Stanc.Std: Move over Analysis module

[WardBrian]

The most notable change here is the addition of our own vendored polymorphic set. This is based on OCaml's set implementation, but with polymorphic comparison swapped in. Remarkably, I've found that it is dramatically faster than Base.Set.Poly in our uses, presumably because Base.Set.Poly is storing the comparison function in the runtime representation still, even though it never changes

Submission Checklist

• Run unit tests
• Documentation
  • If a user-facing facing change was made, the documentation PR is here:
  • OR, no user-facing changes were made

Release notes

Copyright and Licensing

By submitting this pull request, the copyright holder is agreeing to
license the submitted work under the BSD 3-clause license (https://opensource.org/licenses/BSD-3-Clause)

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[codecov]

Codecov Report

❌ Patch coverage is 93.33333% with 28 lines in your changes missing coverage. Please review.
✅ Project coverage is 92.12%. Comparing base (c2093d3) to head (76c1fb4).

Files with missing lines	Patch %	Lines
src/analysis_and_optimization/Factor_graph.ml	78.26%	10 Missing ⚠️
src/analysis_and_optimization/Memory_patterns.ml	90.90%	4 Missing ⚠️
src/analysis_and_optimization/Mir_utils.ml	81.81%	4 Missing ⚠️
...rc/analysis_and_optimization/Monotone_framework.ml	97.58%	3 Missing ⚠️
src/analysis_and_optimization/Optimize.ml	94.82%	3 Missing ⚠️
src/analysis_and_optimization/Pedantic_analysis.ml	95.91%	2 Missing ⚠️
src/analysis_and_optimization/Partial_evaluator.ml	83.33%	1 Missing ⚠️
src/std/std.ml	85.71%	1 Missing ⚠️

Additional details and impacted files

@@                    Coverage Diff                    @@
##           std/stan_math_backend    #1661      +/-   ##
=========================================================
- Coverage                  92.17%   92.12%   -0.05%     
=========================================================
  Files                         70       70              
  Lines                      10128    10141      +13     
=========================================================
+ Hits                        9335     9342       +7     
- Misses                       793      799       +6     

Files with missing lines	Coverage Δ
src/analysis_and_optimization/Dataflow_types.ml	25.00% <100.00%> (+25.00%)	⬆️
src/analysis_and_optimization/Dataflow_utils.ml	100.00% <100.00%> (ø)
...analysis_and_optimization/Debug_data_generation.ml	81.63% <100.00%> (ø)
...c/analysis_and_optimization/Dependence_analysis.ml	100.00% <100.00%> (ø)
...nalysis_and_optimization/Pedantic_dist_warnings.ml	91.70% <100.00%> (ø)
src/middle/Index.ml	85.18% <ø> (ø)
src/stan_math_backend/Transform_Mir.ml	95.54% <100.00%> (ø)
src/analysis_and_optimization/Partial_evaluator.ml	90.95% <83.33%> (+0.02%)	⬆️
src/std/std.ml	90.65% <85.71%> (+0.55%)	⬆️
src/analysis_and_optimization/Pedantic_analysis.ml	96.08% <95.91%> (+0.49%)	⬆️
... and 5 more

... and 2 files with indirect coverage changes

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[nhuurre]

Looks like constant propagation got a bit smarter, but why?

[WardBrian]

I spent a few hours on trying to debug this and I couldn’t pinpoint the change.

I also threw whatever free credits of Claude github gives me, and it spun in circles but couldn’t identify anything either after spending the entire month’s allocation.

In the end, I think the fact that this wasn’t being propagated in master was a bug, and the relevant optimizations are only turned on for Oexperimental, so I gave up looking for the cause… if you can find anything without wasting too much time, I would still be curious!