Converting a large mathematical software package written in C++ to C++20 modules

I really wonder whether LLMs are helpful in this case. This kind of task should be the forte of LLMs: well-defined syntax and requirements, abundant training material available, and outputs that are verifiable and validatable.

Perhaps we should use LLMs to convert all the legacy programs written in Fortran or COBOL into modern languages.

You are far from the first person to have this very, very bad idea.

No, LLMs are not good at refactoring.