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Primitive Rewriting [chapter]

Nachum Dershowitz
2005 Lecture Notes in Computer Science  
It comes as no surprise that rewrite systems have the same computational power as the other basic models. 2 Moreover, rewrite systems may be restricted in various ways, including left-linearity, orthogonality  ...  This paper present some undecidability results for "primitive" term rewriting systems, which encode primitive-recursive definitions. Primitive rewriting is defined in Sect. 3.  ...  Acknowledgement I thank the referees for their critical reading and constructive suggestions.  ... 
doi:10.1007/11601548_10 fatcat:ndwwizgbe5gzzj2quk743cq3yy

Page 5207 of Mathematical Reviews Vol. , Issue 2002G [page]

2002 Mathematical Reviews  
(YV-SBOL-AM; Caracas) Strictly orthogonal left linear rewrite systems and primitive recursion. (English summary) Proceedings of the XIth Latin American Symposium on Mathematical Logic (Mérida, 1998).  ...  The main theorem shows that if the rewrite rules behave in a reasonable way (i.e. the system is strictly orthogonal left linear) then bounds on lengths of the derivations of irreducible terms can be computed  ... 

Definitions by Rewriting in the Calculus of Constructions [article]

Frédéric Blanqui
2006 arXiv   pre-print
As examples, we show that two important systems satisfy these conditions: a sub-system of the Calculus of Inductive Constructions which is the basis of the proof assistant Coq, and the Natural Deduction  ...  The main novelty of this paper is to consider an extension of the Calculus of Constructions where predicates can be defined with a general form of rewrite rules.  ...  Acknowledgments : I would like to thank Daria Walukiewicz, Gilles Dowek, Jean-Pierre Jouannaud and Christine Paulin for useful comments on previous versions of this work.  ... 
arXiv:cs/0610065v1 fatcat:hvwyvhtr7bc75cdznu2ztg5jde

Natural termination

Nachum Dershowitz, Charles Hoot
1995 Theoretical Computer Science  
The second approach uses restricted derivations, called "forward closures", for proving termination of orthogonal and overlaying systems.  ...  For recent surveys of the theory of rewriting, see [-9, 17, 33]. If no infinite sequences of rewrites are possible, a rewrite system is said to have the termination property.  ...  An orthogonal system is nonoverlapping and left-linear.  ... 
doi:10.1016/0304-3975(94)00275-4 fatcat:t42jm4unqnccfnipfcufmlozxi

Computing in unpredictable environments: semantics, reduction strategies, and program transformations

Björn Lisper
1998 Theoretical Computer Science  
combined system, provided the environment behaves in a "fair" manner, and certain program transformations, such as folding and unfolding with respect to deterministic rules, will preserve the semantics  ...  An application is evaluation strategies and program transformations for concurrent languages.  ...  Acknowledgements I want to thank Vincent van Oostrom and Jan Willem Klop for their kind assistance regarding higher order rewriting formalisms, and the anonymous referees for their valuable comments.  ... 
doi:10.1016/s0304-3975(97)00084-4 fatcat:vjnjfcqk6ngxvagmqtpmuv6mui

The Power of Closed Reduction Strategies

Sandra Alves, Maribel Fernández, Mario Florido, Ian Mackie
2007 Electronical Notes in Theoretical Computer Science  
We show that a linear System T with closed reduction offers a huge increase in expressive power over the usual linear systems, which are 'closed by construction' rather than 'closed at reduction'.  ...  The main contribution of this paper is a new application of this strategy to a linear version of Gödel's System T.  ...  Acknowledgement We are grateful to the anonymous referees for their comments, and to Bernhard Gramlich for pointing out relevant references.  ... 
doi:10.1016/j.entcs.2007.02.047 fatcat:mag4honadbbqjdqo45w657mrrm

A rationale for conditional equational programming

Nachum Dershowitz, Mitsuhiro Okada
1990 Theoretical Computer Science  
Together, rewriting and narrowing provide increased expressive power.  ...  The simplest provide a convenient interface between resolutionbased goal reduction and rewrite-based term evaluation, by using rewrite rules to normalize terms (i.e. rewriting them to terms that cannot  ...  If ajirst-order conditional rewrite system is terminating, then the system extended by higher-order constructor-based primitive recursive rules and the typed A-calculus is also terminating.  ... 
doi:10.1016/0304-3975(90)90064-o fatcat:rojkwf4kx5avrk7kcs23gkyogi

Strong normalization proofs for cut elimination in Gentzen's sequent calculi

Elias Bittar
1999 Banach Center Publications  
We give a strong normalization proof by applying orthogonal term rewriting results for a confluent restriction of the mix elimination system E LKsp .  ...  This modification allows us to interpret a symmetrical system of mix elimination rules E LKsp by a finite rewriting system; the termination of this rewriting system can be machine checked.  ...  rules is left linear.  ... 
doi:10.4064/-46-1-179-225 fatcat:s63qp5afl5bbrkz4xnkeokhzua

On sharing, memoization, and polynomial time

Martin Avanzini, Ugo Dal Lago
2018 Information and Computation  
We extend upon Leivant's notion of ramified recursive functions [20] by allowing definitions by generalised ramified simultaneous recurrence (GRSR for short).  ...  We then extend the underlying rewriting based semantics with memoization, i.e. intermediate results are automatically tabulated to avoid expensive re-computation (Section 4).  ...  Moreover, we require that P is orthogonal, that is, the following two requirements are met: 1. left-linearity: the left-hand sides l of each rule l → r ∈ R is linear; and 2. non-ambiguity: there are no  ... 
doi:10.1016/j.ic.2018.05.003 fatcat:jqh5pmhx5neergx7qholahw76e

Page 6898 of Mathematical Reviews Vol. , Issue 2001J [page]

2001 Mathematical Reviews  
Cichon and E. Tahhan-Bittar, Strictly orthogonal left linear rewrite systems and primitive recursion (79- 101); Marcelo E.  ...  Diaz Varela, On subvarieties of symmetric closure algebras (137-152); Jiirgen Dix, Mauricio Osorio and Claudia Zepeda, A general theory of confluent rewriting systems for logic programming and its applica  ... 

From Rules to Constraint Programs with the Rules2CP Modelling Language [chapter]

François Fages, Julien Martin
2009 Lecture Notes in Computer Science  
We present a general purpose rule-based modelling language, called Rules2CP, and describe its compilation to constraint programs over finite domains with reified and global constraints, using term rewriting  ...  and partial evaluation.  ...  The first author is also grateful to the previous collaboration he had on this topic in the RNTL project Manifico with Christian de Sainte Marie and Xavier Ceugniet from ILOG and Claude Kirchner and Pierre-Etienne  ... 
doi:10.1007/978-3-642-03251-6_5 fatcat:uxdbkolugrgtncuvmlzsqx63am

Least Upper Bounds on the Size of Church-Rosser Diagrams in Term Rewriting and λ-Calculus [chapter]

Jeroen Ketema, Jakob Grue Simonsen
2010 Lecture Notes in Computer Science  
In contrast, for orthogonal term rewriting systems R we prove that there is a constant k such that vsR(m, n) is bounded from above by a function exponential in k and independent of the size of s.  ...  We study the Church-Rosser property-which is also known as confluence-in term rewriting and λ-calculus.  ...  We would like to thank Richard Statman and Andrzej Filinski for providing valuable answers to some of our questions.  ... 
doi:10.1007/978-3-642-12251-4_20 fatcat:2qwpq67xiffixbnrklwnohti5m

The taming of the rew: a type theory with computational assumptions

Jesper Cockx, Nicolas Tabareau, Théo Winterhalter
2021 Proceedings of the ACM on Programming Languages (PACMPL)  
To overcome the lack of certain programming primitives or logical principles in those systems, it is common to appeal to axioms to postulate their existence.  ...  We further describe an algorithm to check that the triangle criterion indeed holds for a given rewrite system, as well as our implementation of rewrite rules for the Agda system, in Sect. 7.  ...  He shows that combining two left-linear higher-order rewrite systems is confluent if the systems are individually confluent and weakly orthogonal (i.e., all critical pairs between them are trivial).  ... 
doi:10.1145/3434341 fatcat:nuswqtklpfgi3f6xmkzfksnudi

Query Languages for Bags and Aggregate Functions

Leonid Libkin, Limsoon Wong
1997 Journal of computer and system sciences (Print)  
Structural recursion on bags is shown to be equivalent to the bounded loop operator and strictly more powerful than the powerbag primitive.  ...  To enhance the expressiveness of BQL, we consider non-polynomial primitives such as powerbag, structural recursion, and bounded loop.  ...  We gratefully acknowledge the support of an AT&T Doctoral Fellowship and NSF Grant IRI-90-04137 (for Libkin) and NSF Grant IRI-90-04137 and ARO Grant DAALO3-89-C-0031-PRIME (for Wong).  ... 
doi:10.1006/jcss.1997.1523 fatcat:7m2vmj7fdzgpljfzcwysodcktq

A verifying core for a cryptographic language compiler

Lee Pike, Mark Shields, John Matthews
2006 Proceedings of the sixth international workshop on the ACL2 theorem prover and its applications - ACL2 '06  
Finally, we describe an ACL2 book of primitive operations for the general specification and verification of encryption algorithms.  ...  The compiler also supplies measure functions that ACL2 uses to automatically prove termination of µCryptol programs, including programs with mutually-recursive cliques of streams.  ...  Acknowledgments We received advice and comments from the following individuals: David Hardin, Eric Smith, and Tom Johnson, Konrad Slind, our anonymous reviewers, and Matt Kaufmann and the other participants  ... 
doi:10.1145/1217975.1217977 dblp:conf/acl2/PikeSM06 fatcat:pubnl7wmrbhaff7oqggojutmsi
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