional programming.
unlinesF :: [L s String] -> L s String unlinesF  = new "" unlinesF (x:xs) = catLineF x (unlinesF xs) where catLineF = lift2 catLineL
lift2 :: Lens' (a,b) c -> (forall s. L s a -> L s b -> L s
new :: a -> (forall s. L s a) lift lenses to functions.
The former is for binary lenses and the latter is for constant
lenses. We can then apply lenses as functions, alleviating the
need of specialized combinators. In the above, we omitted the
definition of a primitive lens
catLineL :: Lens' (String, String)
String that concatenates two strings with a newline in between.
Simply unlifting (
unliftT) such "lens functions"
gives us the desired lenses.
unlinesL :: Lens' [String] String unlinesL = unliftT unlinesF
The obtained lens works as expected.
>>> ["banana", "orange", "apple"] ^. unlinesL "banana\norange\napple\n" >>> ["banana", "orange", "apple"] & unlinesL .~ "Banana\nOrange\nApple\n" ["Banana","Orange","Apple"]
One may prefer to define
foldr. Indeed, we can
foldr as below because
unlinesF are simply
unlinesF = foldr (lift2 catLineL) (new "")
Here, the program is written in a point-free manner similar to that
of the other lens frameworks. But note that this
foldr is just
foldr, instead of a special combinator for lenses.
More examples can be found at "Examples" in the source code https://bitbucket.org/kztk/app-lens/downloads.
Remark. The applicative-style programming is possible in our implementation because a function representation different from Kmett's is used for lenses. As a result, when we program record-field access chains such as
src .^ l1 . l2 src & l1 . l2 .~ tgt'
The order of composition is inverted in our implementation.
src .^ unlift (lift l2 . lift l1) src & unlift (lift l2 . lift l1) .~ tgt'
This difference causes slight inconvenience for record updates, but is crucial in allowing the applicative-style lens programming we aim for.