The Concrete Optimizer is invoked on a representation of the program
in the high-level FHELinalg / FHE Dialects and yields a solution with
a one-to-one mapping of operations to keys. However, the abstractions
used by these dialects do not allow for references to keys and the
application of the solution is delayed until the pipeline reaches a
representation of the program in the lower-level TFHE dialect. Various
transformations applied by the pipeline along the way may break the
one-to-one mapping and add indirections into producer-consumer
relationships, resulting in ambiguous or partial mappings of TFHE
operations to the keys. In particular, explicit frontiers between
optimizer partitions may not be recovered.
This commit preserves explicit frontiers between optimizer partitions
as `optimizer.partition_frontier` operations and lowers these to
keyswitch operations before parametrization of TFHE operations.
The current pass applying the parameters determined by the optimizer
to the IR propagates the parametrized TFHE types to operations not
directly tagged with an optimizer ID only under certain conditions. In
particular, it does not always properly propagate types into nested
regions (e.g., of `scf.for` loops).
This burdens preceding transformations that are applied in between the
invocation of the optimizer and the parametrization pass with
data-flow analysis and book-keeping in order to tag newly inserted
operations with the right optimizer IDs that ensure proper
parametrization.
This commit replaces the current parametrization pass with a new pass
that propagates parametrized TFHE types up and down def-use chains
using type inference and a proper rewriter. The pass is limited to the
operations supported by `TFHEParametrizationTypeResolver::resolve`.
