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Make DefaultStable and DefaultUnstable dispatchable and display without internals #56661

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Previously, DEFAULT_STABLE was a giant chain of algorithms reflecting the full sorting dispatch system. Now, it's simply DefaultStable(). This has a few minor impacts:

Previously, the public binding Base.Sort.DEFAULT_STABLE documented non-public implementation details of sorting dispatch in its extended help with a caviat that they are internal. Now, Base.Sort.DEFAULT_STABLE refers to the non-public binding Base.Sort.DefaultStable and implementation details are documented there with a warning that they are non-public.

Previously, dispatching on Base.Sort.DEFAULT_STABLE required writing ::typeof(Base.Sort.DEFAULT_STABLE) whereas now one could alternatively dispatch on the (internal) type Base.Sort.DefaultStable.

Previously Base.Sort.DEFAULT_STABLE === Base.Sort.DEFAULT_UNSTABLE so when writing sorting algorithms for custom collections it was impossible to determine if the user asked for a stable algorithm. Now DEFAULT_STABLE is DefaultStable() and DEFAULT_UNSTABLE is DefaultUnstable(). Both the algorithms expand to the same large chain of algorithms _DEFAULT_ALGORITHMS_FOR_VECTORS but it is possible to intercept them before that happens.

Base.Sort.DEFAULT_STABLE now prints as DefaultStable() instead of

julia> Base.Sort.DEFAULT_STABLE
Base.Sort.SubArrayOptimization(
    Base.Sort.MissingOptimization(
        Base.Sort.BoolOptimization(
            Base.Sort.Small{10}(
                Base.Sort.InsertionSortAlg(),
                Base.Sort.IEEEFloatOptimization(
                    Base.Sort.IsUIntMappable(
                        Base.Sort.Small{40}(
                            Base.Sort.InsertionSortAlg(),
                            Base.Sort.CheckSorted(
                                Base.Sort.ComputeExtrema(
                                    Base.Sort.ConsiderCountingSort(
                                        Base.Sort.CountingSort(),
                                        Base.Sort.ConsiderRadixSort(
                                            Base.Sort.RadixSort(),
                                            Base.Sort.Small{80}(
                                                Base.Sort.InsertionSortAlg(),
                                                Base.Sort.ScratchQuickSort(missing, missing,
                                                    Base.Sort.InsertionSortAlg()))))))),
                        Base.Sort.StableCheckSorted(
                            Base.Sort.ScratchQuickSort(missing, missing,
                                Base.Sort.InsertionSortAlg()))))))))

Factored out of #54494 at Triage's request (the git history reflects this history).

@LilithHafner LilithHafner added the sorting Put things in order label Nov 23, 2024
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