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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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Cited by 34 (20 self)
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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
Rewriting calculus with(out) types
 Proceedings of the fourth workshop on rewriting logic and applications
, 2002
"... The last few years have seen the development of a new calculus which can be considered as an outcome of the last decade of various researches on (higher order) term rewriting systems, and lambda calculi. In the Rewriting Calculus (or Rho Calculus, ρCal), algebraic rules are considered as sophisticat ..."
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Cited by 26 (13 self)
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The last few years have seen the development of a new calculus which can be considered as an outcome of the last decade of various researches on (higher order) term rewriting systems, and lambda calculi. In the Rewriting Calculus (or Rho Calculus, ρCal), algebraic rules are considered as sophisticated forms of “lambda terms with patterns”, and rule applications as lambda applications with pattern matching facilities. The calculus can be customized to work modulo sophisticated theories, like commutativity, associativity, associativitycommutativity, etc. This allows us to encode complex structures such as list, sets, and more generally objects. The calculus can either be presented “à la Curry ” or “à la Church ” without sacrificing readability and without complicating too much the metatheory. Many static type systems can be easily pluggedin on top of the calculus in the spirit of the rich typeoriented literature. The Rewriting Calculus could represent a lingua franca to encode many paradigms of computations together with a formal basis used to build powerful theorem provers based on lambda calculus and efficient rewriting, and a step towards new proof engines based on the CurryHoward isomorphism. 1
HigherOrder Rewriting
 12th Int. Conf. on Rewriting Techniques and Applications, LNCS 2051
, 1999
"... This paper will appear in the proceedings of the 10th international conference on rewriting techniques and applications (RTA'99). c flSpringer Verlag. ..."
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Cited by 24 (1 self)
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This paper will appear in the proceedings of the 10th international conference on rewriting techniques and applications (RTA'99). c flSpringer Verlag.
Combining HigherOrder and FirstOrder Computation Using ρcalculus: Towards a Semantics of ELAN
 In Frontiers of Combining Systems 2
, 1999
"... The ρcalculus permits to express in a uniform and simple way firstorder rewriting, λcalculus and nondeterministic computations as well as their combination. In this paper, we present the main components of the ρcalculus and we give a full firstorder presentation of this rewriting calculus using ..."
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Cited by 22 (10 self)
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The ρcalculus permits to express in a uniform and simple way firstorder rewriting, λcalculus and nondeterministic computations as well as their combination. In this paper, we present the main components of the ρcalculus and we give a full firstorder presentation of this rewriting calculus using an explicit substitution setting, called ρσ, that generalizes the λσcalculus. The basic properties of the nonexplicit and explicit substitution versions are presented. We then detail how to use the ρcalculus to give an operational semantics to the rewrite rules of the ELAN language. 1
Simplifying transformations of OCL constraints
 Proceedings, Model Driven Engineering Languages and Systems (MoDELS), Montego
, 2005
"... Abstract. With the advent of Model Driven Architecture, OCL constraints are no longer necessarily written by humans. They can be part of models that emerge from a chain of transformations. They might be the result of instantiating templates, of combining prefabricated parts, or of more general compu ..."
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Cited by 12 (1 self)
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Abstract. With the advent of Model Driven Architecture, OCL constraints are no longer necessarily written by humans. They can be part of models that emerge from a chain of transformations. They might be the result of instantiating templates, of combining prefabricated parts, or of more general computation. Such generated specifications will often contain redundancies that reduce their readability. In this paper, we explore the possibilities of transforming OCL formulae to a simpler form through the repeated application of simple rules. We discuss the different kinds of rules that are needed, and we describe a prototypical implementation of the approach. 1
Translating Combinatory Reduction Systems into the Rewriting Calculus
 in « 4th International Workshop on RuleBased Programming (RULE 2003
, 2003
"... The last few years have seen the development of the rewriting calculus (or rhocalculus, ρCal) that extends first order term rewriting and λcalculus. The integration of these two latter formalisms has been already handled either by enriching firstorder rewriting with higherorder capabilities, like ..."
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Cited by 5 (1 self)
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The last few years have seen the development of the rewriting calculus (or rhocalculus, ρCal) that extends first order term rewriting and λcalculus. The integration of these two latter formalisms has been already handled either by enriching firstorder rewriting with higherorder capabilities, like in the Combinatory Reduction Systems, or by adding to λcalculus algebraic features. The different higherorder rewriting systems and the rewriting calculus share similar concepts and have similar applications, and thus, it seems natural to compare these formalisms. We analyze in this paper the relationship between the Rewriting Calculus and the Combinatory Reduction Systems and we present a translation of CRSterms and rewrite rules into rhoterms and we show that for any CRSreduction we have a corresponding rhoreduction. 1
Strong Normalization in two Pure Pattern Type Systems
 in "Mathematical Structures in Computer Science", to appear, 2007, http://hal.inria.fr/inria00186815/en/. Publications in Conferences and Workshops
"... Pure Pattern Type Systems (P 2 T S) combine in a unified setting the frameworks and capabilities of rewriting and λcalculus. Their type systems, adapted from Barendregt’s λcube, are especially interesting from a logical point of view. Strong normalization, an essential property for logical soundne ..."
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Cited by 3 (0 self)
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Pure Pattern Type Systems (P 2 T S) combine in a unified setting the frameworks and capabilities of rewriting and λcalculus. Their type systems, adapted from Barendregt’s λcube, are especially interesting from a logical point of view. Strong normalization, an essential property for logical soundness, had only been conjectured so far: in this paper, we give a positive answer for the simplytyped system and the dependentlytyped system. The proof is based on a translation of terms and types from P 2 T S into the λcalculus. First, we deal with untyped terms, ensuring that reductions are faithfully mimicked in the λcalculus. For this, we rely on an original encoding of the pattern matching capability of P 2 T S into the System Fω. Then we show how to translate types: the expressive power of System Fω is needed in order to fully reproduce the original typing judgments of P 2 T S. We prove that the encoding is correct with respect to reductions and typing, and we conclude with the strong normalization of simplytyped P 2 T S terms. The strong normalization with dependent types is in turn obtained by an intermediate translation into simplytyped terms.
HigherOrder rewriting: Framework, Confluence and termination
 Processes, Terms and Cycles: Steps on the road to infinity. Essays Dedicated to Jan Willem Klop on the occasion of his 60th Birthday. LNCS 3838
, 2005
"... Equations are ubiquitous in mathematics and in computer science as well. This first sentence of a survey on firstorder rewriting borrowed again and again characterizes best the fundamental reason why rewriting, as a technology for processing equations, is so important in our discipline [10]. ..."
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Cited by 2 (1 self)
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Equations are ubiquitous in mathematics and in computer science as well. This first sentence of a survey on firstorder rewriting borrowed again and again characterizes best the fundamental reason why rewriting, as a technology for processing equations, is so important in our discipline [10].
Residuals in higherorder rewriting
 Proceedings of Rewriting Techniques and Applications (RTA’03
, 2003
"... Abstract. Residuals have been studied for various forms of rewriting setting. In this article we study residuals in orthogonal Pattern Rewriting Systems (PRSs). First, the rewrite relation is defined by means of a higherorder rewriting logic, and proof terms are defined that witness reductions. The ..."
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Abstract. Residuals have been studied for various forms of rewriting setting. In this article we study residuals in orthogonal Pattern Rewriting Systems (PRSs). First, the rewrite relation is defined by means of a higherorder rewriting logic, and proof terms are defined that witness reductions. Then, we have the formal machinery to define a residual operator for PRSs, and we will prove that an orthogonal PRS together with the residual operator mentioned above, is a residual system. As a sideeffect, all results of (abstract) residual theory are inherited by orthogonal PRSs, such as confluence, and the notion of permutation equivalence of reductions. 1
Higherorder rewriting via conditional firstorder rewriting in the open calculus of constructions
 Informatik Berichte. Department of Computer Science
"... Abstract. Although higherorder rewrite systems (HRS) seem to have a firstorder flavor, the direct translation into firstorder rewrite systems, using e.g. explicit substitutions, is by no means trivial. In this paper, we explore a twostage approach, by showing how higherorder pattern rewrite sys ..."
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Abstract. Although higherorder rewrite systems (HRS) seem to have a firstorder flavor, the direct translation into firstorder rewrite systems, using e.g. explicit substitutions, is by no means trivial. In this paper, we explore a twostage approach, by showing how higherorder pattern rewrite systems, and in fact a somewhat more general class, can be expressed by conditional firstorder rewriting in the open calculus of constructions (OCC), which itself has been presented and implemented using explicit substitutions. The key feature of OCC that we exploit is that conditions are allowed to contain quantifiers and equations which can be solved using firstorder matching. The way we express HRS works in spite of the fact that structural equality of OCC does not subsume αconversion. Another topic that we touch upon in this paper is the use of higherorder abstract syntax in a classical framework like OCC, because it is often used in connection with higherorder rewriting. 1