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Compositional compiler verification is a difficult problem that focuses on separate compilation of program components with possibly different verified compilers. Logical relations are widely used in proving correctness of program transformations in higher-order languages; however, they do not scale to compositional verification of multi-pass compilers due to their lack of transitivity. The only known technique to apply to compositional verification of multi-pass compilers for higher-order languages is parametric inter-language simulations (PILS), which is however significantly more complicated than traditional proof techniques for compiler correctness. In this paper, we present a novel verification framework forlightweight compositional compiler correctness. We demonstrate that by imposing the additional restriction that program components are compiled by pipelines that go throughthe same sequence of intermediate representations, logical relation proofs can be transitively composed in order to derive an end-to-end compositional specification for multi-pass compiler pipelines. Unlike traditional logical-relation frameworks, our framework supports divergence preservation—even when transformations reduce the number of program steps. We achieve this by parameterizing our logical relations with a pair ofrelational invariants. We apply this technique to verify a multi-pass, optimizing middle-end pipeline for CertiCoq, a compiler from Gallina (Coq’s specification language) to C. The pipeline optimizes and closure-converts an untyped functional intermediate language (ANF or CPS) to a subset of that language without nested functions, which can be easily code-generated to low-level languages. Notably, our pipeline performs more complex closure-allocation optimizations than the state of the art in verified compilation. Using our novel verification framework, we prove an end-to-end theorem for our pipeline that covers both termination and divergence and applies to whole-program and separate compilation, even when different modules are compiled with different optimizations. Our results are mechanized in the Coq proof assistant.
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Fully Composable and Adequate Verified Compilation with Direct Refinements between Open Modules
Verified compilation of open modules (i.e., modules whose functionality depends on other modules) provides a foundation for end-to-end verification of modular programs ubiquitous in contemporary software. However, despite intensive investigation in this topic for decades, the proposed approaches are still difficult to use in practice as they rely on assumptions about the internal working of compilers which make it difficult for external users to apply the verification results. We propose an approach to verified compositional compilation without such assumptions in the setting of verifying compilation of heterogeneous modules written in first-order languages supporting global memory and pointers. Our approach is based on the memory model of CompCert and a new discovery that a Kripke relation with a notion of memory protection can serve as a uniform and composable semantic interface for the compiler passes. By absorbing the rely-guarantee conditions on memory evolution for all compiler passes into this Kripke Memory Relation and by piggybacking requirements on compiler optimizations onto it, we get compositional correctness theorems for realistic optimizing compilers as refinements that directly relate native semantics of open modules and that are ignorant of intermediate compilation processes. Such direct refinements support all the compositionality and adequacy properties essential for verified compilation of open modules. We have applied this approach to the full compilation chain of CompCert with its Clight source language and demonstrated that our compiler correctness theorem is open to composition and intuitive to use with reduced verification complexity through end-to-end verification of non-trivial heterogeneous modules that may freely invoke each other (e.g., mutually recursively).
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- PAR ID:
- 10602772
- Publisher / Repository:
- Association for Computing Machinery (ACM)
- Date Published:
- Journal Name:
- Proceedings of the ACM on Programming Languages
- Volume:
- 8
- Issue:
- POPL
- ISSN:
- 2475-1421
- Format(s):
- Medium: X Size: p. 2160-2190
- Size(s):
- p. 2160-2190
- Sponsoring Org:
- National Science Foundation
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