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20
Generating Polynomial Orderings for Termination Proofs
 In Proc. 6th RTA, LNCS 914
, 1995
"... Most systems for the automation of termination proofs using polynomial orderings are only semiautomatic, i.e. the "right" polynomial ordering has to be given by the user. We show that a variation of Lankford's partial derivative technique leads to an easier and slightly more powerful method than mo ..."
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Cited by 46 (22 self)
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Most systems for the automation of termination proofs using polynomial orderings are only semiautomatic, i.e. the "right" polynomial ordering has to be given by the user. We show that a variation of Lankford's partial derivative technique leads to an easier and slightly more powerful method than most other semiautomatic approaches. Based on this technique we develop a method for the automated synthesis of a suited polynomial ordering.
The Calculus of Algebraic Constructions
 In Proc. of the 10th Int. Conf. on Rewriting Techniques and Applications, LNCS 1631
, 1999
"... Abstract. In a previous work, we proved that an important part of the Calculus of Inductive Constructions (CIC), the basis of the Coq proof assistant, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions with functions and predicates defined by hi ..."
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Cited by 27 (10 self)
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Abstract. In a previous work, we proved that an important part of the Calculus of Inductive Constructions (CIC), the basis of the Coq proof assistant, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions with functions and predicates defined by higherorder rewrite rules. In this paper, we prove that almost all CIC can be seen as a CAC, and that it can be further extended with nonstrictly positive types and inductiverecursive types together with nonfree constructors and patternmatching on defined symbols. 1.
Relating Two Categorical Models of Term Rewriting
 Rewriting Techniques and Applications, volume 914 of LNCS
, 1995
"... . In the last years there has been a growing interest towards categorical models for term rewriting systems (trs's). In our opinion, very interesting are those associating to each trs's a catenriched structure: a category whose homsets are categories. Interpreting rewriting steps as morphisms ..."
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Cited by 18 (11 self)
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. In the last years there has been a growing interest towards categorical models for term rewriting systems (trs's). In our opinion, very interesting are those associating to each trs's a catenriched structure: a category whose homsets are categories. Interpreting rewriting steps as morphisms in homcategories, these models provide rewriting systems with a concurrent semantics in a clean algebraic way. In this paper we provide a unified presentation of two models recently proposed in literature by Jos'e Meseguer [Mes90, Mes92, MOM93] and John Stell [Ste92, Ste94], respectively, pursuing a critical analysis of both of them. More precisely, we show why they are to a certain extent unsatisfactory in providing a concurrent semantics for rewriting systems. It turns out that the derivation space of Meseguer's Rewriting Logic associated with each term (i.e., the set of coinitial computations) fails in general to form a prime algebraic domain: a condition that is generally cons...
Code generation based on formal BURS theory and heuristic search
 Acta Informatica
, 1997
"... BURS theory provides a powerful mechanism to efficiently generate pattern matches in a given expression tree. BURS, which stands for bottomup rewrite system, is based on term rewrite systems, to which costs are added. We formalise the
underlying theory, and derive an algorithm that computes all pat ..."
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Cited by 17 (2 self)
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BURS theory provides a powerful mechanism to efficiently generate pattern matches in a given expression tree. BURS, which stands for bottomup rewrite system, is based on term rewrite systems, to which costs are added. We formalise the
underlying theory, and derive an algorithm that computes all pattern matches. This algorithm terminates if the term rewrite system is finite. We couple this algorithm with
the wellknown search algorithm A* that carries out pattern selection. The search algorithm is directed by a cost heuristic that estimates the minimum cost of code that
has yet to be generated. The advantage of using a search algorithm is that we need to compute only those costs that may be part of an optimal rewrite sequence (and not the costs of all possible rewrite sequences as in dynamic programming). A system that implements the algorithms presented in this work has been built.
Cubical Sets And Their Site
 Theory Appl. Categ
, 2003
"... Extended cubical sets (with connections and interchanges) are presheaves on a ground category, the extended cubical site K, corresponding to the (augmented) simplicial site, the category of finite ordinals. We prove here that K has characterisations similar to the classical ones for the simplicia ..."
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Cited by 15 (3 self)
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Extended cubical sets (with connections and interchanges) are presheaves on a ground category, the extended cubical site K, corresponding to the (augmented) simplicial site, the category of finite ordinals. We prove here that K has characterisations similar to the classical ones for the simplicial analogue, by generators and relations, or by the existence of a universal symmetric cubical monoid ; in fact, K is the classifying category of a monoidal algebraic theory of such monoids. Analogous results are given for the restricted cubical site I of ordinary cubical sets (just faces and degeneracies) and for the intermediate site J (including connections). We also consider briefly the reversible analogue, !K.
Inductive types in the calculus of algebraic constructions
 FUNDAMENTA INFORMATICAE 65(12) (2005) 61–86 JOURNAL VERSION OF TLCA’03
, 2005
"... In a previous work, we proved that almost all of the Calculus of Inductive Constructions (CIC), the basis of the proof assistant Coq, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions with functions and predicates defined by higherorder rewrit ..."
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Cited by 15 (4 self)
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In a previous work, we proved that almost all of the Calculus of Inductive Constructions (CIC), the basis of the proof assistant Coq, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions with functions and predicates defined by higherorder rewrite rules. In this paper, we prove that CIC as a whole can be seen as a CAC, and that it can be extended with nonstrictly positive types and inductiverecursive types together with nonfree constructors and patternmatching on defined symbols.
Scrimshaw: A language for document queries and transformations
 Electronic Publishing
, 1993
"... this paper is as follows. In Section 2 we look at some simple document queries. In Section 3 we look at more complex query examples. Section 4 considers a document type conversion example. Section 5 has conclusions. ..."
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Cited by 14 (0 self)
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this paper is as follows. In Section 2 we look at some simple document queries. In Section 3 we look at more complex query examples. Section 4 considers a document type conversion example. Section 5 has conclusions.
Feedback in an interactive equation solver
 Proceedings of the Web Advanced Learning Conference and Exhibition, WebALT 2006
, 2006
"... www.cs.uu.nl ..."
Complexity Classes and Rewrite Systems With Polynomial Interpretation
, 1998
"... We are concerned with functions over words which are computable by means of a rewrite system admitting polynomial interpretation termination proofs. We classify them according to the interpretations of successor symbols. This leads to the definition of three classes, which turn out to be exactly the ..."
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Cited by 9 (4 self)
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We are concerned with functions over words which are computable by means of a rewrite system admitting polynomial interpretation termination proofs. We classify them according to the interpretations of successor symbols. This leads to the definition of three classes, which turn out to be exactly the polytime, linear exponentialtime and doubly linear exponential time computable functions. As a consequence, we also characterize linear space computable. 1 Introduction We are interested in studying the relationship between termination orderings for rewrite systems and feasible computation. One might suspect that polynomial interpretations, introduced in [9], would be a good candidate for the investigation of small complexity classes of functions. Various implementations have been carried out [2, 6]. However, [8] have shown that any rewrite system with a polynomial interpretation termination proof admits doublyexponential derivations. The work of [3] initiated an alternative analysis of...
A formal theory of key conjuring
 In Proceedings of the 20th IEEE Computer Security Foundations Symposium (CSF’07
, 2007
"... apport de recherche ISSN 02496399 ISRN INRIA/RR6134FR+ENG ..."
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Cited by 6 (3 self)
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apport de recherche ISSN 02496399 ISRN INRIA/RR6134FR+ENG