Automatic Verification of BitVector Identities in SSA-Based Compiler IRs

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• Tobias Grosser (University of Cambridge)
• Thursday 28 November 2024, 17:00-18:00
• MR14 Centre for Mathematical Sciences.

If you have a question about this talk, please contact Jonas Bayer.

There is an increasing need for domain-specific reasoning in modern compilers. This has fueled the use of tailored intermediate representations (IRs) based on static single assignment (SSA), like in the MLIR compiler framework. Interactive theorem provers (ITPs) provide strong guarantees for the end-to-end verification of compilers (e.g., CompCert). However, modern compilers and their IRs evolve at a rate that makes proof engineering alongside them prohibitively expensive. Nevertheless, well-scoped push-button automated verification tools such as the Alive peephole verifier for LLVM -IR gained recognition in domains where SMT solvers offer efficient (semi) decision procedures. In this paper, we aim to combine the convenience of automation with the versatility of ITPs for verifying peephole rewrites across domain-specific IRs. We formalize a core calculus for SSA -based IRs that is generic over the IR and covers so-called regions (nested scoping used by many domain-specific IRs in the MLIR ecosystem). Our mechanization in the Lean proof assistant provides a user-friendly frontend for translating MLIR syntax into our calculus. We provide scaffolding for defining and verifying peephole rewrites, offering tactics to eliminate the abstraction overhead of our SSA calculus. We prove correctness theorems about peephole rewriting, as well as two classical program transformations. To evaluate our framework, we consider three use cases from the MLIR ecosystem that cover different levels of abstractions: (1) bitvector rewrites from LLVM , (2) structured control flow, and (3) fully homomorphic encryption. We envision that our mechanization provides a foundation for formally verified rewrites on new domain-specific IRs.

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This talk is part of the Formalisation of mathematics with interactive theorem provers series.

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