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24
A Typed Pattern Calculus
 ACM Trans. Program. Lang. Syst
, 1996
"... The theory of programming with patternmatching function definitions has been studied mainly in the framework of firstorder rewrite systems. We present a typed functional calculus that emphasizes the strong connection between the structure of whole pattern definitions and their types. In this calcu ..."
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Cited by 66 (15 self)
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The theory of programming with patternmatching function definitions has been studied mainly in the framework of firstorder rewrite systems. We present a typed functional calculus that emphasizes the strong connection between the structure of whole pattern definitions and their types. In this calculus typechecking guarantees the absence of runtime errors caused by nonexhaustive patternmatching definitions. Its operational semantics is deterministic in a natural way, without the imposition of adhoc solutions such as clause order or "best fit". In the spirit of the CurryHoward isomorphism, we design the calculus as a computational interpretation of the Gentzen sequent proofs for the intuitionistic propositional logic. We prove the basic properties connecting typing and evaluation: subject reduction and strong normalization. We believe that this calculus offers a rational reconstruction of the patternmatching features found in successful functional languages. CNRS and Laboratoire...
Rewriting calculus with fixpoints: Untyped and firstorder systems
 In Postproceedings of TYPES, Lecture Notes in Computer Science
, 2003
"... Abstract The rewriting calculus, also called ρcalculus, is a framework embedding λcalculus and rewriting capabilities, by allowing abstraction not only on variables but also on patterns. The higherorder mechanisms of the λcalculus and the pattern matching facilities of the rewriting are then bot ..."
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Cited by 26 (10 self)
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Abstract The rewriting calculus, also called ρcalculus, is a framework embedding λcalculus and rewriting capabilities, by allowing abstraction not only on variables but also on patterns. The higherorder mechanisms of the λcalculus and the pattern matching facilities of the rewriting are then both available at the same level. Many type systems for the λcalculus can be generalized to the ρcalculus: in this paper, we study extensively a firstorder ρcalculus à la Church, called ρ stk The type system of ρ stk � allows one to type (object oriented flavored) fixpoints, leading to an expressive and safe calculus. In particular, using pattern matching, one can encode and typecheck term rewriting systems in a natural and automatic way. Therefore, we can see our framework as a starting point for the theoretical basis of a powerful typed rewritingbased language.
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 22 (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
A rewriting calculus for cyclic higherorder term graphs
 in "2nd International Workshop on Term Graph Rewriting  TERMGRAPH’2004
, 2004
"... graphs ..."
A DomainSpecific Language for Incremental and Modular Design of LargeScale VerifiablySafe Flow Networks (Preliminary Report)
"... We define a domainspecific language (DSL) to inductively assemble flow networks from small networks or modules to produce arbitrarily large ones, with interchangeable functionallyequivalent parts. Our small networks or modules are “small ” only as the building blocks in this inductive definition ( ..."
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Cited by 5 (4 self)
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We define a domainspecific language (DSL) to inductively assemble flow networks from small networks or modules to produce arbitrarily large ones, with interchangeable functionallyequivalent parts. Our small networks or modules are “small ” only as the building blocks in this inductive definition (there is no limit on their size). Associated with our DSL is a type theory, a system of formal annotations to express desirable properties of flow networks together with rules that enforce them as invariants across their interfaces, i.e., the rules guarantee the properties are preserved as we build larger networks from smaller ones. A prerequisite for a type theory is a formal semantics, i.e., a rigorous definition of the entities that qualify as feasible flows through the networks, possibly restricted to satisfy additional efficiency or safety requirements. This can be carried out in one of two ways, as a denotational semantics or as an operational (or reduction) semantics; we choose the first in preference to the second, partly to avoid exponentialgrowth rewriting in the operational approach. We set up a typing system and prove its soundness for our DSL. 1
The rewriting calculus as a combinatory reduction system
 In Foundations of Software Science and Computation Structures – FoSSaCS’07, LNCS
, 2007
"... Abstract. The last few years have seen the development of the rewriting calculus (also called rhocalculus or ρcalculus) that uniformly integrates firstorder term rewriting and λcalculus. The combination of these two latter formalisms has been already handled either by enriching firstorder rewri ..."
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Cited by 5 (1 self)
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Abstract. The last few years have seen the development of the rewriting calculus (also called rhocalculus or ρcalculus) that uniformly integrates firstorder term rewriting and λcalculus. The combination of these two latter formalisms has been already handled either by enriching firstorder rewriting with higherorder capabilities, like in the Combinatory Reduction Systems (crs), or by adding to λcalculus algebraic features. In a previous work, the authors showed how the semantics of crs can be expressed in terms of the ρcalculus. The converse issue is adressed here: rewriting calculus derivations are simulated by Combinatory Reduction Systems derivations. As a consequence of this result, important properties, like standardisation, are deduced for the rewriting calculus.
A framework for defining logical frameworks
 University of Udine
, 2006
"... Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be ..."
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Cited by 4 (1 self)
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Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be
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 3 (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
A Conditional Logical Framework ⋆
"... Abstract. The Conditional Logical Framework LFK is a variant of the HarperHonsellPlotkin’s Edinburgh Logical Framemork LF. It features a generalized form of λabstraction where βreductions fire under the condition that the argument satisfies a logical predicate. The key idea is that the type syst ..."
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Cited by 3 (2 self)
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Abstract. The Conditional Logical Framework LFK is a variant of the HarperHonsellPlotkin’s Edinburgh Logical Framemork LF. It features a generalized form of λabstraction where βreductions fire under the condition that the argument satisfies a logical predicate. The key idea is that the type system memorizes under what conditions and where reductions have yet to fire. Different notions of βreductions corresponding to different predicates can be combined in LFK. The framework LFK subsumes, by simple instantiation, LF (in fact, it is also a subsystem of LF!), as well as a large class of new generalized conditional λcalculi. These are appropriate to deal smoothly with the sideconditions of both Hilbert and Natural Deduction presentations of Modal Logics. We investigate and characterize the metatheoretical properties of the calculus underpinning LFK, such as subject reduction, confluence, strong normalization. 1
From functional programs to interaction nets via the Rewriting Calculus
 WRS 2006 PRELIMINARY VERSION
, 2006
"... We use the ρcalculus as an intermediate language to compile functional languages with patternmatching features, and give an interaction net encoding of the ρterms arising from the compilation. This encoding gives rise to new strategies of evaluation, where patternmatching and ‘traditional ’ βre ..."
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Cited by 3 (0 self)
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We use the ρcalculus as an intermediate language to compile functional languages with patternmatching features, and give an interaction net encoding of the ρterms arising from the compilation. This encoding gives rise to new strategies of evaluation, where patternmatching and ‘traditional ’ βreduction can proceed in parallel without overheads.