Practical Formal Verification for MLIR Programs

2026-05-01

AI Summary

This work proposes a hybrid concrete-symbolic interpretation method to efficiently verify semantic equivalence between original and optimized programs in MLIR, ensuring the correctness of optimization transformations. The approach supports diverse syntactic, scheduling, and memory representations and theoretically achieves linear-time complexity for equivalence checking. Building upon this method, the authors develop a formal verifier for a subset of MLIR and successfully apply it to the AMD MLIR-AIR and MLIR-AIE toolchains as well as the standard mlir-opt infrastructure. Evaluation across hundreds of benchmark variants demonstrates the verifier’s effectiveness in validating optimization pipelines, significantly enhancing the reliability of compiler optimizations within the MLIR ecosystem.

Abstract

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.

Problem

• formal verification
• semantic equivalence
• MLIR
• compiler optimization
• program correctness

Innovation

• formal verification
• semantic equivalence
• hybrid concrete-symbolic interpretation
• MLIR
• compiler correctness