构造演算的类型化闭包转换

W. J. Bowman, Amal J. Ahmed
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引用次数: 10

摘要

依赖类型语言(如Coq)用于指定和验证源程序的完整功能正确性。通过编译生成的目标语言程序,可以使用保类型编译来保留这些规范和正确性证明。不幸的是,依赖类型的类型保持编译是困难的。本质上,问题在于依赖类型系统是围绕高级组合抽象设计的,以决定类型检查,但是编译会干扰用于推断运行时术语的类型系统规则。我们开发了一种类型保持的闭包转换转换,从具有强依赖对(Σ类型)的构造演算(CC) - coq的核心语言的一个子集-到类型安全的,依赖类型的编译器中间语言CC-CC。这项工作的核心挑战是如何将用于推理函数的源类型系统规则转换为用于推理闭包的目标类型系统规则。为了证明这些规则的正确性,我们在CC中给出了一个模型,证明了CC-CC的合理性,并证明了单独编译的正确性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Typed closure conversion for the calculus of constructions
Dependently typed languages such as Coq are used to specify and verify the full functional correctness of source programs. Type-preserving compilation can be used to preserve these specifications and proofs of correctness through compilation into the generated target-language programs. Unfortunately, type-preserving compilation of dependent types is hard. In essence, the problem is that dependent type systems are designed around high-level compositional abstractions to decide type checking, but compilation interferes with the type-system rules for reasoning about run-time terms. We develop a type-preserving closure-conversion translation from the Calculus of Constructions (CC) with strong dependent pairs (Σ types)—a subset of the core language of Coq—to a type-safe, dependently typed compiler intermediate language named CC-CC. The central challenge in this work is how to translate the source type-system rules for reasoning about functions into target type-system rules for reasoning about closures. To justify these rules, we prove soundness of CC-CC by giving a model in CC. In addition to type preservation, we prove correctness of separate compilation.
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