## ELAN from a rewriting logic point of view (2002)

Venue: | Theoretical Computer Science |

Citations: | 59 - 5 self |

### BibTeX

@ARTICLE{Kirchner02elanfrom,

author = {Claude Kirchner and Hélène Kirchner and Pierre-etienne Moreau},

title = {ELAN from a rewriting logic point of view},

journal = {Theoretical Computer Science},

year = {2002},

pages = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

ELAN implements computational systems, a concept that combines two first class entities: rewrite rules and rewriting strategies. ELAN can be used either as a logical framework or to describe and execute deterministic as well as non-deterministic rule based processes. With the general goal to make precise a rewriting logic based semantics of ELAN, this paper has three contributions: a presentation of the concepts of rules and strategies available in ELAN, an expression of rewrite rules with matching conditions in conditional rewriting logic, and finally an enrichment mechanism of a rewrite theory into a strategy theory in conditional rewriting logic.

### Citations

1042 |
Term Rewriting and All That
- Baader, Nipkow
- 1998
(Show Context)
Citation Context ...ion 8 draws some perspectives of further extensions of the language. 2 Preliminary concepts and notations We assume the reader familiar with basic definitions of term rewriting given in particular in =-=[31,45,4]-=-. We briefly recall and introduce notations for a few concepts that will be used along this paper. The definitions below are given in the many-sorted case. The order-sorted case can be handled in a si... |

857 |
The B-Book: Assigning Programs to Meanings
- ABRIAL
- 1996
(Show Context)
Citation Context ...t the semantics level [27] as well as implementation levels [36,35]. Proving: ELAN was used to implement a predicate prover based on the rules proposed by J.-R. Abrial, and implemented in the B-tools =-=[1]-=-. We developed also a propositional sequent calculus, completion procedures for rewrite systems [52], and sufficient conditions for the termination problem. In particular, criteria for termination hav... |

91 | M.: Elan: A logical framework based on computational systems
- Borovansky, Kirchner, et al.
- 1996
(Show Context)
Citation Context ...ted by the Esprit Basic Research Working Group 22457 - Construction of Computational Logics II. Preprint submitted to Elsevier Preprint 20 February 2002An ELAN program defines a computational system =-=[48,72,16]-=- given by a signature providing the syntax, a set of conditional rewrite rules describing the computation as well as the deduction mechanism, and strategies to guide application of rewrite rules. ELAN... |

68 | W.: Basic paramodulation
- Bachmair, Ganzinger, et al.
- 1995
(Show Context)
Citation Context ...ational rewrite system U is assumed to be confluent and terminating modulo A. Achieving these properties may involve advanced saturation techniques from automated theorem proving, such as proposed in =-=[69,67,6,64]-=-. Equality in the theory E can be decided by rewriting modulo A with U and then checking A equivalence of the results. Sentences built on a given signature are defined as sequents of the form π : 〈t〉 ... |

57 |
Complexity of matching problems
- Benanav, Kapur, et al.
- 1987
(Show Context)
Citation Context ...n symbols, AC matching is invoked. The term l is said to AC match another term t if there exists a substitution σ such that lσ =AC t. AC matching has already been extensively studied, for instance in =-=[43,9,55,32,5,56,37]-=-. In general, AC matching can return several solutions, which introduces a need for backtracking for conditional rules: as long as there is a solution to the AC matching problem for which the matching... |

47 | Rewriting with strategies in ELAN: A functional semantics
- Borovanský, Kirchner, et al.
(Show Context)
Citation Context ...the top level evaluation mechanism. It is less convenient to describe the details of the evaluation mechanism. For that purpose, a different semantics can be given to ELAN using a functional approach =-=[15,17]-=-, or more generally using the rewriting calculus [21], a uniform extension of both rewriting and the lambda calculus which is developed in the untyped [25,23], simply typed [24] or generally typed [28... |

43 | Controlling rewriting by rewriting
- Borovansky, Kirchner, et al.
(Show Context)
Citation Context ...guages used in theorem proving. ELAN has a functional semantics described in [15], and logical foundations based on rewriting logic [61,58] and detailed in this paper, which is a revised extension of =-=[14]-=-. So the simple and well-known paradigm of term rewriting provides both the logical framework in which deduction systems can be expressed and combined, and the evaluation mechanism of the language. Th... |

31 |
Automatically Proving Termination and Innermost Normalization of Term Rewriting Systems
- Arts
- 1997
(Show Context)
Citation Context ...cient condition is to have a confluent and terminating system which can be obtained through standard completion techniques. Few results are known on proving these properties under specific strategies =-=[41,3,38]-=-. During the evaluation process, unlabelled rules are applied eagerly, before each application of labelled rules. Assuming that the set of unlabelled rules E is confluent and terminating, the congruen... |

26 |
Calcul de réécriture : fondements et applications. Thèse de Doctorat d’Université, Université Henri Poincaré - Nancy I
- Cirstea
- 2000
(Show Context)
Citation Context ...o a view of strategies in reflective logics (in particular, rewriting logic) developed in [30]. Strategies can also be expressed in the rewriting calculus [25], a different point of view developed in =-=[21]-=-. The strategy notion is a main concept in theorem proving, constraint solving and in programming languages. It is specially useful when search is involved and has been very often treated in a built-i... |

24 | Autarkic Computations in Formal Proofs
- Barendregt, Barendsen
- 2002
(Show Context)
Citation Context ...tions, performed by unlabelled rules, and deductions, performed by labelled rules under certain strategies. This is a very convenient approach to implement deduction modulo [34], or what is called in =-=[7]-=- the Poincaré Principle. The interest of distinguishing between logical deduction and computation in various areas of automated deduction and program construction is argued in [33]. ELAN can be consid... |

22 |
Associative-commutative discrimination nets
- Bachmair, Chen, et al.
- 1993
(Show Context)
Citation Context ...n symbols, AC matching is invoked. The term l is said to AC match another term t if there exists a substitution σ such that lσ =AC t. AC matching has already been extensively studied, for instance in =-=[43,9,55,32,5,56,37]-=-. In general, AC matching can return several solutions, which introduces a need for backtracking for conditional rules: as long as there is a solution to the AC matching problem for which the matching... |

22 | Combining Higher-Order and First-Order Computation Using ρ-calculus: Towards a semantics of ELAN
- Cirstea, Kirchner
- 1998
(Show Context)
Citation Context ...given to ELAN using a functional approach [15,17], or more generally using the rewriting calculus [21], a uniform extension of both rewriting and the lambda calculus which is developed in the untyped =-=[25,23]-=-, simply typed [24] or generally typed [28] cases. The rewriting calculus, also called ρ-calculus, allows us to deal with explicit rule application, explicit handling of result sets, and is parameteri... |

21 |
Building Constraint Satisfaction Problem Solvers Using Rewrite Rules and Strategies
- Castro
- 1998
(Show Context)
Citation Context ...s also a library of standard ELAN modules, a user manual and examples of applications. Among those, let us mention for instance the design of rules and strategies for constraint satisfaction problems =-=[19]-=-, theorem proving tools in first-order logic with equality [52,22], the combination of unification algorithms and of decision procedures in various equational theories [66,50]. More information on the... |

20 | Implementation of Higher-Order Unification Based on Calculus of Explicit Substitutions
- Borovanský
- 1995
(Show Context)
Citation Context ...esigned in the ELAN framework [50], since its operational semantics is clearly formalised as rewrite rules, although the application strategy is often defined in an informal way. Some implementations =-=[10]-=- related to a calculus of explicit substitutions (the first-order rewrite system λσ that mimics λ-calculus) open the way of implementing higher-order logic programming languages via a first-order sett... |

20 |
A functional view of rewriting and strategies for a semantics of ELAN
- Borovanský, Kirchner, et al.
- 1998
(Show Context)
Citation Context ...ule-based computation at the strategy level (not only at the first-order level) distinguishes ELAN from others strategy languages used in theorem proving. ELAN has a functional semantics described in =-=[15]-=-, and logical foundations based on rewriting logic [61,58] and detailed in this paper, which is a revised extension of [14]. So the simple and well-known paradigm of term rewriting provides both the l... |

14 |
contrôle de la réécriture: étude et implantation d’un formalisme de stratégies. Thèse de Doctorat d’Universite
- Le
- 1998
(Show Context)
Citation Context ...erms is given by simplification rules for elementary strategies: [] id ; S → S [] S ; id → S [] dc(S, S) → S [] dk(S, S) → S More sophisticated examples of using the strategy language can be found in =-=[11]-=-. 3.6 Labelled and unlabelled rules The evaluation process considered here makes an important difference between labelled and unlabelled rules. – Labelled rules are applied under the full control of s... |

14 | Solving Binary CSP using Computational Systems
- Castro
- 1996
(Show Context)
Citation Context ... tested on several examples of constraint solvers for various computation domains and combinations like abstract domains [50,66] (term algebras) and more concrete ones (booleans, integers, reals). In =-=[18,19]-=-, it is shown how to use computational systems as a general framework for handling Constraint Satisfaction Problems (CSP for short). The approach leads to the design in ELAN of COLETTE [20], a solver ... |

11 | elan for equational reasoning in coq
- Alvarado, Nguyen
(Show Context)
Citation Context ...f rewriting was either inefficient or potentially unsafe, depending on the way it was implemented. On the skeptical (and therefore safe) way we have designed a cooperation schema between COQ and ELAN =-=[2]-=- that provides a safe as well as efficient way to implement normalization in proof assistants. This is extended to deal with conditional rewriting modulo associativity and commutativity in [63]. Solvi... |

10 | C.: The simply typed rewriting calculus
- Cirstea, Kirchner
- 2000
(Show Context)
Citation Context ...functional approach [15,17], or more generally using the rewriting calculus [21], a uniform extension of both rewriting and the lambda calculus which is developed in the untyped [25,23], simply typed =-=[24]-=- or generally typed [28] cases. The rewriting calculus, also called ρ-calculus, allows us to deal with explicit rule application, explicit handling of result sets, and is parameterised by a matching 3... |

5 | Cooperation of Constraint Solvers: Using the New Process Control Facilities of ELAN. This volume
- Borovanský, Castro
(Show Context)
Citation Context ...ems (CSP for short). The approach leads to the design in ELAN of COLETTE [20], a solver for constraints over integers and finite domains. A generalisation of the ELAN strategy language is proposed in =-=[12]-=- for programming the cooperation of constraint solvers. Another class of applications that can be identified concerns proof and program transformations. In particular XML transformations are currently... |

4 |
Prototyping CSP Solvers Using a Rule-Based Language
- COLETTE
- 1998
(Show Context)
Citation Context ...ls). In [18,19], it is shown how to use computational systems as a general framework for handling Constraint Satisfaction Problems (CSP for short). The approach leads to the design in ELAN of COLETTE =-=[20]-=-, a solver for constraints over integers and finite domains. A generalisation of the ELAN strategy language is proposed in [12] for programming the cooperation of constraint solvers. Another class of ... |

3 | Verification of timed automata using rewrite rules and strategies
- Beffara, Bournez, et al.
(Show Context)
Citation Context ...n-conditional rewrite rules [39]. Timed automata is a particular class of continuous real-time models of reactive systems for which model-checking algorithms have been designed and prototyped in ELAN =-=[8]-=-. The verification of protocols can also be easily and efficiently designed in ELAN. In particular the experiments reported in [26] show very competitive performances together with high level, abstrac... |

3 | C.: Using rewriting and strategies for describing the B predicate prover
- Cirstea, Kirchner
- 1998
(Show Context)
Citation Context ...amples of applications. Among those, let us mention for instance the design of rules and strategies for constraint satisfaction problems [19], theorem proving tools in first-order logic with equality =-=[52,22]-=-, the combination of unification algorithms and of decision procedures in various equational theories [66,50]. More information on the system can be found on the web site http://elan.loria.fr. This pa... |