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Checking Overlaps of Nominal Rewriting Rules

Mauricio Ayala-Rincón, Maribel Fernández, Murdoch James Gabbay, Ana Cristina Rocha-Oliveira
2016 Electronical Notes in Theoretical Computer Science  
We also show how to refine the notion of rule overlap to derive confluence of the closed rewriting relation. The conditions that we define are easy to check using a nominal unification algorithm.  ...  In this paper, we give sufficient conditions for (local) confluence of closed nominal rewriting theories, based on the analysis of rule overlaps.  ...  Conclusion We have presented easy-to-check criteria for confluence of nominal rewriting theories (Theorem 4.6 and Lemma 4.9, and Theorems 5.6 and 5.8), improving previous criteria [7, 19] .  ... 
doi:10.1016/j.entcs.2016.06.004 fatcat:3khq65svebalndqv6pfp2ihhfu

Matching and alpha-equivalence check for nominal terms

Christophe Calvès, Maribel Fernández
2010 Journal of computer and system sciences (Print)  
In this paper, we describe efficient algorithms to check the validity of equations involving binders and to solve matching problems modulo α-equivalence, using the nominal approach.  ...  nominal approach well adapted to the specification of systems that involve binders.  ...  We thank James Cheney, Jamie Gabbay, Andrew Pitts, François Pottier and Christian Urban for useful discussions on the topics of this paper.  ... 
doi:10.1016/j.jcss.2009.10.003 fatcat:hpw6tvg2k5hd3jfodmxtqtblsm

Nominal rewriting

Maribel Fernández, Murdoch J. Gabbay
2007 Information and Computation  
Nominal rewriting maintains a strict distinction between variables of the object-language (atoms) and of the meta-language (variables or unknowns).  ...  Nominal rewriting is based on the observation that if we add support for -equivalence to first-order syntax using the nominal-set approach, then systems with binding, including higher-order reduction schemes  ...  We will now show that, thanks to the use of contexts, the framework of nominal rewriting can be easily adapted to express strategies of reduction.  ... 
doi:10.1016/j.ic.2006.12.002 fatcat:myd23ts6s5ernh6gx6gwouy5yu

Parallel Closure Theorem for Left-Linear Nominal Rewriting Systems [chapter]

Kentaro Kikuchi, Takahito Aoto, Yoshihito Toyama
2017 Lecture Notes in Computer Science  
Nominal rewriting has been introduced as an extension of first-order term rewriting by a binding mechanism based on the nominal approach.  ...  In this paper, we extend Huet's parallel closure theorem and its generalisation on confluence of left-linear term rewriting systems to the case of nominal rewriting.  ...  Definition 1 (Nominal rewrite rule).  ... 
doi:10.1007/978-3-319-66167-4_7 fatcat:72fqmusg4bfhzfjsl4zdwye7zq

Nominal rewriting with name generation

Maribel Fernández, Murdoch J. Gabbay
2005 Proceedings of the 7th ACM SIGPLAN international conference on Principles and practice of declarative programming - PPDP '05  
Finally, we study confluence properties of nominal rewriting and its extensions.  ...  Nominal rewriting extends first-order rewriting with Gabbay-Pitts abstractors: bound entities are explicitly named (rather than being nameless, as for de Bruijn indices) yet rewriting respects α-conversion  ...  . left-linear and non-overlapping) systems which we prove in this paper.  ... 
doi:10.1145/1069774.1069779 dblp:conf/ppdp/FernandezG05 fatcat:kz7q6u6szvd6xdd5tdiilp6a5a

Nominal Syntax with Atom Substitutions: Matching, Unification, Rewriting [chapter]

Jesús Domínguez, Maribel Fernández
2019 Lecture Notes in Computer Science  
We consider an extension of nominal syntax with non-capturing substitutions and show that matching is decidable and finitary but unification is undecidable.  ...  We provide a matching algorithm and characterise problems for which matching is unitary, giving rise to expressive and efficient rewriting systems.  ...  This algorithm can then be used to implement rewriting, and also to check closedness of terms and rewrite rules (see [13] ).  ... 
doi:10.1007/978-3-030-25027-0_5 fatcat:fscghmsaurdvpghhxxd45ufegq

Modular and automated type-soundness verification for language extensions

Florian Lorenzen, Sebastian Erdweg
2013 Proceedings of the 18th ACM SIGPLAN international conference on Functional programming - ICFP '13  
In other words, type checking the user-supplied program is sufficient to ensure the absence of type errors in desugared code.  ...  Accordingly, programmers define additional "type" rules using type and kind judgments. We have implemented language extensions of  ...  This way, the rewrite rule desugar-let will only be applied to a let expression that has been checked by T-LET.  ... 
doi:10.1145/2500365.2500596 dblp:conf/icfp/LorenzenE13 fatcat:i7r7qdag5fazfekepe5ts52oym

Modular and automated type-soundness verification for language extensions

Florian Lorenzen, Sebastian Erdweg
2013 SIGPLAN notices  
In other words, type checking the user-supplied program is sufficient to ensure the absence of type errors in desugared code.  ...  Accordingly, programmers define additional "type" rules using type and kind judgments. We have implemented language extensions of  ...  This way, the rewrite rule desugar-let will only be applied to a let expression that has been checked by T-LET.  ... 
doi:10.1145/2544174.2500596 fatcat:nyxnciexlnhc3mjb47bjtuwg2y

Type Safety with JSON Subschema [article]

Andrew Habib, Avraham Shinnar, Martin Hirzel, Michael Pradel
2020 arXiv   pre-print
We apply an implementation of our subschema checking algorithm to 8,548 pairs of real-world JSON schemas from different domains, demonstrating that it can decide the subschema question for most schema  ...  This paper presents a complementary technique: JSON subschema checking, which can be used for static type checking with JSON Schema.  ...  Rule object with overlapping pattern properties rewrites a pair of pattern properties with overlapping regular expressions p i and p j so their regular expressions match only disjoint keys, by replacing  ... 
arXiv:1911.12651v2 fatcat:a4zbh7rvhjebzd3kwkcoq6tutq

Higher-order Rewriting for Executable Compiler Specifications

Kristoffer H. Rose
2011 Electronic Proceedings in Theoretical Computer Science  
In this paper we outline how a simple compiler can be completely specified using higher order rewriting in all stages: parsing, analysis/optimization, and code emission, specifically using the  ...  The author is grateful for insightful comments by the anonymous referees including being made aware of the work in logical frameworks.  ...  So the actual E2 MapConcat rule looks like this: (In practice, such choices are delegated to an analysis phase which drops cookies of some kind into the term to serve as enablers of the overlapping rewrite  ... 
doi:10.4204/eptcs.49.3 fatcat:7rb5qnhmzvdktinhtyg3nyla6i

A functional toolkit for morphological and phonological processing, application to a Sanskrit tagger

2005 Journal of functional programming  
The method uses the toolkit methodology by constructing a non-deterministic transducer, implementing rational rewrite rules, by mechanical decoration of a trie representation of the lexicon index.  ...  An application to the segmentation of Sanskrit by sandhi analysis is demonstrated. Dedicated to Rod Burstall on the occasion of his 65th birthday  ...  The main function compile checks that at the end of the computation the stack is empty, that is no lexicon item is a proper suffix of some left hand side u of a rewrite rule.  ... 
doi:10.1017/s0956796804005416 fatcat:3ry3bjk3jbhtjf2ew5by6xudeq

The rewriting logic semantics project: A progress report

José Meseguer, Grigore Roşu
2013 Information and Computation  
Rewriting logic is an executable logical framework well suited for the semantic definition of languages.  ...  We give a progress report on how researchers in the rewriting logic semantics project are narrowing the gap between theory and practice in areas such as: modular semantic definitions of languages; scalability  ...  We also thank all the researchers involved in the rewriting logic semantics project for their many contributions, which we have tried to summarize in this paper without any claims of completeness.  ... 
doi:10.1016/j.ic.2013.08.004 fatcat:elvl7szyzjgy5mkp2lbeoren4e

Synchronous set relations in rewriting logic

Camilo Rocha, César Muñoz
2014 Science of Computer Programming  
The first author was partially supported by the Assurance of Flight Critical System's project of NASA's Aviation Safety Program at Langley Research Center under Research Cooperative Agreement No.  ...  NNL09AA00A awarded to the National Institute of Aerospace, and also by grants NSF CCF09-05584 and NSF CCF09-05584.  ...  Executability conditions Because rewriting logic's rules of deduction [2] are based on equational deduction, it may be undecidable to check membership in ⇒ R for a rewrite theory R = (Σ, E, R).  ... 
doi:10.1016/j.scico.2013.07.008 fatcat:tjrcre7i3bfvzmetnti6oym2ou

Rewriting Queries for Web Searches That Use Local Expressions [chapter]

Rolf Grütter, Iris Helming, Simon Speich, Abraham Bernstein
2011 Lecture Notes in Computer Science  
Results show that query rewriting significantly improves recall of the searches.  ...  The paper is organized as follows: Section 2 provides an overview of the Region Connection Calculus (RCC) and DL-safe SWRL rules.  ...  In order to infer new from existing knowledge or to check consistency of a knowledge base holding spatial relations, so-called composition tables are used.  ... 
doi:10.1007/978-3-642-22546-8_28 fatcat:dqn3r4svjbad7fday6bw2teav4

Algebraic Tableau Algorithm for ALCOQ

Jocelyne Faddoul, Volker Haarslev, Ralf Möller
2009 International Workshop on Description Logics  
This rule is used to check for empty partitions.  ...  P I cannot overlap with role fillers for role names that do not appear in P since it is assumed to overlap with their complement. This makes all P I disjoint.  ... 
dblp:conf/dlog/FaddoulHM09 fatcat:olezoulenvcnvosdmuo6f2njxa
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