From an optimization perspective, such dialects are pretty much like the intermediate datastructures the "single-IR" style passes build internally anyway (eg. various loop analyses), just in a sharable and more consistent (if less performant) form.
Single IR passes from that perspective are roughly equivalent to MLIR-style `ir = loop_to_generic_dialect(my_loop_optimization(generic_to_loop_dialect(ir))`.
This assumes the existence of bidirectional dialect tranformations. Note that even LLVM IR, while a single IR, is technically multi-level as well, eg. for instruction selection, it needs to be canonicalized & expanded first, and feeding arbitrary IR into that pass will result in an exception (or sometimes even a segfault, considering it is C++).
Also, even though passes for single IR can theoretically be run in an arbitrary order, they are generally run in an order that can re-use (some) intermediate analysis results. This is, again, equivalent to minimizing the number of inter-dialect transformations in a multi-dialect IR.
Single IR passes from that perspective are roughly equivalent to MLIR-style `ir = loop_to_generic_dialect(my_loop_optimization(generic_to_loop_dialect(ir))`.
This assumes the existence of bidirectional dialect tranformations. Note that even LLVM IR, while a single IR, is technically multi-level as well, eg. for instruction selection, it needs to be canonicalized & expanded first, and feeding arbitrary IR into that pass will result in an exception (or sometimes even a segfault, considering it is C++).
Also, even though passes for single IR can theoretically be run in an arbitrary order, they are generally run in an order that can re-use (some) intermediate analysis results. This is, again, equivalent to minimizing the number of inter-dialect transformations in a multi-dialect IR.