Affiliation:
1. University of Illinois at Urbana-Champaign, USA
2. University of Illinois at Urbana-Champaign, USA / Runtime Verification, USA
Abstract
We propose a novel definition of binders using matching logic, where the binding behavior of object-level binders is directly inherited from the built-in exists binder of matching logic. We show that the behavior of binders in various logical systems such as lambda-calculus, System F, pi-calculus, pure type systems, can be axiomatically defined in matching logic as notations and logical theories. We show the correctness of our definitions by proving conservative extension theorems, which state that a sequent/judgment is provable in the original system if and only if it is provable in matching logic, in the corresponding theory. Our matching logic definition of binders also yields models to all binders, which are deductively complete with respect to formal reasoning in the original systems. For lambda-calculus, we further show that the yielded models are representationally complete, a desired property that is not enjoyed by many existing lambda-calculus semantics. This work is part of a larger effort to develop a logical foundation for the programming language semantics framework K (http://kframework.org).
Funder
National Science Foundation
Defense Advanced Research Projects Agency
Publisher
Association for Computing Machinery (ACM)
Subject
Safety, Risk, Reliability and Quality,Software
Cited by
9 articles.
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1. Matching-Logic-Based Understanding of Polynomial Functors and their Initial/Final Models;Electronic Proceedings in Theoretical Computer Science;2023-09-22
2. Generating Proof Certificates for a Language-Agnostic Deductive Program Verifier;Proceedings of the ACM on Programming Languages;2023-04-06
3. Capturing constrained constructor patterns in matching logic;Journal of Logical and Algebraic Methods in Programming;2023-01
4. Matching Logic Based on Ownership Transfer;International Journal of Software Engineering and Knowledge Engineering;2022-11-28
5. Nominal Matching Logic;Proceedings of the 24th International Symposium on Principles and Practice of Declarative Programming;2022-09-20