International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice最新文献

{"title":"A Generic Approach to Proofs about Substitution","authors":"A. Anand, Vincent Rahli","doi":"10.1145/2631172.2631177","DOIUrl":"https://doi.org/10.1145/2631172.2631177","url":null,"abstract":"It is well known that reasoning about substitution is a huge \"distraction\" that inevitably gets in the way of formalizing interesting properties of languages with variable bindings. Most formalizations have their own separate definitions of terms and substitution, and properties about it. However there is a great deal of uniformity in the way substitution works and the reasons why its properties hold. We expose this uniformity by defining terms, substitution and α-equality generically in Coq by parametrizing them over a Context Free Grammar annotated with Variable binding information (CFGV).\u0000 We also provide proofs of many properties about the above definitions (enough to formalize the PER semantics of Nuprl in Coq). Unlike many other tools which generate a custom definition of substitution for each input, all instantiations of our term model share the same substitution function. The proofs about this function have been accepted by Coq's typechecker once and for all.","PeriodicalId":262518,"journal":{"name":"International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice","volume":"1999 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128248709","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}

{"title":"Session Types Meet Separation Logic","authors":"Jesper Bengtson","doi":"10.1145/2631172.2631173","DOIUrl":"https://doi.org/10.1145/2631172.2631173","url":null,"abstract":"Session types and separation logic are two leading methodologies for software verification. Session types allow users to write protocols that concurrent programs must adhere to; a session type specifies the order in which messages have to be exchanged, and the types of the data those messages carry. By checking that programs follow compatible session types, we can reason about the ways processes interact, ultimately guaranteeing the absence of deadlocks and race conditions in sessions. Separation logic is an extension of Hoare logic that is typically used to prove full functional correctness of sequential stateful programs; using separation logic, we can write pre- and post-conditions for program statements that use mutable stores such as a heap and modularly verify that they satisfy these specifications. Separation logic is more expressive than session types when it comes to data: with it we can state properties such as \"x is a number greater than five\", whereas session types can only express that \"x is a number\". On the other hand, session types offer a powerful means of checking that the communications among concurrent programs do not interfere with each other or deadlock.","PeriodicalId":262518,"journal":{"name":"International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115187837","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}

{"title":"Some constructions on ω-groupoids","authors":"Thorsten Altenkirch, Nuo Li, Ondrej Rypacek","doi":"10.1145/2631172.2631176","DOIUrl":"https://doi.org/10.1145/2631172.2631176","url":null,"abstract":"Weak ω-groupoids are the higher dimensional generalisation of setoids and are an essential ingredient of the constructive semantics of Homotopy Type Theory [13]. Following up on our previous formalisation [3] and Brunerie's notes [6], we present a new formalisation of the syntax of weak ω-groupoids in Agda using heterogeneous equality. We show how to recover basic constructions on ω-groupoids using suspension and replacement. In particular we show that any type forms a groupoid and we outline how to derive higher dimensional composition. We present a possible semantics using globular sets and discuss the issues which arise when using globular types instead.","PeriodicalId":262518,"journal":{"name":"International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126002526","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}

{"title":"Proof-Theoretic Foundations of Indexing in Logic Programming","authors":"I. Cervesato","doi":"10.1145/2631172.2631179","DOIUrl":"https://doi.org/10.1145/2631172.2631179","url":null,"abstract":"Indexing is generally viewed as an implementation artifact, indispensable to speed up the execution of logic programs and theorem provers, but with little intrinsically logical about it. We show that indexing can be given a justification in proof theory on the basis of focusing and linearity. We demonstrate this approach on predicate indexing for Horn clauses and several formulations of hereditary Harrop formulas. We also show how to refine this approach to discriminate on function symbols as well.","PeriodicalId":262518,"journal":{"name":"International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125401359","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}

{"title":"Structural logical relations with case analysis and equality reasoning","authors":"U. Rasmussen, Andrzej Filinski","doi":"10.1145/2503887.2503891","DOIUrl":"https://doi.org/10.1145/2503887.2503891","url":null,"abstract":"Formalizing proofs by logical relations in the Twelf proof assistant is known to be notoriously difficult. However, as demonstrated by Schürmann and Sarnat [In Proc. of 23rd Symp. on Logic in Computer Science, 2008] such proofs can be represented and verified in Twelf if done so using a Gentzen-style auxiliary assertion logic which is subsequently proved consistent via cut elimination.\u0000 We demonstrate in this paper an application of the above methodology to proofs of observational equivalence between expressions in a simply typed lambda calculus with a call-by-name operational semantics. Our use case requires the assertion logic to be extended with reasoning principles not present in the original presentation of the formalization method. We address this by generalizing the assertion logic to include dependent sorts, and demonstrate that the original cut elimination proof continues to apply without modification.","PeriodicalId":262518,"journal":{"name":"International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133257971","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}

{"title":"25 years of formal proof cultures: some problems, some philosophy, bright future","authors":"F. Honsell","doi":"10.1145/2503887.2503896","DOIUrl":"https://doi.org/10.1145/2503887.2503896","url":null,"abstract":"Throughout the history of Mathematics, several different proof cultures have co-existed, and still do co-exist. After 25 years of Logical Frameworks, we can say that even as far as proof metalanguages go, a definitive system is utopian and that we are witnessing the continuous development of a diversity of formal proof cultures, see e.g. [10-12, 17, 19, 21, 23, 24, 28]. In this paper, we propose a contribution towards the clarification of some controversial issues that have arisen in the theory and practice of Logical Frameworks, and have possibly motivated such a manifold speciation. Using as a running example the encoding of the critical features of Non- Commutative Linear Logic (NCLL) [26] in the Logical Framework LFP [20], we discuss the notions of adequacy of an encoding, locality of a side-condition, deep and shallow encodings, and how to embed heterogenous justifications or external evidence in LF. This discussion naturally leads to the question of how to express formally the expressive power of a Logical Framework, a minimal requirement being that of encoding itself within itself. We focus on LFP and we discuss its relations to the original LF [17], and briefly to the Conditional LF [21], and the Pattern LF [19] previously introduced by the authors. We conclude the paper by briefly comparing LFP to λ-calculus modulo [12], the Linear LF [9], and the Concurrent LF[28].","PeriodicalId":262518,"journal":{"name":"International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127582708","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}

{"title":"Explicit convertibility proofs in pure type systems","authors":"Floris van Doorn, H. Geuvers, F. Wiedijk","doi":"10.1145/2503887.2503890","DOIUrl":"https://doi.org/10.1145/2503887.2503890","url":null,"abstract":"We define type theory with explicit conversions. When type checking a term in normal type theory, the system searches for convertibility paths between types. The results of these searches are not stored in the term, and need to be reconstructed every time again. In our system, this information is also represented in the term. The system we define has the property that the type derivation of a term has exactly the same structure as the term itself. This has the consequence that there exists a natural LF encoding of such a system in which the encoded type is a dependent parameter of the type of the encoded term.\u0000 For every Pure Type System we define a system in our style. We show that such a system is always equivalent to the normal system without explicit conversions (even for non-functional systems), in the sense that the typability relation can be lifted. This proof has been fully formalised in the Coq system, building on a formalisation by Vincent Siles.\u0000 In our system, explicit conversions are not allowed to be removed when checking for convertibility. This means that all terms in convertibility proofs are well typed, even in the sense of our system.","PeriodicalId":262518,"journal":{"name":"International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice","volume":"157 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128803900","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}

{"title":"First-class substitutions in contextual type theory","authors":"Andrew Cave, B. Pientka","doi":"10.1145/2503887.2503889","DOIUrl":"https://doi.org/10.1145/2503887.2503889","url":null,"abstract":"In this paper, we revisit the theory of first-class substitution in contextual type theory (CTT); in particular, we focus on the abstract notion of substitution variables. This forms the basis for extending Beluga, a dependently typed proof and programming language which already supports first-class contexts and contextual objects, with first-class substitutions. To illustrate the elegance and power of first-class substitution variables, we describe the implementation of a weak normalization proof for the simply-typed lambda-calculus in Beluga.","PeriodicalId":262518,"journal":{"name":"International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123546601","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}

{"title":"A bisimulation between DPLL(T) and a proof-search strategy for the focused sequent calculus","authors":"Mahfuza Farooque, Stéphane Lengrand, A. Mahboubi","doi":"10.1145/2503887.2503892","DOIUrl":"https://doi.org/10.1145/2503887.2503892","url":null,"abstract":"We describe how the Davis-Putnam-Logemann-Loveland procedure DPLL is bisimilar to the goal-directed proof-search mechanism described by a standard but carefully chosen sequent calculus. We thus relate a procedure described as a transition system on states to the gradual completion of incomplete proof-trees.\u0000 For this we use a focused sequent calculus for polarised classical logic, for which we allow analytic cuts. The focusing mechanisms, together with an appropriate management of polarities, then allows the bisimulation to hold: The class of sequent calculus proofs that are the images of the DPLL runs finishing on UNSAT, is identified with a simple criterion involving polarities.\u0000 We actually provide those results for a version DPLL(T) of the procedure that is parameterised by a background theory T for which we can decide whether conjunctions of literals are consistent. This procedure is used for Satisfiability Modulo Theories (SMT) generalising propositional SAT. For this, we extend the standard focused sequent calculus for propositional logic in the same way DPLL(T) extends DPLL: with the ability to call the decision procedure for T.\u0000 DPLL(T) is implemented as a plugin for Psyche, a proof-search engine for this sequent calculus, to provide a sequent-calculus based SMT-solver.","PeriodicalId":262518,"journal":{"name":"International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127665426","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}

{"title":"Foundational proof certificates: making proof universal and permanent","authors":"D. Miller","doi":"10.1145/2503887.2503894","DOIUrl":"https://doi.org/10.1145/2503887.2503894","url":null,"abstract":"Consider a world where exporting proof evidence into a declarative, universal, and permanent format is taken as ``feature zero'' for computational logic systems. In such a world, provers will be able to communicate and share theorems and proofs; libraries can archive and organize proofs; and marketplaces of proofs would be open to any prover that admits checkable proof objects. In that world, proof checkers must be entrusted with the task of checking whether or not such proof evidence elaborates into a formal proof. A key to developing such a universal and permanent approach to proof evidence is the selection of an appropriate logical framework for defining the semantics of proof evidence.\u0000 Recent developments in structural proof theory provide a foundational approach to proof certificates. In particular, the focused proof systems LJF, LKF, and LKU for classical and intuitionistic logics can be fashioned into a high-level and declarative framework for defining the semantics of a wide range of proof evidence. The resulting framework is an approach to foundational proof certificates (FPCs) that provides precise descriptions of proofs that are both independent of the technology that produced them as well as flexible enough to allow encoding a rich collection of proof structures such as, for example, Frege proofs, natural deductions, resolution refutations, and Herbrand disjunctions.\u0000 The lambda Prolog programming language is an appropriate programming language for implementing a checker for FPC (over first-order logic proofs) and for specifying the semantics of proof evidence. While lambda Prolog contains typing, abstract datatypes, and higher-order programming in a style similar to ML---the first programming language designed for implementing proof checkers---it goes beyond ML by providing a logically clean notion of binding and (object-level) substitution. Furthermore, lambda Prolog implements both unification and backtracking search, two features critical for implementing proof reconstruction. These two features will allow proof certificates to have the option of eliding some proof evidence in the hope that the proof checker can reconstruct the missing details. Allowing a trade-off between certificate size and checking (and proof reconstruction) time is a valuable aid in designing flexible proof certificate formats.\u0000 The progress and plans for the ProofCert project within the Parsifal team at INRIA will be presented in this talk.","PeriodicalId":262518,"journal":{"name":"International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129292825","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}