  Polyhedral optimisation, a methodology that views nested loops as polyhedra
and searches for their optimal transformation regarding specific objectives
(parallelism, locality, etc.), sounds promising for mitigating difficulties in
automatically optimising hardware designs described by high-level synthesis
(HLS), which are typically software programs with nested loops. Nevertheless,
existing polyhedral tools cannot meet the requirements from HLS developers for
platform-specific customisation and software/hardware co-optimisation. This
paper proposes $\phi_{sm}$ (phism), a polyhedral HLS framework built on MLIR,
to address these challenges through progressive lowering multi-level
intermediate representations (IRs) from polyhedra to HLS designs.
