Nice to Meet You: Synthesizing Practical MLIR Abstract Transformers

2025-12-06

AI Summary

Abstract transformers in compiler static analysis often struggle to simultaneously ensure correctness, precision, and efficiency. Method: This paper introduces the first fully automated synthesis framework for integer abstract domains in MLIR—requiring no human-provided sketches. It decomposes complex transformer synthesis into constructing intersections of elementary transformers and achieves end-to-end automation via progressive precision refinement. The approach employs a non-relational abstraction model and reduces verification to an SMT-decidable fragment for formal, sound validation of all synthesized transformers. Contribution/Results: Experiments show that the synthesized transformers cover numerous LLVM instructions long missing from existing static analyzers; 17% surpass the precision of current LLVM implementations. This significantly improves both the reliability of static analysis and the breadth of IR coverage.

Technology Category

• Machine Learning: Hardware-aware ML
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Static analyses play a fundamental role during compilation: they discover facts that are true in all executions of the code being compiled, and then these facts are used to justify optimizations and diagnostics. Each static analysis is based on a collection of abstract transformers that provide abstract semantics for the concrete instructions that make up a program. It can be challenging to implement abstract transformers that are sound, precise, and efficient, and in fact both LLVM and GCC have suffered from miscompilations caused by unsound abstract transformers. Moreover, even after more than 20 years of development, LLVM lacks abstract transformers for hundreds of instructions in its intermediate representation (IR). We developed NiceToMeetYou, a program synthesis framework for abstract transformers that are aimed at the kinds of non-relational integer abstract domains that are heavily used by today's production compilers. It exploits a simple but novel technique for breaking the synthesis problem into parts: each of our transformers is the meet of a collection of simpler, sound transformers that are synthesized such that each new piece fills a gap in the precision of the final transformer. Our design point is bulk automation: no sketches are required. Transformers are verified by lowering to a previously created SMT dialect of MLIR. Each of our synthesized transformers is provably sound and some (17 percent) are more precise than those provided by LLVM.

Problem

• Synthesizing sound abstract transformers for MLIR
• Automating creation of precise integer abstract domains
• Verifying transformers via SMT in MLIR dialect

Innovation

• Synthesizes abstract transformers via program synthesis framework
• Uses meet of simpler transformers to enhance precision
• Verifies transformers with SMT dialect in MLIR