[Q] A few questions on additional variable metadata and C++ codegen

I have a few questions on how to improve the implementations for the upcoming varmat and OpenCL PRs and make them more maintainable. This would also cleanup how we do the transform MIR with OpenCL.

• how to store metadata for the variable to change the C++ codegen?

Example:

For matrix[N, N] a; in the parameters/TP/model block the default codegen is

Eigen::Matrix<local_scalar_t__, -1, -1> a;

but with "varmat" we may want to generate that as

conditional_var_value_t<local_scalar_t__, Eigen::MatrixXd> a;

if applicable (conditional_var_value becomes var_value<Eigen::MatrixXd> if local_scalar_t__ = var.
Additionally if we want this parameter to reside on the GPU, that would be

conditional_var_value_t<local_scalar_t__, matrix_cl<double>> a;

We need info on what the underlying C++ type will be in the codegen as well as in the transform MIR passes where we try to figure out if varmat/opencl is applicable for a variable. Current OpenCL implementation and also my development branches rely un suffixes (opencl_ and varmat__) to store this info during transform MIR phase and to generate the different C++. But that is not ideal and also not maintainable I guess.

• how to best represent if a given Stan Math function signature is supported by varmat and OpenCL

We need lists of supported functions for both varmat and OpenCL. One idea would be to just have separate lists but I was hoping we could add this to the Stan Math signatures somehow.

The issue names no files, tests, or entry points. Start by locating the transform MIR and C++ codegen components, then identify where variable metadata and Stan Math function signatures are represented; done requires an agreed maintainable approach for varmat and OpenCL support.