Using lenses to mappend two fields of a record

Question

I'm trying to get used to some basic lens features. I started with the following type and function, before trying to introduce lenses:

import qualified Data.Set as S

data Sets = Sets {pending, placed, open :: S.Set Int}
interesting :: Sets -> [Int]
interesting = toList . pending <> placed

i.e., I want the union of the pending and placed nodes, expressed as a list (I later use the result in a list comprehension, so a set is inconvenient).

My basic question is: How do I replicate this using tools from lens? What follows below is skippable if you have a good answer to that question; it's a record of my own beginner explorations of that space.

I renamed the fields to give myself lenses:

{-# LANGUAGE TemplateHaskell #-}
import Control.Lens
import qualified Data.Set as S

data Sets = Sets {_pending, _placed, _open :: S.Set Int}
makeLenses ''Sets

and now wish to reimplement interesting. Of course, it is not hard to do without lenses (toList . _pending <> _placed), but I am trying to get the hang of lenses, and this seems a useful exercise.

My first thought is that pending and placed are still both functions, and I still want to pointwise-mappend things that are sorta related to their results but not really, so pending <> placed ought to be at least interesting to look at:

*Main Data.Foldable> :t pending <> placed
pending <> placed
  :: (Semigroup (f Sets), Functor f) =>
     (S.Set Int -> f (S.Set Int)) -> Sets -> f Sets

Now, what is this type, and what operations can I perform on it? It looks sorta like a constrained Getter, maybe, even though I can't get GHCI to tell me what the constraints are by writing :t pending <> placed :: Getter _s _a. We can try passing it to view anyway, which wants a Getter, and that works:

*Main Data.Foldable> :t view (pending <> placed)
view (pending <> placed) :: MonadReader Sets m => m (S.Set Int)

which, okay, that's a generalization of Sets -> S.Set Int, and I can compose that with toList to get back what I had to begin with:

*Main Data.Foldable> :t toList . view (pending <> placed)
toList . view (pending <> placed) :: Sets -> [Int]

But this doesn't seem very satisfying: it's just what I had before but with an extra view call, and I don't feel like I used any of the power of lenses here. I also don't really understand what pending <> placed "means" in this context.

The other thing I considered is that what I want to do is a lot like foldMap, and what I have is kinda like a Getter, so I should be able to do some foldMapOf.

*Main Data.Foldable> :t foldMapOf (pending <> placed)
foldMapOf (pending <> placed)
  :: Semigroup r => (S.Set Int -> r) -> Sets -> r

This needs one more argument, and the obvious candidate is toList:

*Main Data.Foldable> :t foldMapOf (pending <> placed) toList
foldMapOf (pending <> placed) toList :: Sets -> [Int]

This has the right type, but alas different semantics: it uses <> after the conversion to [Int] rather than on the underlying Set Ints, so if _pending and _placed share elements, we get duplicate copies in the result.

Another thing I could do would be to use toListOf (pending <> placed), yielding a list of sets, and then use ordinary non-lens functions to mush those together:

*Main Data.Foldable> :t toList . mconcat . toListOf (pending <> placed)
toList . mconcat . toListOf (pending <> placed) :: Sets -> [Int]

This works, but is rather ugly and seems to miss the point.

So, do lenses give me any better tools here? Have I chosen a problem so simple that I can't see the advantage of lenses over simple record-field getters?

Answer 1

Have I chosen a problem so simple that I can't see the advantage of lenses over simple record-field getters?

That's largely it, I'd say. Intuitively, pending <> placed is a read-only target: there is no sensible way to modify the union of the two sets as a part of the Sets structure, as it doesn't corresponds to anything actually in it. That's why you end up with a getter, which is, as you have found out, essentially a function.

*Main Data.Foldable> :t pending <> placed
pending <> placed
  :: (Semigroup (f Sets), Functor f) =>
     (S.Set Int -> f (S.Set Int)) -> Sets -> f Sets

Now, what is this type, and what operations can I perform on it? It looks sorta like a constrained Getter, maybe, even though I can't get GHCI to tell me what the constraints are by writing :t pending <> placed :: Getter _s _a.

While the type allows for some other not very relevant things, what you really want from it is f ~ Const (S.Set Int), which makes the mappend on the lenses actually mappend the retrieved sets. Specialising to Const does give you a getter, or, being fussy, a Getting. :t on that is slightly more helpful:

ghci> :t pending <> placed :: Getting _ _ _

<interactive>:1:34: error:
    • Found type wildcard ‘_’ standing for ‘S.Set Int’
      To use the inferred type, enable PartialTypeSignatures
    • In the third argument of ‘Getting’, namely ‘_’
      In the type ‘Getting _ _ _’
      In an expression type signature: Getting _ _ _

<interactive>:1:32: error:
    • Found type wildcard ‘_’ standing for ‘Sets’
      To use the inferred type, enable PartialTypeSignatures
    • In the second argument of ‘Getting’, namely ‘_’
      In the type ‘Getting _ _ _’
      In an expression type signature: Getting _ _ _

<interactive>:1:30: error:
    • Found type wildcard ‘_’ standing for ‘_’
      Where: ‘_’ is a rigid type variable bound by
               the inferred type of
                 it :: Semigroup _ => Getting _ Sets (S.Set Int)
               at <interactive>:1:1
      To use the inferred type, enable PartialTypeSignatures
    • In the first argument of ‘Getting’, namely ‘_’
      In the type ‘Getting _ _ _’
      In an expression type signature: Getting _ _ _