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Page 7275 of Mathematical Reviews Vol. , Issue 2004i [page]

<span title="">2004</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Only simple examples of term rewriting systems are given, just to il- lustrate the definitions. A preliminary discussion of equational reasoning and its semantics is given.  ...  Then the focus shifts to the question of whether, and under what conditions, properties such as confluence and termination are preserved when term rewriting systems with these properties are combined.  ... 
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Higher-order rewrite systems and their confluence

Richard Mayr, Tobias Nipkow
<span title="">1998</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
We define pattern rewrite systems (PRSs) as a special case of HRSs and extend three confluence results from term rewriting to PRSs: the critical pair lemma by Knuth and Bendix, confluence of rewriting  ...  modulo equations i la Huet, and confluence of orthogonal PRSs.  ...  Acknowledgement This paper has benefitted enormously from the amazing scrutiny of Ralph Matthes who was volunteered to present very preliminary fragments of it in a seminar.  ... 
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The taming of the rew: a type theory with computational assumptions

Jesper Cockx, Nicolas Tabareau, Théo Winterhalter
<span title="2021-01-04">2021</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dqy7qc7jkzal5bz3gueys3siz4" style="color: black;">Proceedings of the ACM on Programming Languages (PACMPL)</a> </i> &nbsp;
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.  ...  To ensure type soundness of RTT-as well as effective type checking-we provide a framework where confluence of user-defined rewrite rules can be checked modularly and automatically, and where adding new  ...  Confluence of the rewrite system for one-step reduction then follows from Equation 1. □ The triangle property holds for λΠ, the restriction of Martin-Löf type theory to its functional part.  ... 
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The Graph Rewriting Calculus: Confluence and Expressiveness [chapter]

Clara Bertolissi
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The proof of this result is quite elaborated, due to the non-termination of the system and to the fact that we work on equivalence classes of terms.  ...  This leads to a term-graph representation in an equational style where terms consist of unordered lists of equations. In this paper we show that the (linear) ρg-calculus is confluent.  ...  patterns and matching equations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11560586_10">doi:10.1007/11560586_10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x6b7s5apkbfbfhqp6vfaczi2oy">fatcat:x6b7s5apkbfbfhqp6vfaczi2oy</a> </span>
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Twenty Years Later [chapter]

Jean-Pierre Jouannaud
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Back in the late 80s, many of us feared that this would soon be the case, that research in rewrite systems was deepening the gap with everyday's computer science practice, and that we should develop rewrite-based  ...  Twenty years later is the title of a novel by the french writer Alexandre Dumas.  ...  with a uniform technique to reason about the word problem in an arbitrary equational theory, which is based on the existence of normal forms.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-32033-3_27">doi:10.1007/978-3-540-32033-3_27</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6xggpx3i7ve7rfewekdb4vfiv4">fatcat:6xggpx3i7ve7rfewekdb4vfiv4</a> </span>
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Abstract Modularity [chapter]

Michael Abbott, Neil Ghani, Christoph Lüth
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Research has typically focused on reasoning about the modularity of specific properties for specific ways of combining specific forms of rewriting.  ...  A priori there is no reason to believe that anything can actually be said about modularity without reference to the specifics of the particular systems etc.  ...  If we are going to reason about rewriting using M -rewrite systems, we need a definition of properties in terms of the representing monad M R .  ... 
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Type Theory Unchained: Extending Agda with User-Defined Rewrite Rules

Jesper Cockx, Assia Mahboubi, Marc Bezem
<span title="2020-09-24">2020</span> <i title="Schloss Dagstuhl - Leibniz-Zentrum für Informatik"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bg7eff2ccngt5gat6bipkw45b4" style="color: black;">Types for Proofs and Programs</a> </i> &nbsp;
Thus rewrite rules break the chains on computation and put its power back into the hands of its rightful owner: yours.  ...  Rewrite rules are a form of equality reflection that is applied automatically by the typechecker.  ...  The official documentation of rewrite rules in Agda is available in the user manual 1 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.types.2019.2">doi:10.4230/lipics.types.2019.2</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/types/Cockx19.html">dblp:conf/types/Cockx19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2ieag5d5tnazviahqquzip3pca">fatcat:2ieag5d5tnazviahqquzip3pca</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201212182136/https://drops.dagstuhl.de/opus/volltexte/2020/13066/pdf/LIPIcs-TYPES-2019-2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b6/f4/b6f401d07bef1a132336196b517bbba22a23556c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.types.2019.2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Developing developments

Vincent van Oostrom
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
In the absence of termination, confluence of rewriting systems is often hard to establish.  ...  The class of orthogonal rewriting systems is the main class of not-necessarily-terminating, but confluent rewriting systems.  ...  PRSs are rewriting systems which employ simply typed jb-calculus with pqa-conversion, and where left-hand sides of rewrite rules are restricted to the so-called patterns.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0304-3975(96)00173-9">doi:10.1016/s0304-3975(96)00173-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dmhrwtsgyvel5gogpybpihkccq">fatcat:dmhrwtsgyvel5gogpybpihkccq</a> </span>
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Problems in rewriting III [chapter]

Nachum Dershowitz, Jean-Pierre Jouannaud, Jan Willem Klop
<span title="">1995</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Acknowledgements We thank all the individuals who contributed questions, updates and solutions. Many thanks to Stefan Blom for substantial help producing this list.  ...  For higher-order rewrite formats as given by combinatory reduction systems [62] and higher-order rewrite systems [80; 96] , confluence has been proved in the restricted case of orthogonal systems.  ...  For left-linear AC systems, on the other hand, it is decidable [55] . What can be said more generally about restrictions on extended rewriting that give decidability?  ... 
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More problems in rewriting [chapter]

Nachum Dershowitz, Jean-Pierre Jouannaud, Jan Willem Klop
<span title="">1993</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
One of the earliest results established on modularity of combinations of term-rewriting systems is the confluence of the union of two confluent systems which share no symbols [Toyama, 1987] ; if symbols  ...  In contrast to term rewriting, confluence of general (hyper-)graph rewriting--in the "Berlin approach"--is undecidable, even for terminating systems [Plump, 1993] .  ... 
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PhD Abstracts

GRAHAM HUTTON
<span title="">2018</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uxwkeespobabbhdznzmxrfucny" style="color: black;">Journal of functional programming</a> </i> &nbsp;
As a service to the community, the Journal of Functional Programming publishes the abstracts from PhD dissertations completed during the previous year.  ...  This thesis is devoted to the mechanized confluence analysis of rewrite systems.  ...  The importance of these aspects is witnessed by the annual international confluence competition, where the leading automated tools analyze confluence of rewrite systems.  ... 
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Rewriting Modulo β in the λΠ-Calculus Modulo

Ronan Saillard
<span title="2015-07-27">2015</span> <i title="Open Publishing Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qzezkwolyvf33pglm2jldjklca" style="color: black;">Electronic Proceedings in Theoretical Computer Science</a> </i> &nbsp;
We prove that confluence of rewriting modulo beta is enough to ensure subject reduction and uniqueness of types.  ...  To handle the case where non confluence comes from the interference between the beta-reduction and rewrite rules with lambda-abstraction on their left-hand side, we introduce a notion of rewriting modulo  ...  The author thanks very much Ali Assaf, Olivier Hermant, Pierre Jouvelot and the reviewers for their very careful reading and many suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.185.6">doi:10.4204/eptcs.185.6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pdvyqqdeevg4fljifdsqwk45pe">fatcat:pdvyqqdeevg4fljifdsqwk45pe</a> </span>
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Basic Pattern Matching Calculi: a Fresh View on Matching Failure [chapter]

Wolfram Kahl
<span title="">2004</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Compared with the functional rewriting strategy usually employed to define the operational semantics of pattern matching in non-strict functional programming languages like Haskell or Clean, our pattern  ...  The main device is to embed into expressions the separate syntactic category of matchings; the resulting language naturally encompasses pattern guards and Boolean guards as special cases.  ...  With respect to reasoning, the full internalisation of pattern matching eliminates the problem of all priority systems that what is written down as an unconditional equation only applies to certain patterns  ... 
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Proving Ground Confluence of Equational Specifications Modulo Axioms [chapter]

Francisco Durán, José Meseguer, Camilo Rocha
<span title="">2018</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Third: to show ground confluence of the original specification, prove also ground joinable the equations added.  ...  achieve local confluence or reduce the number of critical pairs.  ...  Bouhoula proposes an inference system for simultaneously checking the sufficient completeness and ground confluence of constructor-based equational specifications.  ... 
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RAPT: A Program Transformation System Based on Term Rewriting [chapter]

Yuki Chiba, Takahito Aoto
<span title="">2006</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This paper describes a design and implementation of RAPT which implements this framework. RAPT transforms a term rewriting system according to a specified program transformation template.  ...  Chiba et al. (2005) proposed a framework of program transformation by template and automated verification of its correctness based on term rewriting.  ...  This work was partially supported by a grant from Japan Society for the Promotion of Science, No. 14580357 and grants from Ministry of Education, Culture, Sports, Science and Technology, Nos. 16016202  ... 
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