## A reflective extension of ELAN (1996)

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Venue: | Electronic Notes in Theoretical Computer Science |

Citations: | 4 - 1 self |

### BibTeX

@INPROCEEDINGS{Kirchner96areflective,

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

title = {A reflective extension of ELAN},

booktitle = {Electronic Notes in Theoretical Computer Science},

year = {1996},

publisher = {Elsevier Science Publishers}

}

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### Abstract

The expressivity of rewriting logic as meta-logic has been already convincingly illustrated. The goal of this paper is to explore the reflective capabilities of ELAN, a language based on the concepts of computational systems and rewriting logic. We define a universal theory for the class of ELAN programs and the representation function associated to this universal theory. Then we detail the effective transformations to implement and propose the definition of two built-in modules that provide the last step to get the reflective capabilities we want for the ELAN system. 1

### Citations

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(Show Context)
Citation Context ...roviding the syntax, a set of conditional rewrite rules describing the deduction mechanism, and a strategy to guide application of rewrite rules. Formally, this is a rewrite theory in rewriting logic =-=[Mes92]-=-, [MOM93], together with a notion of strategy to select relevant computations. Strategy definitions in the currently distributed version of ELAN are based on a c○ 1998 Elsevier Science B. V.H. Kirchn... |

461 |
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Citation Context ...anism, and the ability to read and modify sources of programs. Several reflective languages have been designed in functional programming [Smi84], logic programming [BK82], object-oriented programming =-=[Mae87]-=- and rewrite system based languages [KSO95]. There is some hope of providing metalogical foundations for reflection in [CM96] that would unify many different approaches, and this is the reason why we ... |

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Citation Context ...anks to reflection, an extensible and flexible computation mechanism, and the ability to read and modify sources of programs. Several reflective languages have been designed in functional programming =-=[Smi84]-=-, logic programming [BK82], object-oriented programming [Mae87] and rewrite system based languages [KSO95]. There is some hope of providing metalogical foundations for reflection in [CM96] that would ... |

168 |
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(Show Context)
Citation Context ...ented in order to get the reflective capabilities we want for the ELAN system. Section 5 mentions some related work. 2 General setting This section briefly presents the main concepts of general logic =-=[Mes89]-=- and rewriting logic [Mes92]. We slightly generalise the syntax and proof theory of conditional rewriting logic by introducing rules with local affectations. The notion of universal theory proposed by... |

161 | Solving equations in abstract algebras: A rulebased survey of unification - Jouannaud, Kirchner - 1991 |

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- 2000
(Show Context)
Citation Context ...the syntax, a set of conditional rewrite rules describing the deduction mechanism, and a strategy to guide application of rewrite rules. Formally, this is a rewrite theory in rewriting logic [Mes92], =-=[MOM93]-=-, together with a notion of strategy to select relevant computations. Strategy definitions in the currently distributed version of ELAN are based on a c○ 1998 Elsevier Science B. V.H. Kirchner, P-E. ... |

145 |
Completion of a set of rules modulo a set of equations
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Citation Context ... class of a term t modulo E is denoted 〈t〉 E or just 〈t〉. For details and general results on calculus modulo 3H. Kirchner, P-E. Moreau equational axioms, the reader is invited to consult for example =-=[JK86]-=-. To simplify notation, we denote a sequence of objects (a1, . . .,an) by a or a n . Syntax. The syntax needed for defining a logic is provided by a signature which allows building sentences. In rewri... |

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(Show Context)
Citation Context ...nsible and flexible computation mechanism, and the ability to read and modify sources of programs. Several reflective languages have been designed in functional programming [Smi84], logic programming =-=[BK82]-=-, object-oriented programming [Mae87] and rewrite system based languages [KSO95]. There is some hope of providing metalogical foundations for reflection in [CM96] that would unify many different appro... |

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Citation Context ...,GT92], NuPRL [C + 86,KC86], or ELF [Pfe94] to cite a few, are providing interesting meta-reasoning capabilities. A survey and critique on metatheory and reflection in theorem proving can be found in =-=[Har95]-=-. On the other hand, in computer science, reflection takes its roots in universal Turing machines and functions. Designers of programming languages have been most interested, as we are in this paper, ... |

42 | Controlling Rewriting by Rewriting
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(Show Context)
Citation Context ...n automated deduction it is now a common approach to use a metalanguage to write strategies and tactics, specifying how object logic inference rules are composed to build proofs. We have developed in =-=[BKK96a]-=- a powerful strategy language for ELAN that is reflective in the sense that it is defined in rewriting logic. In order to implement it as an extension of the actual system, a systematic enrichment of ... |

35 | Axiomatizing Reflective Logics and Languages
- Clavel, Meseguer
- 1996
(Show Context)
Citation Context ...ing logic as a meta-logic able to encode various object logics, has been already convincingly illustrated in [Mes92,MOM93,KKV95a]. Reflective properties of rewriting logic are studied for instance in =-=[CM96]-=-, in which metalogical axioms for reflective logics and declarative languages in general are proposed. The two notions of universal theory for a class of representable theories and of representation f... |

27 | Reflection in constructive and non-constructive automated reasoning - Giunchiglia, Smaill - 1988 |

25 | The GETFOL Manual - GETFOL version 1 - Giunchiglia - 1992 |

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22 | A Metatheory of a Mechanized Object Theory
- Sera, Giunchiglia, et al.
- 1996
(Show Context)
Citation Context ...be an object theory, to derive statements about the object theory, to control the search or to talk about provability in the object theory. Reflection up and down are two inference rules mentioned in =-=[GT92]-=- to formalise switching levels, and to theoretically justify for instance the combination of object-level and metalevel proofs and search in theorem proving. Logical frameworks and theorem provers, su... |

21 | ELAN: Un cadre logique pour le prototypage de langages de programmation avec contraintes. Thèse de Doctorat d’Université, Université Henri Poincaré – Nancy 1 - Vittek - 1994 |

15 | Prototyping completion with constraints using computational systems. Pages 438–443 of
- Kirchner, Moreau
- 1995
(Show Context)
Citation Context ...schema that consists of applying rewrite rules on formulas with some strategy, until getting specific normal forms. In this sense they can be understood as computational systems. We have described in =-=[KM95]-=- completion algorithms in ELAN, in which rules to be completed are represented by terms, and the mechanism of simplification (ie. rewriting steps) is described in ELAN. In a reflective extension, we c... |

7 | Elf: A meta-language for deductive systems (system description
- Pfenning
(Show Context)
Citation Context ...n of object-level and metalevel proofs and search in theorem proving. Logical frameworks and theorem provers, such as the systems FOL [Wey80,GS89] and GETFOL [Giu92,GT92], NuPRL [C + 86,KC86], or ELF =-=[Pfe94]-=- to cite a few, are providing interesting meta-reasoning capabilities. A survey and critique on metatheory and reflection in theorem proving can be found in [Har95]. On the other hand, in computer sci... |

1 |
Reflective computation in term rewriting systems
- Kurihara, Sato, et al.
- 1995
(Show Context)
Citation Context ...ious section can be explained in terms of meta-level objects (such as signatures or sets of labelled rewrite rules and strategies) and base-level objects that are only terms. Using the terminology of =-=[KSO95]-=-, we can call metatransformation the representation function, that transforms meta-level objects into base-level objects, and base-transformation the converse transformation. In order to distinguish s... |