[WIP] Closures prototype

[nhuurre]

Summary

See the desing-doc stan-dev/design-docs#6 and the forum discussion https://discourse.mc-stan.org/t/closures-discussion/14932/

A proptotype autodiff interface for closures.

This builds on the variadic ODEs #1641

Checklist

• Math issue: ???

• Copyright holder: Niko Huurre

  The copyright holder is typically you or your assignee, such as a university or company. By submitting this pull request, the copyright holder is agreeing to the license the submitted work under the following licenses:
  - Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
  - Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

• the basic tests are passing

  • unit tests pass (to run, use: ./runTests.py test/unit)
  • header checks pass, (make test-headers)
  • dependencies checks pass, (make test-math-dependencies)
  • docs build, (make doxygen)
  • code passes the built in C++ standards checks (make cpplint)

• the code is written in idiomatic C++ and changes are documented in the doxygen

• the new changes are tested

[SteveBronder]

@nhuurre variadic ODEs are in, does this have blockers still?

[bbbales2]

@nhuurre Hey Niko, apologies it took me so long to get back to this, but is now a good time to work on this? It would be cool to get closures in for the next release (3 months from now).

[bbbales2]

@SteveBronder Oh yeah I was one of the blockers lol.

[nhuurre]

Superseded by #2094