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Formal Design, Implementation and Verification of Blockchain Languages (Invited Talk) 区块链语言的形式化设计、实现与验证(特邀演讲)
International Conference on Formal Structures for Computation and Deduction Pub Date : 2018-07-01 DOI: 10.4230/LIPIcs.FSCD.2018.2
Grigore Roşu
{"title":"Formal Design, Implementation and Verification of Blockchain Languages (Invited Talk)","authors":"Grigore Roşu","doi":"10.4230/LIPIcs.FSCD.2018.2","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.2","url":null,"abstract":"This invited paper describes recent, ongoing and planned work on the use of the rewrite-based semantic framework K to formally design, implement and verify blockchain languages and virtual machines. Both academic and commercial endeavors are discussed, as well as thoughts and directions for future research and development.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125721322","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: 6
Decreasing Diagrams with Two Labels Are Complete for Confluence of Countable Systems 可数系统合流的两标号递减图是完备的
International Conference on Formal Structures for Computation and Deduction Pub Date : 2018-07-01 DOI: 10.4230/LIPIcs.FSCD.2018.14
J. Endrullis, J. Klop, R. Overbeek
{"title":"Decreasing Diagrams with Two Labels Are Complete for Confluence of Countable Systems","authors":"J. Endrullis, J. Klop, R. Overbeek","doi":"10.4230/LIPIcs.FSCD.2018.14","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.14","url":null,"abstract":"Like termination, confluence is a central property of rewrite systems. Unlike for termination, however, there exists no known complexity hierarchy for confluence. In this paper we investigate whether the decreasing diagrams technique can be used to obtain such a hierarchy. The decreasing diagrams technique is one of the strongest and most versatile methods for proving confluence of abstract reduction systems, it is complete for countable systems, and it has many well-known confluence criteria as corollaries. So what makes decreasing diagrams so powerful? In contrast to other confluence techniques, decreasing diagrams employ a labelling of the steps ? with labels from a well-founded order in order to conclude confluence of the underlying unlabelled relation. Hence it is natural to ask how the size of the label set influences the strength of the technique. In particular, what class of abstract reduction systems can be proven confluent using decreasing diagrams restricted to 1 label, 2 labels, 3 labels, and so on? Surprisingly, we find that two labels su ce for proving confluence for every abstract rewrite system having the cofinality property, thus in particular for every confluent, countable system. We also show that this result stands in sharp contrast to the situation for commutation of rewrite relations, where the hierarchy does not collapse. Finally, as a background theme, we discuss the logical issue of first-order definability of the notion of confluence.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124698306","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
Strict Ideal Completions of the Lambda Calculus λ微积分的严格理想补全
International Conference on Formal Structures for Computation and Deduction Pub Date : 2018-05-17 DOI: 10.4230/LIPIcs.FSCD.2018.8
P. Bahr
{"title":"Strict Ideal Completions of the Lambda Calculus","authors":"P. Bahr","doi":"10.4230/LIPIcs.FSCD.2018.8","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.8","url":null,"abstract":"The infinitary lambda calculi pioneered by Kennaway et al. extend the basic lambda calculus by metric completion to infinite terms and reductions. Depending on the chosen metric, the resulting infinitary calculi exhibit different notions of strictness. To obtain infinitary normalisation and infinitary confluence properties for these calculi, Kennaway et al. extend $beta$-reduction with infinitely many `$bot$-rules', which contract meaningless terms directly to $bot$. Three of the resulting B\"ohm reduction calculi have unique infinitary normal forms corresponding to B\"ohm-like trees. \u0000In this paper we develop a corresponding theory of infinitary lambda calculi based on ideal completion instead of metric completion. We show that each of our calculi conservatively extends the corresponding metric-based calculus. Three of our calculi are infinitarily normalising and confluent; their unique infinitary normal forms are exactly the B\"ohm-like trees of the corresponding metric-based calculi. Our calculi dispense with the infinitely many $bot$-rules of the metric-based calculi. The fully non-strict calculus (called $111$) consists of only $beta$-reduction, while the other two calculi (called $001$ and $101$) require two additional rules that precisely state their strictness properties: $lambda x.bot to bot$ (for $001$) and $bot,M to bot$ (for $001$ and $101$).","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133273711","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
The clocks they are adjunctions: Denotational semantics for Clocked Type Theory 时钟它们是修饰词:时钟类型理论的指称语义
International Conference on Formal Structures for Computation and Deduction Pub Date : 2018-04-18 DOI: 10.4230/LIPIcs.FSCD.2018.23
B. Mannaa, Rasmus Ejlers Møgelberg
{"title":"The clocks they are adjunctions: Denotational semantics for Clocked Type Theory","authors":"B. Mannaa, Rasmus Ejlers Møgelberg","doi":"10.4230/LIPIcs.FSCD.2018.23","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.23","url":null,"abstract":"Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract form of step-indexing. CloTT has previously been shown to enjoy a number of syntactic properties including strong normalisation, canonicity and decidability of type checking. In this paper we present a denotational semantics for CloTT useful, e.g., for studying future extensions of CloTT with constructions such as path types. \u0000The main challenge for constructing this model is to model the notion of ticks used in CloTT for coinductive reasoning about coinductive types. We build on a category previously used to model guarded recursion, but in this category there is no object of ticks, so tick-assumptions in a context can not be modelled using standard tools. Instead we show how ticks can be modelled using adjoint functors, and how to model the tick constant using a semantic substitution.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"204 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115307209","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: 12
The Delta-calculus: syntax and types delta演算:语法和类型
International Conference on Formal Structures for Computation and Deduction Pub Date : 2018-03-26 DOI: 10.4230/LIPIcs.FSCD.2019.28
L. Liquori, C. Stolze
{"title":"The Delta-calculus: syntax and types","authors":"L. Liquori, C. Stolze","doi":"10.4230/LIPIcs.FSCD.2019.28","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2019.28","url":null,"abstract":"We present the Delta-calculus, an explicitly typed lambda-calculus with strong pairs, projections and explicit type coercions. The calculus can be parametrized with different intersection type theories T, e.g. the Coppo-Dezani, the Coppo-Dezani-Salle', the Coppo-Dezani-Venneri and the Barendregt-Coppo-Dezani ones, producing a family of Delta-calculi with related intersection type systems. We prove the main properties like Church-Rosser, unicity of type, subject reduction, strong normalization, decidability of type checking and type reconstruction. We state the relationship between the intersection type assignment systems a` la Curry and the corresponding intersection type systems a` la Church by means of an essence function translating an explicitly typed Delta-term into a pure lambda-term one. We finally translate a Delta-term with type coercions into an equivalent one without them; the translation is proved to be coherent because its essence is the identity. The generic Delta-calculus can be parametrized to take into account other intersection type theories as the ones in the Barendregt et al. book.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132953223","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
Counting Environments and Closures 计算环境和闭包
International Conference on Formal Structures for Computation and Deduction Pub Date : 2018-02-02 DOI: 10.4230/LIPIcs.FSCD.2018.11
Maciej Bendkowski, P. Lescanne
{"title":"Counting Environments and Closures","authors":"Maciej Bendkowski, P. Lescanne","doi":"10.4230/LIPIcs.FSCD.2018.11","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.11","url":null,"abstract":"Environments and closures are two of the main ingredients of evaluation in lambda-calculus. A closure is a pair consisting of a lambda-term and an environment, whereas an environment is a list of lambda-terms assigned to free variables. In this paper we investigate some dynamic aspects of evaluation in lambda-calculus considering the quantitative, combinatorial properties of environments and closures. Focusing on two classes of environments and closures, namely the so-called plain and closed ones, we consider the problem of their asymptotic counting and effective random generation. We provide an asymptotic approximation of the number of both plain environments and closures of size $n$. Using the associated generating functions, we construct effective samplers for both classes of combinatorial structures. Finally, we discuss the related problem of asymptotic counting and random generation of closed environemnts and closures.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121179899","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
Call-by-name Gradual Type Theory 按名称调用渐进类型理论
International Conference on Formal Structures for Computation and Deduction Pub Date : 2018-01-31 DOI: 10.23638/LMCS-16(1:7)2020
Max S. New, Daniel R. Licata
{"title":"Call-by-name Gradual Type Theory","authors":"Max S. New, Daniel R. Licata","doi":"10.23638/LMCS-16(1:7)2020","DOIUrl":"https://doi.org/10.23638/LMCS-16(1:7)2020","url":null,"abstract":"We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to new judgments for gradual type and term dynamism, which were developed in blame calculi and to state the \"gradual guarantee\" theorem of gradual typing. Combined with the ordinary extensionality ($eta$) principles that type theory provides, we show that most of the standard operational behavior of casts is uniquely determined by the gradual guarantee. This provides a semantic justification for the definitions of casts, and shows that non-standard definitions of casts must violate these principles. Our type theory is the internal language of a certain class of preorder categories called equipments. We give a general construction of an equipment interpreting gradual type theory from a 2-category representing non-gradual types and programs, which is a semantic analogue of Findler and Felleisen's definitions of contracts, and use it to build some concrete domain-theoretic models of gradual typing.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114426196","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: 12
Higher-Order Equational Pattern Anti-Unification [Preprint] 高阶方程模式反统一[预印本]
International Conference on Formal Structures for Computation and Deduction Pub Date : 2018-01-23 DOI: 10.4230/LIPIcs.FSCD.2018.12
David M. Cerna, Temur Kutsia
{"title":"Higher-Order Equational Pattern Anti-Unification [Preprint]","authors":"David M. Cerna, Temur Kutsia","doi":"10.4230/LIPIcs.FSCD.2018.12","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.12","url":null,"abstract":"We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the form of higher-order patterns. The problem is finitary: the minimal complete set of generalizations contains finitely many elements. We define the notion of optimal solution and investigate special fragments of the problem for which the optimal solution can be computed in linear or polynomial time.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"44 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133071729","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 Sequent Calculus for a Semi-Associative Law 一类半结合律的相继演算
International Conference on Formal Structures for Computation and Deduction Pub Date : 2017-09-10 DOI: 10.23638/LMCS-15(1:9)2019
N. Zeilberger
{"title":"A Sequent Calculus for a Semi-Associative Law","authors":"N. Zeilberger","doi":"10.23638/LMCS-15(1:9)2019","DOIUrl":"https://doi.org/10.23638/LMCS-15(1:9)2019","url":null,"abstract":"We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a semi-associative law (equivalently, right rotation). We establish a focusing property for this sequent calculus (a strengthening of cut-elimination), which yields the following coherence theorem: every valid entailment in the Tamari order has exactly one focused derivation. We then describe two main applications of the coherence theorem, including: 1. A new proof of the lattice property for the Tamari order, and 2. A new proof of the Tutte-Chapoton formula for the number of intervals in the Tamari lattice $Y_n$.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115278785","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: 11
Observably Deterministic Concurrent Strategies and Intensional Full Abstraction for Parallel-or 并行或的可观察确定性并发策略和内涵全抽象
International Conference on Formal Structures for Computation and Deduction Pub Date : 2017-09-03 DOI: 10.4230/LIPIcs.FSCD.2017.12
Simon Castellan, P. Clairambault, G. Winskel
{"title":"Observably Deterministic Concurrent Strategies and Intensional Full Abstraction for Parallel-or","authors":"Simon Castellan, P. Clairambault, G. Winskel","doi":"10.4230/LIPIcs.FSCD.2017.12","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2017.12","url":null,"abstract":"Although Plotkin's parallel-or is inherently deterministic, it has a non-deterministic interpretation in games based on (prime) event structures-in which an event has a unique causal history-because they do not directly support disjunctive causality. General event structures can express disjunctive causality and have a more permissive notion of determinism, but do not support hiding. We show that (structures equivalent to) deterministic general event structures do support hiding, and construct a new category of games based on them with a deterministic interpretation of aPCFpor, an affine variant of PCF extended with parallel-or. We then exploit this deterministic interpretation to give a relaxed notion of determinism (observable determinism) on the plain event structures model. Putting this together with our previously introduced concurrent notions of well-bracketing and innocence, we obtain an intensionally fully abstract model of aPCFpor.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114984084","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
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