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Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs最新文献

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A formalization of the Berlekamp-Zassenhaus factorization algorithm Berlekamp-Zassenhaus分解算法的形式化
Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018617
Jose Divasón, Sebastiaan J. C. Joosten, René Thiemann, A. Yamada
{"title":"A formalization of the Berlekamp-Zassenhaus factorization algorithm","authors":"Jose Divasón, Sebastiaan J. C. Joosten, René Thiemann, A. Yamada","doi":"10.1145/3018610.3018617","DOIUrl":"https://doi.org/10.1145/3018610.3018617","url":null,"abstract":"We formalize the Berlekamp–Zassenhaus algorithm for factoring square-free integer polynomials in Isabelle/HOL. We further adapt an existing formalization of Yun’s square-free factorization algorithm to integer polynomials, and thus provide an efficient and certified factorization algorithm for arbitrary univariate polynomials. The algorithm first performs a factorization in the prime field GF(p) and then performs computations in the ring of integers modulo pk, where both p and k are determined at runtime. Since a natural modeling of these structures via dependent types is not possible in Isabelle/HOL, we formalize the whole algorithm using Isabelle’s recent addition of local type definitions. Through experiments we verify that our algorithm factors polynomials of degree 100 within seconds.","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114413762","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: 17
A Coq formal proof of the Lax-Milgram theorem 拉克斯-米尔格拉姆定理的Coq形式证明
Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018625
S. Boldo, F. Clément, Florian Faissole, Vincent Martin, Micaela Mayero
{"title":"A Coq formal proof of the Lax-Milgram theorem","authors":"S. Boldo, F. Clément, Florian Faissole, Vincent Martin, Micaela Mayero","doi":"10.1145/3018610.3018625","DOIUrl":"https://doi.org/10.1145/3018610.3018625","url":null,"abstract":"The Finite Element Method is a widely-used method to solve numerical problems coming for instance from physics or biology. To obtain the highest confidence on the correction of numerical simulation programs implementing the Finite Element Method, one has to formalize the mathematical notions and results that allow to establish the soundness of the method. The Lax–Milgram theorem may be seen as one of those theoretical cornerstones: under some completeness and coercivity assumptions, it states existence and uniqueness of the solution to the weak formulation of some boundary value problems. This article presents the full formal proof of the Lax–Milgram theorem in Coq. It requires many results from linear algebra, geometry, functional analysis, and Hilbert spaces.","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131697417","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: 22
Complx: a verification framework for concurrent imperative programs complex:并发命令式程序的验证框架
Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018627
Sidney Amani, June Andronick, Maksym Bortin, Corey Lewis, C. Rizkallah, Joseph Tuong
{"title":"Complx: a verification framework for concurrent imperative programs","authors":"Sidney Amani, June Andronick, Maksym Bortin, Corey Lewis, C. Rizkallah, Joseph Tuong","doi":"10.1145/3018610.3018627","DOIUrl":"https://doi.org/10.1145/3018610.3018627","url":null,"abstract":"We propose a concurrency reasoning framework for imperative programs, based on the Owicki-Gries (OG) foundational shared-variable concurrency method. Our framework combines the approaches of Hoare-Parallel, a formalisation of OG in Isabelle/HOL for a simple while-language, and Simpl, a generic imperative language embedded in Isabelle/HOL, allowing formal reasoning on C programs. We define the Complx language, extending the syntax and semantics of Simpl with support for parallel composition and synchronisation. We additionally define an OG logic, which we prove sound w.r.t. the semantics, and a verification condition generator, both supporting involved low-level imperative constructs such as function calls and abrupt termination. We illustrate our framework on an example that features exceptions, guards and function calls. We aim to then target concurrent operating systems, such as the interruptible eChronos embedded operating system for which we already have a model-level OG proof using Hoare-Parallel.","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117154361","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
Automatic cyclic termination proofs for recursive procedures in separation logic 分离逻辑中递归过程的自动循环终止证明
Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018623
R. Rowe, J. Brotherston
{"title":"Automatic cyclic termination proofs for recursive procedures in separation logic","authors":"R. Rowe, J. Brotherston","doi":"10.1145/3018610.3018623","DOIUrl":"https://doi.org/10.1145/3018610.3018623","url":null,"abstract":"We describe a formal verification framework and tool implementation, based upon cyclic proofs, for certifying the safe termination of imperative pointer programs with recursive procedures. Our assertions are symbolic heaps in separation logic with user defined inductive predicates; we employ explicit approximations of these predicates as our termination measures. This enables us to extend cyclic proof to programs with procedures by relating these measures across the pre- and postconditions of procedure calls. We provide an implementation of our formal proof system in the Cyclist theorem proving framework, and evaluate its performance on a range of examples drawn from the literature on program termination. Our implementation extends the current state-of-the-art in cyclic proof-based program verification, enabling automatic termination proofs of a larger set of programs than previously possible.","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130315076","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: 35
Equivalence of system F and λ2 in Coq based on context morphism lemmas 基于上下文态射引理的Coq系统F与λ2的等价性
Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018618
Jonas Kaiser, Tobias Tebbi, G. Smolka
{"title":"Equivalence of system F and λ2 in Coq based on context morphism lemmas","authors":"Jonas Kaiser, Tobias Tebbi, G. Smolka","doi":"10.1145/3018610.3018618","DOIUrl":"https://doi.org/10.1145/3018610.3018618","url":null,"abstract":"We give a machine-checked proof of the equivalence of the usual, two-sorted presentation of System F and its single-sorted pure type system variant λ2. This is established by reducing the typability problem of F to λ2 and vice versa. The difficulty lies in aligning different binding-structures and different contexts (dependent vs. non-dependent). The use of de Bruijn syntax, parallel substitutions, and context morphism lemmas leads to an elegant proof. We use the Coq proof assistant and the substitution library Autosubst.","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114873825","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: 8
The next 700 syntactical models of type theory 接下来的700种类型理论的句法模型
Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018620
S. Boulier, Pierre-Marie Pédrot, Nicolas Tabareau
{"title":"The next 700 syntactical models of type theory","authors":"S. Boulier, Pierre-Marie Pédrot, Nicolas Tabareau","doi":"10.1145/3018610.3018620","DOIUrl":"https://doi.org/10.1145/3018610.3018620","url":null,"abstract":"A family of syntactic models for the calculus of construction with universes (CCω) is described, all of them preserving conversion of the calculus definitionally, and thus giving rise directly to a program transformation of CCω into itself. Those models are based on the remark that negative type constructors (e.g. dependent product, coinductive types or universes) are underspecified in type theory-which leaves some freedom on extra intensional specifications. The model construction can be seen as a compilation phase from a complex type theory into a simpler type theory. Such models can be used to derive (the negative part of) independence results with respect to CCω, such as functional extensionality, propositional extensionality, univalence or the fact that bisimulation on a coinductive type may not coincide with equality. They can also be used to add new principles to the theory, which we illustrate by defining a version of CCω with ad-hoc polymorphism that shows in particular that parametricity is not an implicit requirement of type theory. The correctness of some of the models/program transformations have been checked in the Coq proof assistant and have been instrumented as a Coq plugin.","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132112238","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: 62
Mechanized verification of preemptive OS kernels (invited talk) 抢占式操作系统内核的机械化验证(特邀演讲)
Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3023367
Xinyu Feng
{"title":"Mechanized verification of preemptive OS kernels (invited talk)","authors":"Xinyu Feng","doi":"10.1145/3018610.3023367","DOIUrl":"https://doi.org/10.1145/3018610.3023367","url":null,"abstract":"We propose a practical verification framework for preemptive OS kernels. The framework models the correctness of API implementations in OS kernels as contextual refinement of their abstract specifications. It provides a specification language for defining the high-level abstract model of OS kernels, a program logic for refinement verification of concurrent kernel code with multi-level hardware interrupts, and automated tactics for developing mechanized proofs. The whole framework is developed for a practical subset of the C language. We have successfully applied it to verify key modules of a commercial preemptive OS μC/OS-II, including the scheduler, interrupt handlers, message queues, and mutexes, etc. We also verify the priority-inversion-freedom (PIF) in μC/OS-II. All the proofs are mechanized in Coq. To our knowledge, our work is the first to verify the functional correctness of a practical preemptive OS kernel with machine-checkable proofs. More details about the project is available at","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130723617","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
Formal foundations of 3D geometry to model robot manipulators 三维几何模型的正式基础机器人操纵器
Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018629
Reynald Affeldt, C. Cohen
{"title":"Formal foundations of 3D geometry to model robot manipulators","authors":"Reynald Affeldt, C. Cohen","doi":"10.1145/3018610.3018629","DOIUrl":"https://doi.org/10.1145/3018610.3018629","url":null,"abstract":"We are interested in the formal specification of safety properties of robot manipulators down to the mathematical physics. To this end, we have been developing a formalization of the mathematics of rigid body transformations in the Coq proof-assistant. It can be used to address the forward kinematics problem, i.e., the computation of the position and orientation of the end-effector of a robot manipulator in terms of the link and joint parameters. Our formalization starts by extending the Mathematical Components library with a new theory for angles and by developing three-dimensional geometry. We use these theories to formalize the foundations of robotics. First, we formalize a comprehensive theory of three-dimensional rotations, including exponentials of skew-symmetric matrices and quaternions. Then, we provide a formalization of the various representations of rigid body transformations: isometries, homogeneous representation, the Denavit-Hartenberg convention, and screw motions. These ingredients make it possible to formalize robot manipulators: we illustrate this aspect by an application to the SCARA robot manipulator.","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129317398","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
Formalization of Karp-Miller tree construction on petri nets petri网上Karp-Miller树构造的形式化
Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018626
M. Yamamoto, Shogo Sekine, Saki Matsumoto
{"title":"Formalization of Karp-Miller tree construction on petri nets","authors":"M. Yamamoto, Shogo Sekine, Saki Matsumoto","doi":"10.1145/3018610.3018626","DOIUrl":"https://doi.org/10.1145/3018610.3018626","url":null,"abstract":"Karp-Miller tree construction on Petri nets is a classical well-known algorithm to construct the minimal coverability set via forward analysis. It enables us to construct decision procedures for several problems such as coverability and (place) boundedness. This paper formalizes Karp-Miller tree construction on Petri nets, and its correctness with respect to coverability using Coq and Ssreflect. Instead of showing soundness and completeness for trees directly, we prove these properties for transition systems derived from Petri nets, and then relate them with trees so we can make use of well-established libraries and also avoid making proofs complicated. Termination of the tree construction is guaranteed by defining it as a Coq function with a well-foundedness proof. Although the termination proof for Karp-Miller tree is usually made with classical reasoning, we avoided it so the whole formalization can be done in an axiom-free way with respect the default Coq theory. This work will provide us with a basis for further formalization of several optimized algorithms, some of which are known to be error prone, and also a template for Karp-Miller style algorithms on extended variants of Petri nets.","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128362101","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
BliStrTune: hierarchical invention of theorem proving strategies BliStrTune:定理证明策略的分层发明
Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2016-11-26 DOI: 10.1145/3018610.3018619
Jan Jakubuv, J. Urban
{"title":"BliStrTune: hierarchical invention of theorem proving strategies","authors":"Jan Jakubuv, J. Urban","doi":"10.1145/3018610.3018619","DOIUrl":"https://doi.org/10.1145/3018610.3018619","url":null,"abstract":"Inventing targeted proof search strategies for specific problem sets is a difficult task. State-of-the-art automated theorem provers (ATPs) such as E allow a large number of user-specified proof search strategies described in a rich domain specific language. Several machine learning methods that invent strategies automatically for ATPs were proposed previously. One of them is the Blind Strategymaker (BliStr), a system for automated invention of ATP strategies. In this paper we introduce BliStrTune -- a hierarchical extension of BliStr. BliStrTune allows exploring much larger space of E strategies by interleaving search for high-level parameters with their fine-tuning. We use BliStrTune to invent new strategies based also on new clause weight functions targeted at problems from large ITP libraries. We show that the new strategies significantly improve E's performance in solving problems from the Mizar Mathematical Library.","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126701280","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: 19
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