Add functors for the embedded Laplace approximation

[WardBrian]

This is a draft until stan-dev/math#3097 is updated and merged. It could probably also do with some more code-gen tests.

Similar to reduce_sum, these functions have too many rules to fit into the general variadic framework, so they have custom typechecking and errors, which make up most of this PR.

Closes #1511

Submission Checklist

• Run unit tests
• Documentation
  • If a user-facing facing change was made, the documentation PR is here: Issue Documentation for embedded Laplace approximation docs#873

Release notes

Added new functions for the embedded Laplace approximation.

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)

[codecov]

Codecov Report

Attention: Patch coverage is 96.50655% with 8 lines in your changes missing coverage. Please review.

Project coverage is 89.76%. Comparing base (93cda2f) to head (4e51cb8).
Report is 3 commits behind head on master.

Files with missing lines	Patch %	Lines
src/frontend/Typechecker.ml	96.33%	4 Missing ⚠️
src/frontend/SignatureMismatch.ml	90.90%	3 Missing ⚠️
src/frontend/Semantic_error.ml	97.67%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1513      +/-   ##
==========================================
+ Coverage   89.60%   89.76%   +0.15%     
==========================================
  Files          66       66              
  Lines        9707     9895     +188     
==========================================
+ Hits         8698     8882     +184     
- Misses       1009     1013       +4     

Files with missing lines	Coverage Δ
src/analysis_and_optimization/Memory_patterns.ml	89.00% <100.00%> (+0.30%)	⬆️
src/frontend/Pretty_printing.ml	92.38% <100.00%> (+0.07%)	⬆️
src/stan_math_backend/Cpp.ml	89.30% <100.00%> (+0.08%)	⬆️
src/stan_math_backend/Lower_expr.ml	93.93% <100.00%> (+0.28%)	⬆️
src/stan_math_backend/Lower_functions.ml	96.83% <100.00%> (-0.08%)	⬇️
src/stan_math_backend/Lower_program.ml	99.19% <100.00%> (+<0.01%)	⬆️
src/stan_math_backend/Numbering.ml	100.00% <100.00%> (ø)
src/stan_math_signatures/Stan_math_signatures.ml	86.13% <100.00%> (+2.23%)	⬆️
src/frontend/Semantic_error.ml	95.31% <97.67%> (+0.47%)	⬆️
src/frontend/SignatureMismatch.ml	85.88% <90.90%> (+0.28%)	⬆️
... and 1 more

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[WardBrian]

Ok, I think this is pretty much ready on the compiler side. There are a few things that need attention in the codegen or underlying C++:

• all the test models compile locally except laplace_neg_binomial_2_log -- see [WIP] Embedded Laplace Approximation math#3097 (comment) -- and laplace_nested_tuple, which I think is because of an issue in stan::math::apply.
• If I set the CI to use the current math branch, we get failures in the reduce sum code. See e.g. https://jenkins.flatironinstitute.org/blue/organizations/jenkins/Stan%2FStanc3/detail/PR-1513/18/pipeline

cc @SteveBronder

[WardBrian]

As of stan-dev/math@80904889a2, this is now passing CI