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Matching Power
 Proceedings of RTA’2001, Lecture Notes in Computer Science, Utrecht (The Netherlands
, 2001
"... www.loria.fr/{~cirstea,~ckirchne,~lliquori} Abstract. In this paper we give a simple and uniform presentation of the rewriting calculus, also called Rho Calculus. In addition to its simplicity, this formulation explicitly allows us to encode complex structures such as lists, sets, and objects. We pr ..."
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www.loria.fr/{~cirstea,~ckirchne,~lliquori} Abstract. In this paper we give a simple and uniform presentation of the rewriting calculus, also called Rho Calculus. In addition to its simplicity, this formulation explicitly allows us to encode complex structures such as lists, sets, and objects. We provide extensive examples of the calculus, and we focus on its ability to represent some object oriented calculi, namely the Lambda Calculus of Objects of Fisher, Honsell, and Mitchell, and the Object Calculus of Abadi and Cardelli. Furthermore, the calculus allows us to get object oriented constructions unreachable in other calculi. In summa, we intend to show that because of its matching ability, the Rho Calculus represents a lingua franca to naturally encode many paradigms of computations. This enlightens the capabilities of the rewriting calculus based language ELAN to be used as a logical as well as powerful semantical framework. 1
Rewrite Strategies in the Rewriting Calculus
 WRS 2003
, 2003
"... This paper presents an overview on the use of the rewriting calculus to express rewrite strategies. We motivate first the use of rewrite strategies by examples in the ELAN language. We then show how this has been modeled in the initial version of the rewriting calculus and how the matching power of ..."
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Cited by 18 (7 self)
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This paper presents an overview on the use of the rewriting calculus to express rewrite strategies. We motivate first the use of rewrite strategies by examples in the ELAN language. We then show how this has been modeled in the initial version of the rewriting calculus and how the matching power of this framework facilitates the representation of powerful strategies.
Antipattern matching
 In European Symposium on Programming – ESOP 2007, LNCS
, 2007
"... Abstract. It is quite appealing to base the description of patternbased searches on positive as well as negative conditions. We would like for example to specify that we search for white cars that are not station wagons. To this end, we define the notion of antipatterns and their semantics along w ..."
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Cited by 18 (6 self)
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Abstract. It is quite appealing to base the description of patternbased searches on positive as well as negative conditions. We would like for example to specify that we search for white cars that are not station wagons. To this end, we define the notion of antipatterns and their semantics along with some of their properties. We then extend the classical notion of matching between patterns and ground terms to matching between antipatterns and ground terms. We provide a rulebased algorithm that finds the solutions to such problems and prove its correctness and completeness. Antipattern matching is by nature different from disunification and quite interestingly the antipattern matching problem is unitary. Therefore the concept is appropriate to ground a powerful extension to patternbased programming languages and we show how this is used to extend the expressiveness and usability of the Tom language. 1
Termgraph rewriting via explicit paths
"... Abstract. The notion of path is classical in graph theory but not directly used in the term rewriting community. The main idea of this work is to raise the notion of path to the level of firstorder terms, i.e. paths become part of the terms and not just metainformation about them. These paths are ..."
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Cited by 2 (0 self)
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Abstract. The notion of path is classical in graph theory but not directly used in the term rewriting community. The main idea of this work is to raise the notion of path to the level of firstorder terms, i.e. paths become part of the terms and not just metainformation about them. These paths are represented by words of integers (positive or negative) and are interpreted as relative addresses in terms. In this way, paths can also be seen as a generalization of the classical notion of position for the firstorder terms and are inspired by de Bruijn indexes. In this paper, we define an original framework called Referenced Term Rewriting where paths are used to represent pointers between subterms. Using this approach, any termgraph rewriting systems can be simulated using a term rewritebased environment. 1
Decidability of opacity with nonatomic keys
 In Proc. FAST’04
, 2004
"... Abstract The most studied property, secrecy, is not always sufficient to prove the security of a protocol. Other properties such as anonymity, privacy or opacity could be useful. Here, we use a simple definition of opacity which works by looking at the possible traces of the protocol using a new pro ..."
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Abstract The most studied property, secrecy, is not always sufficient to prove the security of a protocol. Other properties such as anonymity, privacy or opacity could be useful. Here, we use a simple definition of opacity which works by looking at the possible traces of the protocol using a new property over messages called similarity. The opacity property becomes a logical constraint involving both similarities and syntactic equalities. The main theorem proves that satisfiability of these constraints and thus opacity are decidable without having to make the hypothesis of atomic keys. Moreover, we use syntactic equalities to model some deductions an intruder could make by performing bittobit comparisons (i.e. knownciphertext attack).
Inversion Strategies
"... . We consider the problem of inversion, for functions dened by groundconvergent rewrite systems. That is, we are looking for an algorithm for nding most general solutions to problems of the form t = ? G where G is a ground term. We rst reformulate the inversion procedure of [DM99] as goal rew ..."
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. We consider the problem of inversion, for functions dened by groundconvergent rewrite systems. That is, we are looking for an algorithm for nding most general solutions to problems of the form t = ? G where G is a ground term. We rst reformulate the inversion procedure of [DM99] as goal rewriting rules directed by strategies. Then, for the typical case of suciently dened specications, we present new rules and strategies for solving the inversion problem. 1 Introduction In rulebased languages like ELAN [BKK + 98] or Claire [CL96] it would be very useful to have an automatic inversion capability which automatically provides inverses of functions dened by the user. We design several new inference systems for solving inversion problems which are geared particularly to suciently complete rewrite systems, including a new failure rule based on an appropriate measure of distance to normal form. We emphasize the explicit description of rule application strategies, making...
A Categorical Approach to Logics and Logic Homomorphisms
, 2007
"... This master’s thesis presents a number of important concepts in logic such as models, entailment, and proof calculi within the framework of category theory. By describing these concepts as categories, a tremendous amount of generality and power is gained. In particular, this approach makes it possib ..."
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This master’s thesis presents a number of important concepts in logic such as models, entailment, and proof calculi within the framework of category theory. By describing these concepts as categories, a tremendous amount of generality and power is gained. In particular, this approach makes it possible to reason about maps from one logic to another in a consistent and convenient manner. By a consistent map is meant that the truth stays invariant, that is, a statement true in the source logic is mapped to a similarly true statement in the target logic. Conversely, a statement false in the source logic is mapped to a statement false in the target logic. While the thesis focuses on the theoretical notions outlined above, a brief coverage of two practical applications is given as a means to illustrate the utility of these notions. Concluding the text is a chapter containing a discussion and a section wherein possible future work is presented. In an effort to make the text mostly selfcontained, concepts beyond basic discrete mathematics are duly introduced with definitions and examples. These include, for
Antipatterns for Rulebased Languages
, 2010
"... Negation is intrinsic to human thinking and most of the time when searching for something, we base our patterns on both positive and negative conditions. This should be naturally reflected in software that provide patternbased searches. We would like for example to specify that we search for white ..."
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Negation is intrinsic to human thinking and most of the time when searching for something, we base our patterns on both positive and negative conditions. This should be naturally reflected in software that provide patternbased searches. We would like for example to specify that we search for white cars that are not station wagons, or that we search for a list of objects that does not contain two identical elements. In this paper we extend the notion of pattern to the one of antipattern, i.e. patterns that may contain complement symbols. This concept is appropriate to design powerful extensions to patternbased programming languages like Ml, Asf+Sdf, Stratego, Maude, Elan or Tom and we show how this is used to extend the expressiveness and usability of the Tom language. We further define formally the semantics of antipatterns both in the syntactic case, i.e. when the symbols have no specific theory associated, and modulo an arbitrary equational theory E. We then extend the classical notion of matching between patterns and ground terms to matching between antipatterns and ground terms. Solving such problems can be performed either using general techniques as disunification, which we exemplify in the syntactical case, or more tailored and efficient approaches, which we chose to illustrate on the specific and very useful case of associativity, possibly with a unity. This allows us to be generic enough to give in this framework a very simple and natural expression of, for instance, the AllDiff standard predicate of constraint programming.
Target Languages
"... Îlots formels et certification du filtrage 31 Gestion mémoire et structures de données 61 Applications 121 Extensions aux antipatterns et aux graphes 155Présentations de Tom ..."
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Îlots formels et certification du filtrage 31 Gestion mémoire et structures de données 61 Applications 121 Extensions aux antipatterns et aux graphes 155Présentations de Tom
Recueil d’articles
"... Annexes du manuscrit d’HDR — Le calcul de réécritureiiSommaire Présentations du calcul de réécriture 1 Propriétés des calculs à motifs 57 Extensions du calcul de réécriture 75 Expressivité du calcul de réécriture 147 Systèmes de types pour le calcul de réécriture 195 Applications 225Présentations du ..."
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Annexes du manuscrit d’HDR — Le calcul de réécritureiiSommaire Présentations du calcul de réécriture 1 Propriétés des calculs à motifs 57 Extensions du calcul de réécriture 75 Expressivité du calcul de réécriture 147 Systèmes de types pour le calcul de réécriture 195 Applications 225Présentations du calcul de réécriture [CK01] [CKL01a]