Abstract
We define nominal equational problems of the form \(\exists \overline{W} \forall \overline{Y} : P\), where \(P\) consists of conjunctions and disjunctions of equations \(s\approx _\alpha t\), freshness constraints \(a\#t\) and their negations: \(s \not \approx _\alpha t\) and , where \(a\) is an atom and \(s, t\) nominal terms. We give a general definition of solution and a set of simplification rules to compute solutions in the nominal ground term algebra. For the latter, we define notions of solved form from which solutions can be easily extracted and show that the simplification rules are sound, preserving, and complete. With a particular strategy for rule application, the simplification process terminates and thus specifies an algorithm to solve nominal equational problems. These results generalise previous results obtained by Comon and Lescanne for first-order languages to languages with binding operators. In particular, we show that the problem of deciding the validity of a first-order equational formula in a language with binding operators (i.e., validity modulo \(\alpha \)-equality) is decidable.
First author partially founded by PrInt MAT-UnB-CAPES and CNPq grant numbers Ed 41/2017 and 07672/2017-4. Third author partially supported by DPI/UnB - 03/2020. Fourth author supported by NWO TOP project “Implicit Complexity through Higher Order Rewriting” (ICHOR), NWO 612.001.803/7571.
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Ayala-Rincón, M., Fernández, M., Nantes-Sobrinho, D., Vale, D. (2021). Nominal Equational Problems. In: Kiefer, S., Tasson, C. (eds) Foundations of Software Science and Computation Structures. FOSSACS 2021. Lecture Notes in Computer Science(), vol 12650. Springer, Cham. https://doi.org/10.1007/978-3-030-71995-1_2
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