Abstract
Constrained constructor patterns are pairs of a constructor term pattern and a quantifier-free first-order logic constraint, built from conjunction and disjunction. They are used to express state predicates for reachability logic defined over rewrite theories. Matching logic has been recently proposed as a unifying foundation for programming languages, specification and verification. It has been shown to capture several logical systems and/or models that are important for programming languages, including first-order logic with fixpoints and order-sorted algebra. In this paper, we investigate the relationship between constrained constructor patterns and matching logic. The comparison result brings us a mutual benefit for the two approaches. Matching logic can borrow computationally efficient proofs for some equivalences, and the language of the constrained constructor patterns can get a more logical flavor and more expressiveness.
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Notes
- 1.
This answers a question asked by Jacques Carette on the mathoverflow site (https://mathoverflow.net/questions/16180/formalizing-no-junk-no-confusion) ten years ago: Are there logics in which these requirements (“no junk, no confusion”) can be internalized?
- 2.
This is an informal notation because \([\![u| \varphi ]\!]\subseteq \bigcup _{i\in I}[\![v_i|\psi _i ]\!]\) is not exactly a formula.
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Chen, X., Lucanu, D., Roşu, G. (2020). Connecting Constrained Constructor Patterns and Matching Logic. In: Escobar, S., Martí-Oliet, N. (eds) Rewriting Logic and Its Applications. WRLA 2020. Lecture Notes in Computer Science(), vol 12328. Springer, Cham. https://doi.org/10.1007/978-3-030-63595-4_2
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