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Analyzing Innermost Runtime Complexity Through Tuple Interpretations 通过元组解释分析最内部的运行时复杂性
Workshop on Logical and Semantic Frameworks with Applications Pub Date : 2023-03-23 DOI: 10.4204/EPTCS.376.5
Liye Guo, Deivid Vale
{"title":"Analyzing Innermost Runtime Complexity Through Tuple Interpretations","authors":"Liye Guo, Deivid Vale","doi":"10.4204/EPTCS.376.5","DOIUrl":"https://doi.org/10.4204/EPTCS.376.5","url":null,"abstract":"Time complexity in rewriting is naturally understood as the number of steps needed to reduce terms to normal forms. Establishing complexity bounds to this measure is a well-known problem in the rewriting community. A vast majority of techniques to find such bounds consist of modifying termination proofs in order to recover complexity information. This has been done for instance with semantic interpretations, recursive path orders, and dependency pairs. In this paper, we follow the same program by tailoring tuple interpretations to deal with innermost complexity analysis. A tuple interpretation interprets terms as tuples holding upper bounds to the cost of reduction and size of normal forms. In contrast with the full rewriting setting, the strongly monotonic requirement for cost components is dropped when reductions are innermost. This weakened requirement on cost tuples allows us to prove the innermost version of the compatibility result: if all rules in a term rewriting system can be strictly oriented, then the innermost rewrite relation is well-founded. We establish the necessary conditions for which tuple interpretations guarantee polynomial bounds to the runtime of compatible systems and describe a search procedure for such interpretations.","PeriodicalId":374401,"journal":{"name":"Workshop on Logical and Semantic Frameworks with Applications","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123846508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ReLo: a Dynamic Logic to Reason About Reo Circuits Reo:一种对Reo电路进行推理的动态逻辑
Workshop on Logical and Semantic Frameworks with Applications Pub Date : 2023-03-23 DOI: 10.4204/EPTCS.376.4
E. Grilo, Bruno Lopes
{"title":"ReLo: a Dynamic Logic to Reason About Reo Circuits","authors":"E. Grilo, Bruno Lopes","doi":"10.4204/EPTCS.376.4","DOIUrl":"https://doi.org/10.4204/EPTCS.376.4","url":null,"abstract":"Critical systems require high reliability and are present in many domains. They are systems in which failure may result in financial damage or even loss of lives. Standard techniques of software engineering are not enough to ensure the absence of unacceptable failures and/or that critical requirements are fulfilled. Reo is a component-based modelling language that aims to provide a framework to build software based on existing pieces of software, which has been used in a wide variety of domains. Its formal semantics provides grounds to certify that systems based on Reo models satisfy specific requirements (i.e., absence of deadlocks). Current logical approaches for reasoning over Reo require the conversion of formal semantics into a logical framework. ReLo is a dynamic logic that naturally subsumes Reo's semantics. It provides a means to reason over Reo circuits. This work extends ReLo by introducing the iteration operator, and soundness and completeness proofs for its axiomatization.","PeriodicalId":374401,"journal":{"name":"Workshop on Logical and Semantic Frameworks with Applications","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124425413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Equational Theorem Proving for Clauses over Strings 字符串上子句的等式定理证明
Workshop on Logical and Semantic Frameworks with Applications Pub Date : 2023-03-23 DOI: 10.4204/EPTCS.376.6
Dohan Kim
{"title":"Equational Theorem Proving for Clauses over Strings","authors":"Dohan Kim","doi":"10.4204/EPTCS.376.6","DOIUrl":"https://doi.org/10.4204/EPTCS.376.6","url":null,"abstract":"Although reasoning about equations over strings has been extensively studied for several decades, little research has been done for equational reasoning on general clauses over strings. This paper introduces a new superposition calculus with strings and present an equational theorem proving framework for clauses over strings. It provides a saturation procedure for clauses over strings and show that the proposed superposition calculus with contraction rules is refutationally complete. This paper also presents a new decision procedure for word problems over strings w.r.t. a set of conditional equations R over strings if R can be finitely saturated under the proposed inference system.","PeriodicalId":374401,"journal":{"name":"Workshop on Logical and Semantic Frameworks with Applications","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116666512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Paraconsistent Transition Systems 不一致的转换系统
Workshop on Logical and Semantic Frameworks with Applications Pub Date : 2023-03-23 DOI: 10.4204/EPTCS.376.3
A. Cruz, A. Madeira, LuA-A-s Soares Barbosa
{"title":"Paraconsistent Transition Systems","authors":"A. Cruz, A. Madeira, LuA-A-s Soares Barbosa","doi":"10.4204/EPTCS.376.3","DOIUrl":"https://doi.org/10.4204/EPTCS.376.3","url":null,"abstract":"Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such formalism: states evolve through two accessibility relations capturing weighted evidence of a transition or its absence, respectively. Their weights come from a specific residuated lattice. A category of these systems, and the corresponding algebra, is defined as providing a formal setting to model different application scenarios. One of them, dealing with the effect of quantum decoherence in quantum programs, is used for illustration purposes.","PeriodicalId":374401,"journal":{"name":"Workshop on Logical and Semantic Frameworks with Applications","volume":"237 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132562553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Formal Proof of the Strong Normalization Theorem for System T in Agda Agda中系统T强归一化定理的形式化证明
Workshop on Logical and Semantic Frameworks with Applications Pub Date : 2023-03-23 DOI: 10.4204/EPTCS.376.8
Sebasti'an Urciuoli
{"title":"A Formal Proof of the Strong Normalization Theorem for System T in Agda","authors":"Sebasti'an Urciuoli","doi":"10.4204/EPTCS.376.8","DOIUrl":"https://doi.org/10.4204/EPTCS.376.8","url":null,"abstract":"We present a framework for the formal meta-theory of lambda calculi in first-order syntax, with two sorts of names, one to represent both free and bound variables, and the other for constants, and by using Stoughton's multiple substitutions. On top of the framework we formalize Girard's proof of the Strong Normalization Theorem for both the simply-typed lambda calculus and System T. As to the latter, we also present a simplification of the original proof. The whole development has been machine-checked using the Agda system.","PeriodicalId":374401,"journal":{"name":"Workshop on Logical and Semantic Frameworks with Applications","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126312945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nominal Sets in Agda - A Fresh and Immature Mechanization 议程中的标称设定——一种新鲜而不成熟的机械化
Workshop on Logical and Semantic Frameworks with Applications Pub Date : 2023-03-23 DOI: 10.4204/EPTCS.376.7
Miguel Pagano, Jos'e E. Solsona
{"title":"Nominal Sets in Agda - A Fresh and Immature Mechanization","authors":"Miguel Pagano, Jos'e E. Solsona","doi":"10.4204/EPTCS.376.7","DOIUrl":"https://doi.org/10.4204/EPTCS.376.7","url":null,"abstract":"In this paper we present our current development on a new formalization of nominal sets in Agda. Our first motivation in having another formalization was to understand better nominal sets and to have a playground for testing type systems based on nominal logic. Not surprisingly, we have independently built up the same hierarchy of types leading to nominal sets. We diverge from other formalizations in how to conceive finite permutations: in our formalization a finite permutation is a permutation (i.e. a bijection) whose domain is finite. Finite permutations have different representations, for instance as compositions of transpositions (the predominant in other formalizations) or compositions of disjoint cycles. We prove that these representations are equivalent and use them to normalize (up to composition order of independent transpositions) compositions of transpositions.","PeriodicalId":374401,"journal":{"name":"Workshop on Logical and Semantic Frameworks with Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133143045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
SeCaV: A Sequent Calculus Verifier in Isabelle/HOL SeCaV:一个序列演算验证器在Isabelle/HOL
Workshop on Logical and Semantic Frameworks with Applications Pub Date : 2022-04-07 DOI: 10.4204/EPTCS.357.4
Asta Halkjær From, Frederik Krogsdal Jacobsen, J. Villadsen
{"title":"SeCaV: A Sequent Calculus Verifier in Isabelle/HOL","authors":"Asta Halkjær From, Frederik Krogsdal Jacobsen, J. Villadsen","doi":"10.4204/EPTCS.357.4","DOIUrl":"https://doi.org/10.4204/EPTCS.357.4","url":null,"abstract":"We describe SeCaV, a sequent calculus verifier for first-order logic in Isabelle/HOL, and the SeCaV Unshortener, an online tool that expands succinct derivations into the full SeCaV syntax. We leverage the power of Isabelle/HOL as a proof checker for our SeCaV derivations. The interactive features of Isabelle/HOL make our system transparent. For instance, the user can simply click on a side condition to see its exact definition. Our formalized soundness and completeness proofs pertain exactly to the calculus as exposed to the user and not just to some model of our tool. Users can also write their derivations in the SeCaV Unshortener, which provides a lighter syntax, and expand them for later verification. We have used both tools in our teaching.","PeriodicalId":374401,"journal":{"name":"Workshop on Logical and Semantic Frameworks with Applications","volume":"259 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116484377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
A Quick Overview on the Quantum Control Approach to the Lambda Calculus Lambda微积分的量子控制方法的快速概述
Workshop on Logical and Semantic Frameworks with Applications Pub Date : 2022-04-07 DOI: 10.4204/EPTCS.357.1
Alejandro D'iaz-Caro
{"title":"A Quick Overview on the Quantum Control Approach to the Lambda Calculus","authors":"Alejandro D'iaz-Caro","doi":"10.4204/EPTCS.357.1","DOIUrl":"https://doi.org/10.4204/EPTCS.357.1","url":null,"abstract":"In this short overview, we start with the basics of quantum computing, explaining the difference between the quantum and the classical control paradigms. We give an overview of the quantum control line of research within the lambda calculus, ranging from untyped calculi up to categorical and realisability models. This is a summary of the last 10+ years of research in this area, starting from Arrighi and Dowek's seminal work until today.","PeriodicalId":374401,"journal":{"name":"Workshop on Logical and Semantic Frameworks with Applications","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116318187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
About Opposition and Duality in Paraconsistent Type Theory 论副相容类型论中的对立与对偶
Workshop on Logical and Semantic Frameworks with Applications Pub Date : 2022-04-07 DOI: 10.4204/EPTCS.357.3
J. C. Agudelo, Andrés Sicard-Ramírez
{"title":"About Opposition and Duality in Paraconsistent Type Theory","authors":"J. C. Agudelo, Andrés Sicard-Ramírez","doi":"10.4204/EPTCS.357.3","DOIUrl":"https://doi.org/10.4204/EPTCS.357.3","url":null,"abstract":"A paraconsistent type theory (an extension of a fragment of intuitionistic type theory by adding opposite types) is here extended by adding co-function types. It is shown that, in the extended paraconsistent type system, the opposite type constructor can be viewed as an involution operation that transforms each type into its dual type. Moreover, intuitive interpretations of opposite and co-function types under different interpretations of types are discussed.","PeriodicalId":374401,"journal":{"name":"Workshop on Logical and Semantic Frameworks with Applications","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121687380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A subexponential view of domains in session types 会话类型域的子指数视图
Workshop on Logical and Semantic Frameworks with Applications Pub Date : 2021-10-08 DOI: 10.4204/EPTCS.357.7
Daniele Nantes, C. Olarte, D. Ventura
{"title":"A subexponential view of domains in session types","authors":"Daniele Nantes, C. Olarte, D. Ventura","doi":"10.4204/EPTCS.357.7","DOIUrl":"https://doi.org/10.4204/EPTCS.357.7","url":null,"abstract":"Linear logic (LL) has inspired the design of many computational systems, offering reasoning tech-niques built on top of its meta-theory. Since its inception, several connections between concurrent systems and LL have emerged from different perspectives. In the last decade, the seminal work of Caires and Pfenning showed that formulas in LL can be interpreted as session types and processes in the π -calculus as proof terms. This leads to a Curry-Howard interpretation where proof reductions in the cut-elimination procedure correspond to process reductions/interactions. The subexponentials in LL have also played an important role in concurrent systems since they can be interpreted in different ways, including timed, spatial and even epistemic modalities in distributed systems. In this paper we address the question: What is the meaning of the subexponentials from the point of view of a session type interpretation? Our answer is a π -like process calculus where agents reside in locations/sites and they make it explicit how the communication among the different sites should happen. The design of this language relies completely on the proof theory of the subexponentials in LL, thus extending the Caires-Pfenning interpretation in an elegant way.","PeriodicalId":374401,"journal":{"name":"Workshop on Logical and Semantic Frameworks with Applications","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115590221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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