## Matching Power (2001)

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Venue: | Proceedings of RTA’2001, Lecture Notes in Computer Science, Utrecht (The Netherlands |

Citations: | 34 - 20 self |

### BibTeX

@INPROCEEDINGS{Cirstea01matchingpower,

author = {Horatiu Cirstea and Claude Kirchner and Luigi Liquori},

title = {Matching Power},

booktitle = {Proceedings of RTA’2001, Lecture Notes in Computer Science, Utrecht (The Netherlands},

year = {2001},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

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

### Citations

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Citation Context ... of the Rho Calculus allows us to encode two major object-calculi which have strongly influenced the type-theoretical research of the last five years: the Object Calculus (ςObj) of Abadi and Cardelli =-=[1]-=- and the Lambda Calculus of Objects of Fisher, Honsell, and Mitchell [14] (λObj). Moreover, we show two examples in Rho Calculus that cannot be encoded in the above calculi. Road Map of the Paper. The... |

670 |
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Citation Context ...rn matching, is present since the beginning of information processing modeling. Instances of it can be traced back to pattern recognition and it has been extensively studied when dealing with strings =-=[26]-=-, trees [19] or feature objects [2]. Matching occurs implicitly in many languages through the parameter passing mechanism but often as a very simple instance, and explicitly in languages like PROLOG a... |

296 | A logic programming language with lambda-abstraction, function variables, and simple unification
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Citation Context ...ng occurs implicitly in many languages through the parameter passing mechanism but often as a very simple instance, and explicitly in languages like PROLOG and ML, where it can be quite sophisticated =-=[28,27]-=-. It is somewhat astonishing that one of the most commonly used model of computation, the lambda calculus, uses only trivial pattern matching. This has been extended, initially for programming concern... |

170 | A lambda-calculus of objects and method specialization
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Citation Context ...have strongly influenced the type-theoretical research of the last five years: the Object Calculus (ςObj) of Abadi and Cardelli [1] and the Lambda Calculus of Objects of Fisher, Honsell, and Mitchell =-=[14]-=- (λObj). Moreover, we show two examples in Rho Calculus that cannot be encoded in the above calculi. Road Map of the Paper. The paper is structured as follows: in Section 2, we present the syntax and ... |

153 |
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Citation Context ...ambda calculus with term rewriting [30,4,16,22], to mention only a few. Embedding more information in the matching process makes it appropriate to deal with complex tasks like program transformations =-=[20]-=- or theorem proving [32]. In that direction, matching in elaborated theories has been also studied extensively, either in equational theories [21,5] or in higher-order logic [12,31], where it is still... |

144 |
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Citation Context ... is present since the beginning of information processing modeling. Instances of it can be traced back to pattern recognition and it has been extensively studied when dealing with strings [26], trees =-=[19]-=- or feature objects [2]. Matching occurs implicitly in many languages through the parameter passing mechanism but often as a very simple instance, and explicitly in languages like PROLOG and ML, where... |

140 |
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Citation Context ... rewriting [30,4,16,22], to mention only a few. Embedding more information in the matching process makes it appropriate to deal with complex tasks like program transformations [20] or theorem proving =-=[32]-=-. In that direction, matching in elaborated theories has been also studied extensively, either in equational theories [21,5] or in higher-order logic [12,31], where it is still an open problem at orde... |

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Citation Context ...on strategy of the condition. Rewriting is central in several programming languages developed since the seventies. Amongst the main ones let us mention OBJ [18], ASF+SDF [35],sMatching Power 79 Maude =-=[10]-=-, CafeOBJ [15], Stratego [38], and ELAN [24,3,34] which has been at the origin of some of the main concepts of the rewriting calculus. In turn, the Rho Calculus provides a natural semantics to such la... |

118 |
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Citation Context ...sed model of computation, the lambda calculus, uses only trivial pattern matching. This has been extended, initially for programming concerns, either by the introduction of patterns in lambda calculi =-=[33,36,11]-=-, or by the introduction of matching and rewrite rules in functional programming languages. And indeed, many works address the integration of term rewriting with lambda calculus, either by enriching f... |

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Citation Context ...entral in several programming languages developed since the seventies. Amongst the main ones let us mention OBJ [18], ASF+SDF [35],sMatching Power 79 Maude [10], CafeOBJ [15], Stratego [38], and ELAN =-=[24,3,34]-=- which has been at the origin of some of the main concepts of the rewriting calculus. In turn, the Rho Calculus provides a natural semantics to such languages, and in particular to ELAN, covering the ... |

90 | Combinatory reduction systems: introduction and survey
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(Show Context)
Citation Context ...erlin Heidelberg 2001s78 H. Cirstea, C. Kirchner, and L. Liquori algebraic features allowing one, in particular, to deal with equality in an efficient way. In the first case, we find the works on CRS =-=[25]-=- and other higher-order rewriting systems [39,29], in the second case the works on combination of lambda calculus with term rewriting [30,4,16,22], to mention only a few. Embedding more information in... |

73 | Exceptions in the rewriting calculus
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(Show Context)
Citation Context ...representation of term rewrite derivations, even in the conditional case. More generally, it allows us to describe traversal, evaluation and search strategies like leftmost innermost, or breath first =-=[7]-=-. In [7], we have shown that conditional rewrite rules of the form “l → r if c” can be faithfully represented in the rewriting calculus as l → (True → r) •(strat •c), where strat is a suitable term re... |

65 |
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Citation Context ...entral in several programming languages developed since the seventies. Amongst the main ones let us mention OBJ [18], ASF+SDF [35],sMatching Power 79 Maude [10], CafeOBJ [15], Stratego [38], and ELAN =-=[24,3,34]-=- which has been at the origin of some of the main concepts of the rewriting calculus. In turn, the Rho Calculus provides a natural semantics to such languages, and in particular to ELAN, covering the ... |

60 |
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Citation Context ...an efficient way. In the first case, we find the works on CRS [25] and other higher-order rewriting systems [39,29], in the second case the works on combination of lambda calculus with term rewriting =-=[30,4,16,22]-=-, to mention only a few. Embedding more information in the matching process makes it appropriate to deal with complex tasks like program transformations [20] or theorem proving [32]. In that direction... |

55 |
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(Show Context)
Citation Context ...an efficient way. In the first case, we find the works on CRS [25] and other higher-order rewriting systems [39,29], in the second case the works on combination of lambda calculus with term rewriting =-=[30,4,16,22]-=-, to mention only a few. Embedding more information in the matching process makes it appropriate to deal with complex tasks like program transformations [20] or theorem proving [32]. In that direction... |

49 | Third order matching is decidable
- Dowek
- 1992
(Show Context)
Citation Context ...ogram transformations [20] or theorem proving [32]. In that direction, matching in elaborated theories has been also studied extensively, either in equational theories [21,5] or in higher-order logic =-=[12,31]-=-, where it is still an open problem at order five. Matching allows one to discriminate between alternatives. Once the patterns are recognized, the action to be taken on the appropriate pattern should ... |

49 | Abstract Data Type Systems
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(Show Context)
Citation Context ...an efficient way. In the first case, we find the works on CRS [25] and other higher-order rewriting systems [39,29], in the second case the works on combination of lambda calculus with term rewriting =-=[30,4,16,22]-=-, to mention only a few. Embedding more information in the matching process makes it appropriate to deal with complex tasks like program transformations [20] or theorem proving [32]. In that direction... |

34 | The Rho Cube
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- 2001
(Show Context)
Citation Context ...and in particular to ELAN, covering the notion of rule application strategy, a fundamental concept of the language. In this paper, we give the newest description of the Rho Calculus, as introduced in =-=[9]-=-. It provides a simplified version of the evaluation rules of the calculus as well as a generic and explicit handling of result structures, a point left open in the previous works [6,7]. The contribut... |

31 | Lambda Calculus with Patterns
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(Show Context)
Citation Context ...sed model of computation, the lambda calculus, uses only trivial pattern matching. This has been extended, initially for programming concerns, either by the introduction of patterns in lambda calculi =-=[33,36,11]-=-, or by the introduction of matching and rewrite rules in functional programming languages. And indeed, many works address the integration of term rewriting with lambda calculus, either by enriching f... |

28 |
An introduction to OBJ-3
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Citation Context ...a suitable term representing the normalization strategy of the condition. Rewriting is central in several programming languages developed since the seventies. Amongst the main ones let us mention OBJ =-=[18]-=-, ASF+SDF [35],sMatching Power 79 Maude [10], CafeOBJ [15], Stratego [38], and ELAN [24,3,34] which has been at the origin of some of the main concepts of the rewriting calculus. In turn, the Rho Calc... |

28 | A core language for rewriting
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(Show Context)
Citation Context ... Rewriting is central in several programming languages developed since the seventies. Amongst the main ones let us mention OBJ [18], ASF+SDF [35],sMatching Power 79 Maude [10], CafeOBJ [15], Stratego =-=[38]-=-, and ELAN [24,3,34] which has been at the origin of some of the main concepts of the rewriting calculus. In turn, the Rho Calculus provides a natural semantics to such languages, and in particular to... |

26 |
Calcul de réécriture : fondements et applications. Thèse de Doctorat d’Université, Université Henri Poincaré - Nancy I
- Cirstea
- 2000
(Show Context)
Citation Context ...as introduced in [9]. It provides a simplified version of the evaluation rules of the calculus as well as a generic and explicit handling of result structures, a point left open in the previous works =-=[6,7]-=-. The contributions of this paper are therefore the following: – we provide a broad set of examples showing the expressiveness of the Rho Calculus obtained mainly thanks to its “matching power” and ho... |

26 |
Strong normalizability for the combined system of the typed lambda calculus and an arbitrary convergent term rewrite system
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- 1989
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Citation Context |

25 | An overview of CAFE specification environment – an algebraic approach for creating, verifying, and maintaining formal specification over networks - Futatsugi, Nakagawa - 1997 |

19 |
The Clausal Theory of Types, volume 21 of Cambridge Tracts
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(Show Context)
Citation Context ...er, and L. Liquori algebraic features allowing one, in particular, to deal with equality in an efficient way. In the first case, we find the works on CRS [25] and other higher-order rewriting systems =-=[39,29]-=-, in the second case the works on combination of lambda calculus with term rewriting [30,4,16,22], to mention only a few. Embedding more information in the matching process makes it appropriate to dea... |

18 | A Lambda Calculus of Objects with Self-Inflicted Extension
- Gianantonio, Honsell, et al.
- 1998
(Show Context)
Citation Context ... is trivially computationally complete, since the lambda calculus is built in the calculus itself. The syntax and the small-step semantics of λObj we present in this paper are inspired by the work of =-=[17]-=-. Syntax and Operational Semantics. The syntax of the calculus is defined as follows: M,N ::= λX.M | MN | X | c | 〈〉|〈M← n = N〉 |〈M ←+ n = N〉 |M ⇐ n | Sel(M, m, N) Let ←∗ be either ← or ←+ ; the small... |

17 |
Matching — A special case of unification
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(Show Context)
Citation Context ... deal with complex tasks like program transformations [20] or theorem proving [32]. In that direction, matching in elaborated theories has been also studied extensively, either in equational theories =-=[21,5]-=- or in higher-order logic [12,31], where it is still an open problem at order five. Matching allows one to discriminate between alternatives. Once the patterns are recognized, the action to be taken o... |

15 | A feature constraint system for logic programming with entailment
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(Show Context)
Citation Context ...ginning of information processing modeling. Instances of it can be traced back to pattern recognition and it has been extensively studied when dealing with strings [26], trees [19] or feature objects =-=[2]-=-. Matching occurs implicitly in many languages through the parameter passing mechanism but often as a very simple instance, and explicitly in languages like PROLOG and ML, where it can be quite sophis... |

15 |
Rewriting, solving, proving. A preliminary version of a book available at www. loria. fr/ckirchne/rsp. ps. gz
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- 1999
(Show Context)
Citation Context ...the application of this rule set terminates and returns either F when there are no substitutions solving the system, or a system T ′ in “normal form” from which the solution can be trivially inferred =-=[23]-=-. This set of rules could be extended to deal with more elaborated theories like commutativity. 2.3 Operational Semantics For a given total ordering ≺ on substitutions (which is left implicit in the n... |

15 |
Higher-order rewriting and equational reasoning
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(Show Context)
Citation Context ...er, and L. Liquori algebraic features allowing one, in particular, to deal with equality in an efficient way. In the first case, we find the works on CRS [25] and other higher-order rewriting systems =-=[39,29]-=-, in the second case the works on combination of lambda calculus with term rewriting [30,4,16,22], to mention only a few. Embedding more information in the matching process makes it appropriate to dea... |

14 |
Decidability of fourth-order matching
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(Show Context)
Citation Context ...ogram transformations [20] or theorem proving [32]. In that direction, matching in elaborated theories has been also studied extensively, either in equational theories [21,5] or in higher-order logic =-=[12,31]-=-, where it is still an open problem at order five. Matching allows one to discriminate between alternatives. Once the patterns are recognized, the action to be taken on the appropriate pattern should ... |

12 | Input/output for ELAN
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(Show Context)
Citation Context ...cations. As we have seen, the are many possible applications of the framework; a track that we have not yet mention in this paper concerns encoding concurrency in the spirit of the early work of Viry =-=[37]-=-. Independently of these ongoing works, we believe that the matching power of the Rho Calculus could be widely used, thanks to its expressiveness and simplicity, as a new model of computation. Acknowl... |

9 |
Associative-commutative pattern matching
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(Show Context)
Citation Context ... deal with complex tasks like program transformations [20] or theorem proving [32]. In that direction, matching in elaborated theories has been also studied extensively, either in equational theories =-=[21,5]-=- or in higher-order logic [12,31], where it is still an open problem at order five. Matching allows one to discriminate between alternatives. Once the patterns are recognized, the action to be taken o... |

7 |
Lazy pattern matching in the ML language
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(Show Context)
Citation Context ...ng occurs implicitly in many languages through the parameter passing mechanism but often as a very simple instance, and explicitly in languages like PROLOG and ML, where it can be quite sophisticated =-=[28,27]-=-. It is somewhat astonishing that one of the most commonly used model of computation, the lambda calculus, uses only trivial pattern matching. This has been extended, initially for programming concern... |

3 |
Une structure de données pour le λ-calcul typé. Private Communication
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(Show Context)
Citation Context ...sed model of computation, the lambda calculus, uses only trivial pattern matching. This has been extended, initially for programming concerns, either by the introduction of patterns in lambda calculi =-=[33,36,11]-=-, or by the introduction of matching and rewrite rules in functional programming languages. And indeed, many works address the integration of term rewriting with lambda calculus, either by enriching f... |

2 |
Matching —Aspecial case of unification
- Bürckert
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(Show Context)
Citation Context ... deal with complex tasks like program transformations [20] or theorem proving [32]. In that direction, matching in elaborated theories has been also studied extensively, either in equational theories =-=[21,5]-=- or in higher-order logic [12,31], where it is still an open problem at order five. Matching allows one to discriminate between alternatives. Once the patterns are recognized, the action to be taken o... |

2 |
The Elan Home Page
- Protheo
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(Show Context)
Citation Context ...entral in several programming languages developed since the seventies. Amongst the main ones let us mention OBJ [18], ASF+SDF [35],sMatching Power 79 Maude [10], CafeOBJ [15], Stratego [38], and ELAN =-=[24,3,34]-=- which has been at the origin of some of the main concepts of the rewriting calculus. In turn, the Rho Calculus provides a natural semantics to such languages, and in particular to ELAN, covering the ... |

1 | The Rho Cube - Power - 2001 |

1 |
Une structure de donnes pour le λ-calcul typé. Private Communication
- Colson
(Show Context)
Citation Context |