Add NonEmptyMap and NonEmptySet to containers

[David Feuer]

There are a few functions that need names and places. In addition to

    insert :: Ord a => a -> NESet a -> NESet a -- or whatever type name
    union :: Ord a => NESet a -> NESet a -> NESet a

we need

    insert?? :: Ord a => a -> Set a -> NESet a
    union?? :: Ord a => Set a -> NESet a -> NESet a

For maps, we probably need unions on both sides to take care of different
biases, and also need to deal with unionWith.

Another question: we currently have

    powerSet :: Set a -> Set (Set a)

Should we change that to

    powerSet :: Set a -> NESet (Set a)

or add a new function for that (where and by what name)?

For power sets of nonempty sets, there are several options, the most
fundamental of which is probably

    ??? :: NESet a -> NESet (NESet a)

Splitting functions for nonempty sets/maps can produce results of various
shapes. In particular, spanAntitone and partition for nonempty sets will
produce two sets, at least one of which is non-empty. Do we want something
like

    partition :: (a -> Bool) -> NESet a
       -> Either (NESet a, Set a) (Set a, NESet a)

or should we stick with

    partition :: (a -> Bool) -> NESet a ->
      (Set a, Set a)

or offer both by different names?

On Thu, Apr 18, 2019, 7:15 PM John Cotton Ericson
<John.Ericson at obsidian.systems> wrote:

> In https://github.com/haskell/containers/issues/608 I proposed adding
> non-empty variants of Map and Set, analogous to Data.List.NonEmpty for
> List, to containers. semigroupoids demonstrates the many uses and
> structure of non-empty containers in general, and libraries such as
> https://github.com/mstksg/nonempty-containers and
> https://github.com/andrewthad/non-empty-containers demonstrate the
> interest in non-empty maps and sets in particular. My favorite use-case is
> that they're needed to "curry" containers: for example, Map (k0, k1) v is
> isomorphic not to Map k0 (Map k1 v) but to Map k0 (NonEmptyMap k1 v). I
> like this use-case because it comes from the containers themselves.
>
>
>
>
> Importantly, there's no good way to do this outside of containers; doing
> so leads to imbalancing / extra indirection, or massive code duplication.
> If one wraps the container was an extra value like Data.List.NonEmpty,
> one's left with an unavoidable extra indirection/imbalance. One can rectify
> this by copying and modifying the implementation of containers, but that's
> hardly maintainable; even as though the algorithms are the same, enough
> lines are touched that merging upstream containers is nigh impossible.
>
> On the other hand, the non-empty containers can be elegantly and
> sufficiently implemented alongside their originals by taking the Bin
> constructor and breaking it out into it's own type, mutually recursive with
> the original. This avoids the indirection/imbalancing and code duplication
> problems: the algorithms work exactly as before creating the same trees
> (remember the UNPACK), and no code duplicated since the functions become
> mutually recursive matching the types.
>
> To briefly summarize the thread:
>
>    1. I proposed the issue after performing this same refactor on the
>    dependent-map package:
>    https://github.com/obsidiansystems/dependent-map/tree/non-empty, a
>    fork of containers.
>    2. I made https://github.com/haskell/containers/pull/616 which just
>    changes the types, to make sure UNPACK preserved the importance.
>    3. https://gist.github.com/Ericson2314/58709d0d99e0c0e83ad266701cd71841
>    the benchmarks showed rather than degrading performance, PR 616 actually
>    *improved* it.
>
>  If there is preliminary consensus, I'll make a second PR on top which
> generalizes the functions like on my dependent-map branch.
>
> Thanks,
>
> John
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