J.-P. Jouannaud and A. Rubio. Higher-order recursive path orderings `a la carte'. 2001. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Well-Founded Recursive Relations - Goubault-Larrecq (2001) (1 citation) (Correct)
....the tradition in calculus circles, exemplified by the Tait Girard technique [10] is to show termination by structural induction on terms, backed by auxiliary well founded inductions. In fact, the recursive path ordering can be proved terminating by structural induction on terms, as noticed in [14]. Prompted by [12] we wrote a direct inductive proof of the termination of the recursive path ordering rpo based on a well founded precedence [4] which turned out to be surprisingly short. Our point is that this proof generalizes considerably, while remaining short and constructive, and ....
....classical in the calculus. Similar techniques are extensively used in [7] where several proofs of termination consist in showing that for every substitution mapping variables to terminating terms, the term t terminates by induction on some well founded measure on t and . Jouannaud and Rubio [14] also notice that recursive path orderings can be shown well founded by the same technique. However, our proof of Theorem 1 is in fact simpler: it does not consider substitutions, and proceeds directly on t. Naturally, Theorem 1 does not consider the higher order case. Theorem 2 does, and this ....
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J.-P. Jouannaud and A. Rubio. Higher-order recursive path orderings a la carte. Draft available at ftp://ftp.lri.fr/LRI/articles/jouannaud/horpo-full.ps.gz, 2001.
A Monotonic Higher-Order Semantic Path Ordering - Borralleras, Rubio (2000) (1 citation) Self-citation (Rubio) (Correct)
....to automatically generate the adequate quasi orderings I and Q (note that we are using the same kind of interpretations as in the first order case) and on the other hand to adapt the notion of dependency graph for the higher order case. 2. We can adapt, in the same way as it can be done for HORPO [JR01], the method to be applicable to higher order rewriting a la Nipkow [MN98] i.e. rewriting on terms in j long fi normal form. 3. We will study other possible interpretations to build I using functionals in a similar way as in [dP96] but with two relevant differences. First due to the fact ....
....if we normalize first, I will include trivially fi reduction. 4. We want to add to HOSPO more powerful cases to deal with terms headed by lambdas, which is, by now, the main weakness of the ordering, as well as some other improvements that have already been added to the initial version of HORPO [JR01]. 5. We want to analyze the relationship between our method and a recent constraintbased method developed in [Pie01] for proving termination of higher order logic programs. ....
J.-P. Jouannaud and A. Rubio. Higher-order Recursive Path Orderings `a la carte (draft), 2001.
A Monotonic Higher-Order Semantic Path Ordering - Borralleras, Rubio (2000) (1 citation) Self-citation (Rubio) (Correct)
....case) The method can be automated and its power has been shown by means of several examples which could not be handled by the previous methods. Finally let us mention some work already in progress and some future work we plan to do. 1. We can adapt, in the same way as it can be done for HORPO [JR01], the method to be applicable to higher order rewriting a la Nipkow [MN98] i.e. rewriting on terms in j long fi normal form. 2. We will study other possible interpretations to build I using functionals in a similar way as in [dP96] but with two relevant differences. First due to the fact ....
....if we normalize first, I will include trivially fi reduction. 3. We want to add to HOSPO more powerful cases to deal with terms headed by lambdas, which is, by now, the main weakness of the ordering, as well as some other improvements that have already been added to the initial version of HORPO [JR01]. 4. We want to analyze the relationship between our method and a recent constraintbased method developed in [Pie01] for proving termination of higher order logic programs. ....
J.-P. Jouannaud and A. Rubio. Higher-order Recursive Path Orderings `a la carte (draft), 2001.
Certified Higher-Order Recursive Path Ordering Adam Koprowski - Eindhoven University Of (Correct)
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J.-P. Jouannaud and A. Rubio. Higher-order recursive path orderings `a la carte'. 2001.
Well-foundedness of the higher-order recursive path ordering in.. - Koprowski (2004) (Correct)
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J.-P. Jouannaud and A. Rubio. Higher-order recursive path orderings ` la carte'. http: //www.lix.polytechnique.fr/Labo/Jean-Pierre.Jouannaud/biblio.html, 2003.
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