Use pure UFL/basix.ufl forms in compilation in DOLFINx Python interface about dolfinx HOT 4 OPEN

def compile_form(form: ufl.Form, comm: MPI.Intracomm) -> GeneralForm:

In most other other functions (mesh, fem, nls modules) the mpi_comm is first argument. Good to keep a consistent API.

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This may be useful for implementing multigrid methods where we also have the same forms defined on different meshes.

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I agree it would be nice to internally split form compilation and form creation, such that is it possible to create forms with different data as you propose.
With that, form creation (Python way) using coefficient and constant indices could be removed, as you can then rewrite the default dolfinx.fem.form() to use the low level compile_form and create_form and deduce maps from provided UFL form if not provided explicitly.

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This may be useful for implementing multigrid methods where we also have the same forms defined on different meshes.

That is one of the motivations, another motivation is to make it possible to make "libraries" of specific forms.
Say you develop some specific scheme for solving a PDE, and would like to publish the code. This makes it possible to publish a single code compatible with both Python and C++.

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