This is probably a good question for @River707 , but I’m curious if there has been any consideration on how one might go about extending the MLIR side effects interfaces, etc. to deal with multiple memories. Effectively, we’re thinking about a model of effects that allows distinct factorings of what looks like classical memory effect (partial) orders. A quick look gives the impression that passes like CSE have the existing MemoryEffects classes baked in, etc.