Practical Formal Verification for MLIR Programs
This work addresses the critical problem of ensuring correctness in optimizing compilers for domain-specific MLIR-based toolchains, providing a practical verification method that is agnostic to program syntax and scheduling.
The paper presents a formal verifier for MLIR programs that checks semantic equivalence between original and transformed programs using a hybrid concrete-symbolic interpretation approach, achieving linear-time verification for a meaningful subset of MLIR. The verifier is demonstrated on AMD MLIR-AIR, MLIR-AIE toolchains, and hundreds of mlir-opt benchmarks.
Optimizing compilers have become a cornerstone for high-performance program generation in research and industry. Optimizations, including those implemented manually by a user and those target-specific and non-target-specific, are used to transform programs to achieve good performance. Although these optimizations are necessary for performance, assessing their correctness has remained a major challenge; the risk of incorrect code being deployed increases with unproven optimization flows. In this work, we target the formal verification of correctness of a transformed program by computing whether a pair of programs are semantically equivalent, one being a transformed version of the other. We restrict the class of programs supported to enable a hybrid concrete-symbolic interpretation approach to equivalence, which in turn is mostly agnostic to how the programs are implemented (syntax, schedule, storage, etc.). This approach can show equivalence in linear time with respect to the operations executed by the programs. We develop a verifier for a meaningful subset of MLIR, and report on the verification of the AMD MLIR-AIR and MLIR-AIE toolchains, as well as the standard mlir-opt on hundreds of benchmarks variants.