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- Article
HORPO with Computability Closure: A Reconstruction
Logic for Programming, Artificial Intelligence, and Reasoning•October 2007, pp 138-150• https://doi.org/10.1007/978-3-540-75560-9_12AbstractThis paper provides a new, decidable definition of the higher-order recursive path ordering in which type comparisons are made only when needed, therefore eliminating the need for the computability closure, and bound variables are handled ...
- research-article
Confluence in Non-Left-Linear Untyped Higher-Order Rewrite Theories
PPDP '21: Proceedings of the 23rd International Symposium on Principles and Practice of Declarative Programming•September 2021, Article No.: 8, pp 1-14• https://doi.org/10.1145/3479394.3479403We develop techniques based on van Oostrom’s decreasing diagrams that reduce confluence proofs to the checking of critical pairs for higher-order rewrite rules extending beta-reduction on pure lambda-terms. We show that confluence is preserved for a ...
- research-article
Drags: A compositional algebraic framework for graph rewriting
Theoretical Computer Science, Volume 777, Issue C•Jul 2019, pp 204-231 • https://doi.org/10.1016/j.tcs.2019.01.029AbstractWe are interested in a natural generalization of term-rewriting techniques to what we call drags, viz. finite, directed, ordered, rooted multigraphs, each vertex of which is labeled by a function symbol. To this end, we develop a rich ...
- research-article
Normal Higher-Order Termination
ACM Transactions on Computational Logic, Volume 16, Issue 2•March 2015, Article No.: 13, pp 1-38 • https://doi.org/10.1145/2699913We extend the termination proof methods based on reduction orderings to higher-order rewriting systems based on higher-order pattern matching. We accommodate, on the one hand, a weakly polymorphic, algebraic extension of Church’s simply typed λ-calculus ...
- article
From diagrammatic confluence to modularity
Theoretical Computer Science, Volume 464•December, 2012, pp 20-34 • https://doi.org/10.1016/j.tcs.2012.08.030This paper builds on a fundamental notion of rewriting theory that characterizes confluence of a (binary) rewriting relation, Klop's cofinal derivations. Cofinal derivations were used by van Oostrom to obtain another characterization of confluence of a ...
- Article
CoQMTU: A Higher-Order Type Theory with a Predicative Hierarchy of Universes Parametrized by a Decidable First-Order Theory
LICS '11: Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science•June 2011, pp 143-151• https://doi.org/10.1109/LICS.2011.37We study a complex type theory, a Calculus of Inductive Constructions with a predicative hierarchy of universes and a first-order theory T built in its conversion relation. The theory T is specified abstractly, by a set of constructors, a set of defined ...
- Article
Infinite families of finite string rewriting systems and their confluence
LPAR'10: Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning•October 2010, pp 387-401We introduce parameterized rewrite systems for describing infinite families of finite string rewrite systems depending upon non-negative integer parameters, as well as ways to reason uniformly over these families. Unlike previous work, the vocabulary on ...
- Article
Diagrammatic Confluence and Completion
ICALP '09: Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II•July 2009, pp 212-222• https://doi.org/10.1007/978-3-642-02930-1_18We give a new elegant proof that decreasing diagrams imply confluence based on a proof reduction technique, which is then the basis of a novel completion method which proof-reduction relation transforms arbitrary proofs into rewrite proofs even in ...
- Article
The Computability Path Ordering: The End of a Quest
CSL '08: Proceedings of the 22nd international workshop on Computer Science Logic•September 2008, pp 1-14• https://doi.org/10.1007/978-3-540-87531-4_1In this paper, we first briefly survey automated termination proof methods for higher-order calculi. We then concentrate on the higher-order recursive path ordering, for which we provide an improved definition, the Computability Path Ordering. This new ...
- Article
HORPO with computability closure: a reconstruction
LPAR'07: Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning•October 2007, pp 138-150This paper provides a new, decidable definition of the higherorder recursive path ordering in which type comparisons are made only when needed, therefore eliminating the need for the computability closure, and bound variables are handled explicitly, ...
- Article
Building decision procedures in the calculus of inductive constructions
CSL'07/EACSL'07: Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic•September 2007, pp 328-342It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an equivalent ...
- article
Polymorphic higher-order recursive path orderings
Journal of the ACM, Volume 54, Issue 1•March 2007, Article No.: 2, pp 1-48 • https://doi.org/10.1145/1206035.1206037This article extends the termination proof techniques based on reduction orderings to a higher-order setting, by defining a family of recursive path orderings for terms of a typed lambda-calculus generated by a signature of polymorphic higher-order ...
- Article
Higher-order termination: from kruskal to computability
LPAR'06: Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning•November 2006, pp 1-14• https://doi.org/10.1007/11916277_1Termination is a major question in both logic and computer science. In logic, termination is at the heart of proof theory where it is usually called strong normalization (of cut elimination). In computer science, termination has always been an important ...
- Article
Modular church-rosser modulo
RTA'06: Proceedings of the 17th international conference on Term Rewriting and Applications•August 2006, pp 96-107• https://doi.org/10.1007/11805618_8In [12], Toyama proved that the union of two confluent term-rewriting systems that share absolutely no function symbols or constants is likewise confluent, a property called modularity. The proof of this beautiful modularity result, technically based on ...
- Article
Higher-order orderings for normal rewriting
RTA'06: Proceedings of the 17th international conference on Term Rewriting and Applications•August 2006, pp 387-399• https://doi.org/10.1007/11805618_29We extend the termination proof methods based on reduction orderings to higher-order rewriting systems à la Nipkow using higher-order pattern matching for firing rules, and accommodate for any use of eta, as a reduction, as an expansion or as an ...
- article
Automatic Complexity Analysis for Programs Extracted from Coq Proof
Electronic Notes in Theoretical Computer Science (ENTCS), Volume 153, Issue 1•March, 2006, pp 35-53 • https://doi.org/10.1016/j.entcs.2005.08.005We describe an automatic complexity analysis mechanism for programs extracted from proofs carried out with the proof assistant Coq. By extraction, we mean the automatic generation of MiniML code [Pierre Letouzey. Programmation fonctionnelle certifiee - ...
- Article
Twenty years later
RTA'05: Proceedings of the 16th international conference on Term Rewriting and Applications•April 2005, pp 368-375• https://doi.org/10.1007/978-3-540-32033-3_27The first RTA conference took place in Dijon, in 1985. This year, 2005, it takes place in Nara. Nara and Dijon share a glorious past but can be considered as being “Sleeping Beauties”, after the title of a book by the Nobel price novelist yasunari ...
- chapter
Higher-Order rewriting: framework, confluence and termination
Equations are ubiquitous in mathematics and in computer science as well. This first sentence of a survey on first-order rewriting borrowed again and again characterizes best the fundamental reason why rewriting, as a technology for processing equations, ...
