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Complexity of Acyclic Term Graph Rewriting 非循环项图改写的复杂性
International Conference on Formal Structures for Computation and Deduction Pub Date : 2016-06-22 DOI: 10.4230/LIPIcs.FSCD.2016.10
Martin Avanzini, G. Moser
{"title":"Complexity of Acyclic Term Graph Rewriting","authors":"Martin Avanzini, G. Moser","doi":"10.4230/LIPIcs.FSCD.2016.10","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2016.10","url":null,"abstract":"Term rewriting has been used as a formal model to reason about the \u0000complexity of logic, functional, and imperative programs. In contrast \u0000to term rewriting, term graph rewriting permits sharing of \u0000common sub-expressions, and consequently is able to capture more \u0000closely reasonable implementations of rule based languages. However, \u0000the automated complexity analysis of term graph rewriting has received \u0000little to no attention. \u0000 \u0000With this work, we provide first steps towards overcoming this \u0000situation. We present adaptions of two prominent complexity techniques \u0000from term rewriting, viz, the interpretation method and \u0000dependency tuples. Our adaptions are non-trivial, in the sense \u0000that they can observe not only term but also graph structures, i.e. \u0000take sharing into account. In turn, the developed methods allow us to \u0000more precisely estimate the runtime complexity of programs where \u0000sharing of sub-expressions is essential.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"176 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121217807","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
Homological Computations for Term Rewriting Systems 项重写系统的同调计算
International Conference on Formal Structures for Computation and Deduction Pub Date : 2016-06-22 DOI: 10.4230/LIPIcs.FSCD.2016.27
P. Malbos, S. Mimram
{"title":"Homological Computations for Term Rewriting Systems","authors":"P. Malbos, S. Mimram","doi":"10.4230/LIPIcs.FSCD.2016.27","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2016.27","url":null,"abstract":"An important problem in universal algebra consists in finding presentations of algebraic theories by generators and relations, which are as small as possible. Exhibiting lower bounds on the number of those generators and relations for a given theory is a difficult task because it a priori requires considering all possible sets of generators for a theory and no general method exists. In this article, we explain how homological computations can provide such lower bounds, in a systematic way, and show how to actually compute those in the case where a presentation of the theory by a convergent rewriting system is known. We also introduce the notion of coherent presentation of a theory in order to consider finer homotopical invariants. In some aspects, this work generalizes, to term rewriting systems, Squier’s celebrated homological and homotopical invariants for string rewriting systems.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127742856","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: 13
Modular Focused Proof Systems for Intuitionistic Modal Logics 直觉模态逻辑的模聚焦证明系统
International Conference on Formal Structures for Computation and Deduction Pub Date : 2016-06-22 DOI: 10.4230/LIPIcs.FSCD.2016.16
Kaustuv Chaudhuri, Sonia Marin, Lutz Straßburger
{"title":"Modular Focused Proof Systems for Intuitionistic Modal Logics","authors":"Kaustuv Chaudhuri, Sonia Marin, Lutz Straßburger","doi":"10.4230/LIPIcs.FSCD.2016.16","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2016.16","url":null,"abstract":"Focusing is a general technique for syntactically compartmentalizing \u0000the non-deterministic choices in a proof system, which not only \u0000improves proof search but also has the representational benefit of \u0000distilling sequent proofs into synthetic normal forms. However, since \u0000focusing is usually specified as a restriction of the sequent \u0000calculus, the technique has not been transferred to logics that lack a \u0000(shallow) sequent presentation, as is the case for some of the logics \u0000of the modal cube. We have recently extended the focusing technique \u0000to classical nested sequents, a generalization of ordinary sequents. \u0000In this work we further extend focusing to intuitionistic nested \u0000sequents, which can capture all the logics of the intuitionistic S5 \u0000cube in a modular fashion. We present an internal cut-elimination \u0000procedure for the focused system which in turn is used to show its \u0000completeness.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124585971","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: 20
Strong Normalization for the Parameter-Free Polymorphic Lambda Calculus Based on the Omega-Rule 基于omega规则的无参数多态λ演算的强归一化
International Conference on Formal Structures for Computation and Deduction Pub Date : 2016-06-01 DOI: 10.4230/LIPIcs.FSCD.2016.5
R. Akiyoshi, K. Terui
{"title":"Strong Normalization for the Parameter-Free Polymorphic Lambda Calculus Based on the Omega-Rule","authors":"R. Akiyoshi, K. Terui","doi":"10.4230/LIPIcs.FSCD.2016.5","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2016.5","url":null,"abstract":"Following Aehlig, we consider a hierarchy F^p= { F^p_n }_{n in Nat} of \u0000parameter-free subsystems of System F, where each F^p_n \u0000corresponds to ID_n, the theory of n-times iterated inductive \u0000definitions (thus our F^p_n corresponds to the n+1th system of \u0000Aehlig). We here present two proofs of strong normalization for \u0000F^p_n, which are directly formalizable with inductive definitions. \u0000The first one, based on the Joachimski-Matthes method, can be fully \u0000formalized in ID_n+1. This provides a tight upper bound on the \u0000complexity of the normalization theorem for System F^p_n. The \u0000second one, based on the Godel-Tait method, can be locally \u0000formalized in ID_n. This provides a direct proof to the known \u0000result that the representable functions in F^p_n are provably \u0000total in ID_n. In both cases, Buchholz' Omega-rule plays a \u0000central role.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129519828","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
Classical Extraction in Continuation Models 延续模型中的经典提取
International Conference on Formal Structures for Computation and Deduction Pub Date : 2016-06-01 DOI: 10.4230/LIPIcs.FSCD.2016.13
Valentin Blot
{"title":"Classical Extraction in Continuation Models","authors":"Valentin Blot","doi":"10.4230/LIPIcs.FSCD.2016.13","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2016.13","url":null,"abstract":"We use the control features of continuation models to interpret proofs \u0000in first-order classical theories. This interpretation is suitable for \u0000extracting algorithms from proofs of Pi^0_2 formulas. It is \u0000fundamentally different from the usual direct interpretation, which is \u0000shown to be equivalent to Friedman's trick. The main difference is \u0000that atomic formulas and natural numbers are interpreted as distinct \u0000objects. Nevertheless, the control features inherent to the \u0000continuation models permit extraction using a special \"channel\" on \u0000which the extracted value is transmitted at toplevel without unfolding \u0000the recursive calls. We prove that the technique fails in Scott \u0000domains, but succeeds in the refined setting of Laird's bistable \u0000bicpos, as well as in game semantics.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115990706","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
Computing Connected Proof(-Structure)s From Their Taylor Expansion 从它们的泰勒展开计算连通证明(-结构)
International Conference on Formal Structures for Computation and Deduction Pub Date : 2016-06-01 DOI: 10.4230/LIPIcs.FSCD.2016.20
Giulio Guerrieri, L. Pellissier, L. Falco
{"title":"Computing Connected Proof(-Structure)s From Their Taylor Expansion","authors":"Giulio Guerrieri, L. Pellissier, L. Falco","doi":"10.4230/LIPIcs.FSCD.2016.20","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2016.20","url":null,"abstract":"We show that every connected Multiplicative Exponential Linear Logic (MELL) proof-structure (with or without cuts) is uniquely determined by a well-chosen element of its Taylor expansion: the one obtained by taking two copies of the content of each box. As a consequence, the relational \u0000model is injective with respect to connected MELL proof-structures.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124420516","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: 21
Non-Omega-Overlapping TRSs are UN 非重叠trs是UN
International Conference on Formal Structures for Computation and Deduction Pub Date : 2016-06-01 DOI: 10.4230/LIPIcs.FSCD.2016.22
Stefan Kahrs, Connor Smith
{"title":"Non-Omega-Overlapping TRSs are UN","authors":"Stefan Kahrs, Connor Smith","doi":"10.4230/LIPIcs.FSCD.2016.22","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2016.22","url":null,"abstract":"This paper solves problem #79 of RTA's list of open \u0000problems --- in the positive. If the rules of a TRS do not overlap w.r.t. \u0000substitutions of infinite terms then the TRS has unique normal forms. \u0000We solve the problem by reducing the problem to one of consistency for \u0000\"similar\" constructor term rewriting systems. For this we introduce \u0000a new proof technique. We define a relation ⇓ that is \u0000consistent by construction, and which --- if transitive --- would \u0000coincide with the rewrite system's equivalence relation =R. \u0000 \u0000We then prove the transitivity of ⇓ by coalgebraic \u0000reasoning. Any concrete proof for instances of this relation only \u0000refers to terms of some finite coalgebra, and we then construct an \u0000equivalence relation on that coalgebra which coincides with ⇓.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131220787","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: 4
Weighted Relational Models for Mobility 流动性加权关系模型
International Conference on Formal Structures for Computation and Deduction Pub Date : 2016-06-01 DOI: 10.4230/LIPIcs.FSCD.2016.24
J. Laird
{"title":"Weighted Relational Models for Mobility","authors":"J. Laird","doi":"10.4230/LIPIcs.FSCD.2016.24","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2016.24","url":null,"abstract":"We investigate operational and denotational semantics for \u0000computational and concurrent systems with mobile names which capture \u0000their computational properties. For example, various properties of \u0000fixed networks, such as shortest or longest path, transition \u0000probabilities, and secure data flows, correspond to the ``sum'' in a \u0000semiring of the weights of paths through the network: we aim to model \u0000networks with a dynamic topology in a similar way. Alongside rich \u0000computational formalisms such as the lambda-calculus, these can be \u0000represented as terms in a calculus of solos with weights from a \u0000complete semiring $R$, so that reduction associates a weight in R to \u0000each reduction path. \u0000 \u0000Taking inspiration from differential nets, we develop a denotational \u0000semantics for this calculus in the category of sets and R-weighted \u0000relations, based on its differential and compact-closed structure, but \u0000giving a simple, syntax-independent representation of terms as \u0000matrices over R. We show that this corresponds to the sum in R of \u0000the values associated to its independent reduction paths, and that our \u0000semantics is fully abstract with respect to the observational \u0000equivalence induced by sum-of-paths evaluation.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125427953","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: 1
Category Theory in Coq 8.5 coq8.5中的范畴论
International Conference on Formal Structures for Computation and Deduction Pub Date : 2015-05-24 DOI: 10.4230/LIPIcs.FSCD.2016.30
Amin Timany, B. Jacobs
{"title":"Category Theory in Coq 8.5","authors":"Amin Timany, B. Jacobs","doi":"10.4230/LIPIcs.FSCD.2016.30","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2016.30","url":null,"abstract":"We report on our experience implementing category theory in Coq 8.5. The repository of this development can be found at this https URL This implementation most notably makes use of features, primitive projections for records and universe polymorphism that are new to Coq 8.5.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117251963","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: 15
Proof Normalisation in a Logic Identifying Isomorphic Propositions 逻辑识别同构命题的证明规范化
International Conference on Formal Structures for Computation and Deduction Pub Date : 2015-01-25 DOI: 10.4230/LIPIcs.FSCD.2019.14
Alejandro Díaz-Caro, Gilles Dowek
{"title":"Proof Normalisation in a Logic Identifying Isomorphic Propositions","authors":"Alejandro Díaz-Caro, Gilles Dowek","doi":"10.4230/LIPIcs.FSCD.2019.14","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2019.14","url":null,"abstract":"We define a fragment of propositional logic where isomorphic propositions, such as $Aland B$ and $Bland A$, or $ARightarrow (Bland C)$ and $(ARightarrow B)land(ARightarrow C)$ are identified. We define System I, a proof language for this logic, and prove its normalisation and consistency.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"20 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123130191","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: 7
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