## Strategic Computation and Deduction (2009)

Citations: | 4 - 3 self |

### BibTeX

@MISC{Kirchner09strategiccomputation,

author = {Claude Kirchner and Florent Kirchner and Hélène Kirchner and Peter B. Andrews},

title = {Strategic Computation and Deduction},

year = {2009}

}

### OpenURL

### Abstract

I'd like to conclude by emphasizing what a wonderful eld this is to work in. Logical reasoning plays such a fundamental role in the spectrum of intellectual activities that advances in automating logic will inevitably have a profound impact in many intellectual disciplines. Of course, these things take time. We tend to be impatient, but we need some historical perspective. The study of logic has a very long history, going back at least as far as Aristotle. During some of this time not very much progress was made. It's gratifying to realize how much has been accomplished in the less than fty years since serious e orts to mechanize logic began.

### Citations

939 |
Term rewriting and all that
- Baader, Nipkow
- 1998
(Show Context)
Citation Context ...graph instead of relation. This is due to the fact that, speaking of derivations, we need to make a di erence between being in relation and being connected . Typically modeling ARS as relations as in =-=[5]-=- allows us to say that, e.g, a and b are in relation but not that there may be several di erent ways to derive b from a. Consequently, we need to use the more expressive approach of [54, 38], based on... |

565 | Term Rewriting Systems
- Klop
- 1992
(Show Context)
Citation Context ...on Let us now come back to the more classical context of rst-order terms and term rewriting to see how it ts to the general notions presented above. Basic de nitions on term rewriting can be found in =-=[33, 37, 5]-=-. The following standard notations will be used in the following. T (F, X ) is the set of rst-order terms built from a given nite set F of function symbols and a denumerable set X of variables. The se... |

560 |
Untersuchungen über das logische Schliessen
- Gentzen
- 1935
(Show Context)
Citation Context ... reduction system framework. Our purpose in this section is not to formalize any particular instance of a deduction system, such as classical natural deduction [52] or intuitionistic sequent calculus =-=[24]-=-: our model is set-theoretic. Roughly, sequents/typing judgements are composed of a nite set of labelled hypotheses, a nite set of labelled conclusions, and a proof term. DEFINITION 19 (Labelled propo... |

165 |
Logic and Computation: Interactive Proof with Cambridge LCF
- Paulson
- 1987
(Show Context)
Citation Context ...2 only if the application of t1 has either failed, or did not modify the proof. All major implementations of proof strategy languages are based on a core set of commands inherited from the lcf prover =-=[50]-=-, namely: then, thenl, orelse, idtac, fail, and repeat. The natural question to ask is whether it is possible to bridge the divide between a lcf-style proof strategy language and the concept of a proo... |

161 | The duality of computation
- Curien, Herbelin
(Show Context)
Citation Context ... logical settings, where the pivotal proof terms might appear, not only at the level of formulas, but also at the level of sequents. For instance, in the case of sequent calculus à la Curien-Herbelin =-=[17]-=-, the sequents Γ ⊢ λx.v : A ⇒ B; ∆ and 〈v|e〉 : (Γ ⊢ ∆), where λx.v and 〈v|e〉 are pivotal ¯ λµ˜µ-proof terms, are well-formed. In our formalism, while the rst sequent is expressed using the aforementio... |

145 |
Completion of a set of rules modulo a set of equations
- Jouannaud, Kirchner
- 1986
(Show Context)
Citation Context ...ere matching is performed modulo an equational theory like associativitycommutativity of some fonction symbols. Strategic rewriting can therefore be de ned for rewriting modulo relations as de ned in =-=[51, 31]-=-. Besides the rewriting relation, another reduction relation, called narrowing, is worth considering to develop an ARS. This well-known process, introduced in [22, 29], is quite similar to rewriting b... |

135 |
Complete sets of reductions for some equational theories
- Peterson, Stickel
- 1981
(Show Context)
Citation Context ...ere matching is performed modulo an equational theory like associativitycommutativity of some fonction symbols. Strategic rewriting can therefore be de ned for rewriting modulo relations as de ned in =-=[51, 31]-=-. Besides the rewriting relation, another reduction relation, called narrowing, is worth considering to develop an ARS. This well-known process, introduced in [22, 29], is quite similar to rewriting b... |

132 | Stratego: A language for program transformation based on rewriting strategies. System description of Stratego 0.5
- Visser
- 2001
(Show Context)
Citation Context ...e system R, moreStrategic Computation and Deduction 3 inria-00433745, version 1 - 20 Nov 2009 elaborated strategies expressions can be built using a strategy language like in ELAN [34, 10], Stratego =-=[56]-=-, TOM [6] or more recently Maude [44]. The semantics of such a language is naturally described in the rewriting calculus [14, 15]. A similar mechanism also exists in proof systems, where a set of core... |

77 |
Term Rewriting Systems
- Terese
- 2003
(Show Context)
Citation Context ...elations as in [5] allows us to say that, e.g, a and b are in relation but not that there may be several di erent ways to derive b from a. Consequently, we need to use the more expressive approach of =-=[54, 38]-=-, based on a notion of oriented graph instead of that of a relation. DEFINITION 1. An abstract reduction system (ARS) is a labelled oriented graph (O, S). The nodes in O are called objects, the orient... |

76 | Theorem proving modulo
- Dowek, Hardin, et al.
(Show Context)
Citation Context ...but will contribute to de ne in a uniform way what strategies are for computation and deduction. The complementarity between deduction and computation, as emphasized in particular in deduction modulo =-=[19]-=-, allows us to now envision a completely new generation of proof assistants where customized deductions are performed modulo appropriate and user de nable computations [11, 12]. This has in particular... |

69 | TPS: A Theorem Proving System for Classical Type Theory
- Andrews, Bishop, et al.
- 1996
(Show Context)
Citation Context ... possible the safe use of existing dedicated proof environments [36, 20, 9]. This generalizes the approaches typical in rst-order theorem proving [45], as well as higher-order ones like PVS [49], TPS =-=[3, 4]-=-, Omega [8, 53] or Coq [21], to mention just a few.2 Claude Kirchner, Florent Kirchner, Hélène Kirchner inria-00433745, version 1 - 20 Nov 2009 To encompass this view of computation and deduction uni... |

69 | Context-sensitive computations in functional and functional logic programs
- Lucas
- 1998
(Show Context)
Citation Context ... rewriting where a redex is chosen in a set of positions. More precisley, here, a replacement map is a mapping µ : F ↦→ P(N) satisfying µ(f) ⊆ {1, . . . , k}, for each k-ary symbol f of a signature F =-=[40]-=-. Replacement maps discriminate the argument positions on which the rewriting steps are allowed. Needed and standard reduction In [27, 28], the notions of needed and strongly needed redexes are de ned... |

60 |
Designing Constraint Logic Programming Languages using Computational Systems
- KIRCHNER, KIRCHNER, et al.
- 1993
(Show Context)
Citation Context ... from a term rewrite system R, moreStrategic Computation and Deduction 3 inria-00433745, version 1 - 20 Nov 2009 elaborated strategies expressions can be built using a strategy language like in ELAN =-=[34, 10]-=-, Stratego [56], TOM [6] or more recently Maude [44]. The semantics of such a language is naturally described in the rewriting calculus [14, 15]. A similar mechanism also exists in proof systems, wher... |

43 | The Implementation of ALF - a Proof Editor based on Martin-Lof's Monomorphic Type Theory with Explicit Substitution", Chalmers University ofTechnology and University ofGoteborg
- Magnusson
- 1995
(Show Context)
Citation Context ...proof term, unanswered. Yet this is a fundamental mechanism in the design of proof assistants. In order to address this question, various18 Claude Kirchner, Florent Kirchner, Hélène Kirchner authors =-=[43, 47, 30]-=- have shown that the syntax of proof terms and sequents can be extended with proof metavariables, that represent the still unknown parts of a proof. inria-00433745, version 1 - 20 Nov 2009 DEFINITION ... |

41 | Rewriting with strategies in ELAN: a functional semantics
- Borovansk´y, Kirchner, et al.
(Show Context)
Citation Context ... from a term rewrite system R, moreStrategic Computation and Deduction 3 inria-00433745, version 1 - 20 Nov 2009 elaborated strategies expressions can be built using a strategy language like in ELAN =-=[34, 10]-=-, Stratego [56], TOM [6] or more recently Maude [44]. The semantics of such a language is naturally described in the rewriting calculus [14, 15]. A similar mechanism also exists in proof systems, wher... |

35 | Strong Normalisation of Cut-Elimination in Classical Logic
- Urban, Bierman
(Show Context)
Citation Context ...sing the same process as in Example 21, the second sequent is trivially represented by the isomorphic triple 〈v|e〉 ∴ (Γ ⊢ ∆), in which no `∗' label appear. The same holds for Urban's sequent calculus =-=[55]-=-, which places all proof terms on the same level as the antecedents and consequents. Finally we need to add a notion of list of sequents: therefore we introduce the usual list constructors cons and ni... |

34 | A tactic language for the system Coq
- Delahaye
- 2000
(Show Context)
Citation Context ...xists in proof systems, where a set of core strategies, historically derived from the language lcf, is used to program sophisticated proof search patterns. The semantics of such a language appears in =-=[18, 30, 35]-=-. Building upon the de nition of abstract reduction systems (recalled in Section 2), the main contributions of this paper are as follows: we propose in Section 3 a notion of abstract strategies togeth... |

30 | Termination of on-demand rewriting and termination of OBJ programs
- Lucas
- 2001
(Show Context)
Citation Context ...on 1 - 20 Nov 2009 term t, the next redex is chosen according to LS(f) where f is the top operator of the term t. Context-sensitive reduction Local strategies are close to context-sensitive rewriting =-=[41, 42, 1]-=-, where rewriting is also allowed only at some speci ed positions in the terms. The former specify an ordering on these rewriting positions, so they are more speci c than context-sensitive rewriting w... |

28 |
A metalanguage for interactive proof in LCF
- Gordon, Milner, et al.
- 1978
(Show Context)
Citation Context ...to the semantics of proof systems. 6.2 Proof rewriting strategies The need for the creation of a mechanism for proof strategies was acknowledged along with the rst theorem provers implementations. In =-=[26]-=-, the authors remark that their initial attempts at using lcf [46], one of the rst deduction software, were limited by the commands , xed, and rather primitive, nature of its repertoire ofStrategic C... |

28 |
PVS: A prototype veri cation system
- Owre, Rushby, et al.
(Show Context)
Citation Context ...13] making possible the safe use of existing dedicated proof environments [36, 20, 9]. This generalizes the approaches typical in rst-order theorem proving [45], as well as higher-order ones like PVS =-=[49]-=-, TPS [3, 4], Omega [8, 53] or Coq [21], to mention just a few.2 Claude Kirchner, Florent Kirchner, Hélène Kirchner inria-00433745, version 1 - 20 Nov 2009 To encompass this view of computation and d... |

26 |
An introduction to OBJ3
- Goguen, Kirchner, et al.
- 1988
(Show Context)
Citation Context ...e performed with other mechanisms, such as local strategies or context-sensitive rewriting. Reduction under local strategies Local strategies on operators, used for instance in the OBJ-like languages =-=[25]-=-, introduce a function LS from F to the set L(N) of lists of integers to specify which and in which order the arguments of each function symbol have to be reduced. At each step of the derivation, for ... |

26 |
Towards a strategy language for Maude
- Martí-Oliet, Meseguer, et al.
- 2005
(Show Context)
Citation Context ...n and Deduction 3 inria-00433745, version 1 - 20 Nov 2009 elaborated strategies expressions can be built using a strategy language like in ELAN [34, 10], Stratego [56], TOM [6] or more recently Maude =-=[44]-=-. The semantics of such a language is naturally described in the rewriting calculus [14, 15]. A similar mechanism also exists in proof systems, where a set of core strategies, historically derived fro... |

24 |
TPS: A hybrid automatic-interactive system for developing proofs
- Andrews, Brown
(Show Context)
Citation Context ... possible the safe use of existing dedicated proof environments [36, 20, 9]. This generalizes the approaches typical in rst-order theorem proving [45], as well as higher-order ones like PVS [49], TPS =-=[3, 4]-=-, Omega [8, 53] or Coq [21], to mention just a few.2 Claude Kirchner, Florent Kirchner, Hélène Kirchner inria-00433745, version 1 - 20 Nov 2009 To encompass this view of computation and deduction uni... |

23 | Lazy rewriting on eager machinery
- Fokkink, Kamperman, et al.
- 2000
(Show Context)
Citation Context ...sition ω in t is such that there is no su x (resp. pre x) position ω ′ of ω such that t rewrites at position ω ′ . Lazy reduction Lazy reduction, as performed in Haskell for instance, or described in =-=[23]-=-, combines innermost and outermost strategies, in order to avoid redundant rewrite steps. For that, operators of the signature have labels specifying which arguments are lazy or eager. Positions in te... |

22 |
Implementation and applications of Scott’s logic for computable functions
- Milner
- 1972
(Show Context)
Citation Context ...The need for the creation of a mechanism for proof strategies was acknowledged along with the rst theorem provers implementations. In [26], the authors remark that their initial attempts at using lcf =-=[46]-=-, one of the rst deduction software, were limited by the commands , xed, and rather primitive, nature of its repertoire ofStrategic Computation and Deduction 21 The strategy language of modern proced... |

21 | Termination of Rewriting With Strategy Annotations
- Lucas
- 2001
(Show Context)
Citation Context ...on 1 - 20 Nov 2009 term t, the next redex is chosen according to LS(f) where f is the top operator of the term t. Context-sensitive reduction Local strategies are close to context-sensitive rewriting =-=[41, 42, 1]-=-, where rewriting is also allowed only at some speci ed positions in the terms. The former specify an ordering on these rewriting positions, so they are more speci c than context-sensitive rewriting w... |

19 | Embedding pure type systems in the lambda-pi-calculus modulo
- Cousineau, Dowek
- 2007
(Show Context)
Citation Context ...ed deductions are performed modulo appropriate and user de nable computations [11, 12]. This has in particular the advantage to allow for a uniform implementation of higher-order and rst-order logics =-=[16, 13]-=- making possible the safe use of existing dedicated proof environments [36, 20, 9]. This generalizes the approaches typical in rst-order theorem proving [45], as well as higher-order ones like PVS [49... |

18 | Rewrite strategies in the rewriting calculus
- Cirstea, Kirchner, et al.
- 2003
(Show Context)
Citation Context ...ons can be built using a strategy language like in ELAN [34, 10], Stratego [56], TOM [6] or more recently Maude [44]. The semantics of such a language is naturally described in the rewriting calculus =-=[14, 15]-=-. A similar mechanism also exists in proof systems, where a set of core strategies, historically derived from the language lcf, is used to program sophisticated proof search patterns. The semantics of... |

18 | Arithmetic as a theory modulo
- Dowek, Werner
(Show Context)
Citation Context ...11, 12]. This has in particular the advantage to allow for a uniform implementation of higher-order and rst-order logics [16, 13] making possible the safe use of existing dedicated proof environments =-=[36, 20, 9]-=-. This generalizes the approaches typical in rst-order theorem proving [45], as well as higher-order ones like PVS [49], TPS [3, 4], Omega [8, 53] or Coq [21], to mention just a few.2 Claude Kirchner... |

16 | Correct and complete (positive) strategy annotations F. Durán et al
- Alpuente, Escobar, et al.
- 2004
(Show Context)
Citation Context ...on 1 - 20 Nov 2009 term t, the next redex is chosen according to LS(f) where f is the top operator of the term t. Context-sensitive reduction Local strategies are close to context-sensitive rewriting =-=[41, 42, 1]-=-, where rewriting is also allowed only at some speci ed positions in the terms. The former specify an ordering on these rewriting positions, so they are more speci c than context-sensitive rewriting w... |

16 | The rewriting calculus Part I
- Cirstea, Kirchner
- 2001
(Show Context)
Citation Context ...ons can be built using a strategy language like in ELAN [34, 10], Stratego [56], TOM [6] or more recently Maude [44]. The semantics of such a language is naturally described in the rewriting calculus =-=[14, 15]-=-. A similar mechanism also exists in proof systems, where a set of core strategies, historically derived from the language lcf, is used to program sophisticated proof search patterns. The semantics of... |

15 |
Canonical Forms and Uni - cation
- Hullot
- 1980
(Show Context)
Citation Context ...ng modulo relations as de ned in [51, 31]. Besides the rewriting relation, another reduction relation, called narrowing, is worth considering to develop an ARS. This well-known process, introduced in =-=[22, 29]-=-, is quite similar to rewriting but there, matching is replaced by uni cation. Let us recall its usual de nition: DEFINITION 17 (One step narrowing). Given a term rewrite system R, an algebraic term t... |

14 |
Computer supported mathematics with Omega
- Siekmann, Benzmüller, et al.
(Show Context)
Citation Context ...safe use of existing dedicated proof environments [36, 20, 9]. This generalizes the approaches typical in rst-order theorem proving [45], as well as higher-order ones like PVS [49], TPS [3, 4], Omega =-=[8, 53]-=- or Coq [21], to mention just a few.2 Claude Kirchner, Florent Kirchner, Hélène Kirchner inria-00433745, version 1 - 20 Nov 2009 To encompass this view of computation and deduction uniformly, we star... |

10 | Building decision procedures in the calculus of inductive constructions
- Blanqui, Jouannaud, et al.
- 2007
(Show Context)
Citation Context ...11, 12]. This has in particular the advantage to allow for a uniform implementation of higher-order and rst-order logics [16, 13] making possible the safe use of existing dedicated proof environments =-=[36, 20, 9]-=-. This generalizes the approaches typical in rst-order theorem proving [45], as well as higher-order ones like PVS [49], TPS [3, 4], Omega [8, 53] or Coq [21], to mention just a few.2 Claude Kirchner... |

8 |
Radu Kopetz, Pierre-Etienne Moreau, and Antoine Reilles. Tom: Piggybacking rewriting on Java
- Balland, Brauner
- 2007
(Show Context)
Citation Context ...ould be applied. TOM, ELAN, Maude and Stratego provide exible and expressive strategy languages where highlevel strategies are de ned by combining low-level primitives. In this section, we choose TOM =-=[7]-=- 1 to illustrate the construction of strategy languages of this family and we describe below the main elements of the language. The 1 http://tom.loria.frStrategic Computation and Deduction 13 inria-0... |

8 | Proof-term synthesis on dependent-type systems via explicit substitutions
- Muñoz
(Show Context)
Citation Context ...proof term, unanswered. Yet this is a fundamental mechanism in the design of proof assistants. In order to address this question, various18 Claude Kirchner, Florent Kirchner, Hélène Kirchner authors =-=[43, 47, 30]-=- have shown that the syntax of proof terms and sequents can be extended with proof metavariables, that represent the still unknown parts of a proof. inria-00433745, version 1 - 20 Nov 2009 DEFINITION ... |

8 |
Natural Deduction. A Proof-Theoretical Study, volume 3
- Prawitz
- 1965
(Show Context)
Citation Context ...onstruction mechanism using the abstract reduction system framework. Our purpose in this section is not to formalize any particular instance of a deduction system, such as classical natural deduction =-=[52]-=- or intuitionistic sequent calculus [24]: our model is set-theoretic. Roughly, sequents/typing judgements are composed of a nite set of labelled hypotheses, a nite set of labelled conclusions, and a p... |

7 | Holes with Binding Power
- Jojgov
- 2003
(Show Context)
Citation Context ...xists in proof systems, where a set of core strategies, historically derived from the language lcf, is used to program sophisticated proof search patterns. The semantics of such a language appears in =-=[18, 30, 35]-=-. Building upon the de nition of abstract reduction systems (recalled in Section 2), the main contributions of this paper are as follows: we propose in Section 3 a notion of abstract strategies togeth... |

6 |
et al.: The Coq Proof Assistant Reference Manual, v
- Barras
(Show Context)
Citation Context ...sting dedicated proof environments [36, 20, 9]. This generalizes the approaches typical in rst-order theorem proving [45], as well as higher-order ones like PVS [49], TPS [3, 4], Omega [8, 53] or Coq =-=[21]-=-, to mention just a few.2 Claude Kirchner, Florent Kirchner, Hélène Kirchner inria-00433745, version 1 - 20 Nov 2009 To encompass this view of computation and deduction uniformly, we start from a rul... |

6 | Compact normalisation trace via lazy rewriting
- Nguyen
- 2001
(Show Context)
Citation Context ...re lazy or eager. Positions in terms are then annotated as lazy or eager, and the strategy consists in reducing the eager subterms only when their reduction allows a reduction step higher in the term =-=[48]-=-. Lazy reduction can also be performed with other mechanisms, such as local strategies or context-sensitive rewriting. Reduction under local strategies Local strategies on operators, used for instance... |

3 |
Development of Rewriting Strategies
- Letichevsky
- 1993
(Show Context)
Citation Context ...ns, the idea is now to provide a strategy language to specify which derivations we are interested in. Various approaches have followed, yielding di erent strategy languages such as ELAN [34, 10], APS =-=[39]-=-, Stratego [56], TOM [6] or more recently Maude [44]. All these languages share the concern to provide abstract ways to express control of rule applications, by using re exivity and the metalevel for ... |

2 |
First Order Uni cation in Equational Theories
- Fay
- 1979
(Show Context)
Citation Context ...ng modulo relations as de ned in [51, 31]. Besides the rewriting relation, another reduction relation, called narrowing, is worth considering to develop an ARS. This well-known process, introduced in =-=[22, 29]-=-, is quite similar to rewriting but there, matching is replaced by uni cation. Let us recall its usual de nition: DEFINITION 17 (One step narrowing). Given a term rewrite system R, an algebraic term t... |

2 |
Computational Logic; Essays in Honor of Alan Robinson, chapter
- Huet, Lévy
- 1991
(Show Context)
Citation Context ...g µ(f) ⊆ {1, . . . , k}, for each k-ary symbol f of a signature F [40]. Replacement maps discriminate the argument positions on which the rewriting steps are allowed. Needed and standard reduction In =-=[27, 28]-=-, the notions of needed and strongly needed redexes are de ned for orthogonal rewrite systems. The main idea here is to nd the optimal way, when it exists, to reach the normal form a term. A redex is ... |

2 |
Interoperable proof systems
- Kirchner
- 2007
(Show Context)
Citation Context ...xists in proof systems, where a set of core strategies, historically derived from the language lcf, is used to program sophisticated proof search patterns. The semantics of such a language appears in =-=[18, 30, 35]-=-. Building upon the de nition of abstract reduction systems (recalled in Section 2), the main contributions of this paper are as follows: we propose in Section 3 a notion of abstract strategies togeth... |

1 |
Herbrand Award Acceptance Speech. Journal of automated deduction
- Andrews
(Show Context)
Citation Context ...me not very much progress was made. It's gratifying to realize how much has been accomplished in the less than fty years since serious e orts to mechanize logic began. 1 Introduction Peter B. Andrews =-=[2]-=- Strategies, tactics, tacticals, proof plans, are terms widely used in arti cial intelligence, in automated or interactive reasoning, in semantics of programming languages as well as in every day life... |

1 |
Clément Houtmann, and Claude Kirchner. Principle of superdeduction
- Brauner
- 2007
(Show Context)
Citation Context ...ticular in deduction modulo [19], allows us to now envision a completely new generation of proof assistants where customized deductions are performed modulo appropriate and user de nable computations =-=[11, 12]-=-. This has in particular the advantage to allow for a uniform implementation of higher-order and rst-order logics [16, 13] making possible the safe use of existing dedicated proof environments [36, 20... |

1 | Superdeduction at work
- Brauner, Houtmann, et al.
- 2007
(Show Context)
Citation Context ...ticular in deduction modulo [19], allows us to now envision a completely new generation of proof assistants where customized deductions are performed modulo appropriate and user de nable computations =-=[11, 12]-=-. This has in particular the advantage to allow for a uniform implementation of higher-order and rst-order logics [16, 13] making possible the safe use of existing dedicated proof environments [36, 20... |

1 |
Superdeduction as a Logical Framework. submitted
- Burel
- 2008
(Show Context)
Citation Context ...ed deductions are performed modulo appropriate and user de nable computations [11, 12]. This has in particular the advantage to allow for a uniform implementation of higher-order and rst-order logics =-=[16, 13]-=- making possible the safe use of existing dedicated proof environments [36, 20, 9]. This generalizes the approaches typical in rst-order theorem proving [45], as well as higher-order ones like PVS [49... |

1 |
Strategic Rewriting. Electr. Notes Theor. Comput. Sci
- Kirchner
- 2005
(Show Context)
Citation Context ...ly rewritingbased computations on one hand, rule-based deduction and proof-search on the other hand. We will rely on previous works and strategy languages that have been recently designed and studied =-=[32]-=-. In rewriting, from elementary strategies expressions directly issued from a term rewrite system R, moreStrategic Computation and Deduction 3 inria-00433745, version 1 - 20 Nov 2009 elaborated strat... |

1 |
A preliminary version of a book available at http://www.loria.fr/~ckirchne/=rsp/rsp.pdf
- Rewriting, Proving
- 1999
(Show Context)
Citation Context ...on Let us now come back to the more classical context of rst-order terms and term rewriting to see how it ts to the general notions presented above. Basic de nitions on term rewriting can be found in =-=[33, 37, 5]-=-. The following standard notations will be used in the following. T (F, X ) is the set of rst-order terms built from a given nite set F of function symbols and a denumerable set X of variables. The se... |