abstract={Type-preserving translations are effective rigorous tools in the study of core programming calculi. In this paper, we develop a new typed translation that connects sequential and concurrent calculi; it is governed by type systems that control resource consumption. Our main contribution is the source language, a new resource λ-calculus with non-collapsing non-determinism and failures, dubbed uλ^{↯}_{⊕}. In uλ^{↯}_{⊕}, resources are split into linear and unrestricted; failures are explicit and arise from this distinction. We define a type system based on intersection types to control resources and fail-prone computation. The target language is 𝗌π, an existing session-typed π-calculus that results from a Curry-Howard correspondence between linear logic and session types. Our typed translation subsumes our prior work; interestingly, it treats unrestricted resources in uλ^{↯}_{⊕} as client-server session behaviours in 𝗌π.},
}
@InProceedings{Nantes2022Certified,
author={Ayala-Rinc\'{o}n, Mauricio and Fern\'{a}ndez, Maribel and Silva, Gabriel Ferreira and Sobrinho, Daniele Nantes},
title={{A Certified Algorithm for AC-Unification}},
booktitle={7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
pages={8:1--8:21},
series={Leibniz International Proceedings in Informatics (LIPIcs)},
abstract={Implementing unification modulo Associativity and Commutativity (AC) axioms is crucial in rewrite-based programming and theorem provers. We modify Stickel’s seminal AC-unification algorithm to avoid mutual recursion and formalise it in the PVS proof assistant. More precisely, we prove the adjusted algorithm’s termination, soundness, and completeness. To do this, we adapted Fages' termination proof, providing a unique elaborated measure that guarantees termination of the modified AC-unification algorithm. This development (to the best of our knowledge) provides the first fully formalised AC-unification algorithm.},
}
@InProceedings{Nantes2022Nominal,
author={Schmidt-Schau{\ss}, Manfred and Nantes-Sobrinho, Daniele},
title={{Nominal Anti-Unification with Atom-Variables}},
booktitle={7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
pages={7:1--7:22},
series={Leibniz International Proceedings in Informatics (LIPIcs)},
abstract={Anti-unification is the task of generalizing a set of expressions in the most specific way. It was extended to the nominal framework by Baumgarter, Kutsia, Levy and Villaret, who defined an algorithm solving the nominal anti-unification problem, which runs in polynomial time. Unfortunately, when an infinite set of atoms are allowed in generalizations, a minimal complete set of solutions in nominal anti-unification does not exist, in general. In this paper, we present a more general approach to nominal anti-unification that uses atom-variables instead of explicit atoms, and two variants of freshness constraints: NL_A-constraints (with atom-variables), and Eqr-constraints based on Equivalence relations on atom-variables. The idea of atom-variables is that different atom-variables may be instantiated with identical or different atoms. Albeit simple, this freedom in the formulation increases its application potential: we provide an algorithm that is finitary for the NL_A-freshness constraints, and for Eqr-freshness constraints it computes a unique least general generalization. There is a price to pay in the general case: checking freshness constraints and other related logical questions will require exponential time. The setting of Baumgartner et al. is improved by the atom-only case, which runs in polynomial time and computes a unique least general generalization.},
