Denotation-based Compositional Compiler Verification
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866918413636468736 |
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| author | Cheng, Zhang Wu, Jiyang Wang, Di Cao, Qinxiang |
| author_facet | Cheng, Zhang Wu, Jiyang Wang, Di Cao, Qinxiang |
| contents | A desired but challenging property of compiler verification is compositionality, in the sense that the compilation correctness of a program can be deduced incrementally from that of its substructures ranging from statements, functions, and modules. This article proposes a novel compiler verification framework based on denotational semantics for better compositionality, compared to previous approaches based on small-step operational semantics and simulation theories. Our denotational semantics is defined by semantic functions that map a syntactic component to a semantic domain composed of multiple behavioral \emph{sets}, with compiler correctness established through behavior refinement between the semantic domains of the source and target programs. The main contributions of this article include proposing a denotational semantics for open modules, a novel semantic linking operator, and a refinement algebra that unifies various behavior refinements, making compiler verification structured and compositional. Furthermore, our formalization captures the full meaning of a program and bridges the gap between traditional power-domain-based denotational semantics and the practical needs of compiler verification. We apply our denotation-based framework to verify the front-end of CompCert and typical optimizations on simple prototypes of imperative languages. Our results demonstrate that the compositionality from sub-statements to statements, from functions to modules, and from modules to the whole program can be effectively achieved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17297 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Denotation-based Compositional Compiler Verification Cheng, Zhang Wu, Jiyang Wang, Di Cao, Qinxiang Programming Languages A desired but challenging property of compiler verification is compositionality, in the sense that the compilation correctness of a program can be deduced incrementally from that of its substructures ranging from statements, functions, and modules. This article proposes a novel compiler verification framework based on denotational semantics for better compositionality, compared to previous approaches based on small-step operational semantics and simulation theories. Our denotational semantics is defined by semantic functions that map a syntactic component to a semantic domain composed of multiple behavioral \emph{sets}, with compiler correctness established through behavior refinement between the semantic domains of the source and target programs. The main contributions of this article include proposing a denotational semantics for open modules, a novel semantic linking operator, and a refinement algebra that unifies various behavior refinements, making compiler verification structured and compositional. Furthermore, our formalization captures the full meaning of a program and bridges the gap between traditional power-domain-based denotational semantics and the practical needs of compiler verification. We apply our denotation-based framework to verify the front-end of CompCert and typical optimizations on simple prototypes of imperative languages. Our results demonstrate that the compositionality from sub-statements to statements, from functions to modules, and from modules to the whole program can be effectively achieved. |
| title | Denotation-based Compositional Compiler Verification |
| topic | Programming Languages |
| url | https://arxiv.org/abs/2404.17297 |