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.
References
Arusoaie, A., Lucanu, D.: Unification in matching logic. In: ter Beek, M.H., McIver, A., Oliveira, J.N. (eds.) FM 2019. LNCS, vol. 11800, pp. 502–518. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-30942-8_30
Chen, X., Roşu, G.: Applicative matching logic. Technical report (2019). http://hdl.handle.net/2142/104616. University of Illinois at Urbana-Champaign
Chen, X., Rosu, G.: Matching \(\mu \)-logic. In: Proceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2019), Vancouver, Canada, pp. 1–13. IEEE (2019). https://doi.org/10.1109/LICS.2019.8785675
Escobar, S., Sasse, R., Meseguer, J.: Folding variant narrowing and optimal variant termination. J. Log. Algebraic Program. 81(7–8), 898–928 (2012). https://doi.org/10.1016/j.jlap.2012.01.002
Futatsugi, K.: Fostering proof scores in CafeOBJ. In: Dong, J.S., Zhu, H. (eds.) ICFEM 2010. LNCS, vol. 6447, pp. 1–20. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16901-4_1
Goguen, J.A., Thatcher, J.W., Wagner, E.G.: An initial algebra approach to the specification, correctness, and implementation of abstract data types. Technical report. RC 6487, IBM Res. Rep (1976). See also Current Trends in Programming Methodology, vol. 4: Data Structuring, R. T. Yeh, Ed. Englewood Cliffs, NJ: Prentice-Hall 1978, 80–149 (1976)
Meseguer, J.: Variant-based satisfiability in initial algebras. Sci. Comput. Program. 154, 3–41 (2018). https://doi.org/10.1016/j.scico.2017.09.001
Meseguer, J.: Generalized rewrite theories, coherence completion, and symbolic methods. J. Log. Algebraic Methods Program. 110 (2020). https://doi.org/10.1016/j.jlamp.2019.100483
Meseguer, J.: Twenty years of rewriting logic. J. Log. Algebraic Program. 81(7), 721–781 (2012). https://doi.org/10.1016/j.jlap.2012.06.003
Roşu, G.: Matching logic. Log. Methods Comput. Sci. 13(4), 1–61 (2017)
Skeirik, S., Stefanescu, A., Meseguer, J.: A constructor-based reachability logic for rewrite theories. In: Fioravanti, F., Gallagher, J.P. (eds.) LOPSTR 2017. LNCS, vol. 10855, pp. 201–217. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94460-9_12
Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pac. J. Math. 5(2), 285–309 (1955)
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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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