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

Markov processes in Isabelle/HOL Isabelle/HOL中的马尔可夫过程

Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018628

J. Hölzl

{"title":"Markov processes in Isabelle/HOL","authors":"J. Hölzl","doi":"10.1145/3018610.3018628","DOIUrl":"https://doi.org/10.1145/3018610.3018628","url":null,"abstract":"Markov processes with discrete time and arbitrary state spaces are important models in probability theory. They model the infinite steps of non-terminating programs with (not just discrete) probabilistic choice and form the basis for further probabilistic models. Their transition behavior is described by Markov kernels, i.e. measurable functions from a state to a distribution of states. Markov kernels can be composed in a monadic way from distributions (normal, exponential, Bernoulli, etc.), other Markov kernels, and even other Markov processes. In this paper we construct discrete-time Markov processes with arbitrary state spaces, given the transition probabilities as a Markov kernel. We show that the Markov processes form again Markov kernels. This allows us to prove a bisimulation argument between two Markov processes and derive the strong Markov property. We use the existing probability theory in Isabelle/HOL and extend its capability to work with Markov kernels. As application we construct continuous-time Markov chains (CTMCs). These are constructed as jump & hold processes, which are discrete-time Markov processes where the state space is a product of continuous holding times and discrete states. We prove the Markov property of CTMCs using the bisimulation argument for discrete-time Markov processes, and that the transition probability is the solution of a differential equation.","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"182 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":"124596858","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: 10

Verifying dynamic race detection 验证动态竞态检测

Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018611

William Mansky, Yuanfeng Peng, S. Zdancewic, Joseph Devietti

引用次数: 10

Verifying a hash table and its iterators in higher-order separation logic 在高阶分离逻辑中验证哈希表及其迭代器

Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018624

F. Pottier

引用次数: 15

Porting the HOL light analysis library: some lessons (invited talk) 移植HOL光分析库:一些经验教训(特邀演讲)

Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3023366

Lawrence Charles Paulson

{"title":"Porting the HOL light analysis library: some lessons (invited talk)","authors":"Lawrence Charles Paulson","doi":"10.1145/3018610.3023366","DOIUrl":"https://doi.org/10.1145/3018610.3023366","url":null,"abstract":"The HOL Light proof assistant is famous for its huge multivariate analysis library: nearly 300,000 lines of code and 13,000 theorems. A substantial fraction of this library has been manually ported to Isabelle/HOL. The Isabelle analysis library contains approximately 7400 named theorems, including Cauchy's integral and residue theorems, the Liouville theorem, the open mapping and domain invariance theorems, the maximum modulus principle and the Krein-Milman Minkowski theorem. Why port proofs manually given so much work on porting proofs automatically? Typical approaches rely on low level encodings that seldom yield natural-looking results. Manual porting has allowed us to generalise many results from n-dimensional vector spaces to metric or topological spaces. The transition from the traditional LCF/HOL proof style (which has hardly changed since 1985) to structured proofs has produced a dramatic improvement in the legibility of the material. Automatic porting generally yields a list of theorem statements but no intelligible proofs. This project has highlighted three features of Isabelle working well together: heuristic automation, structured proofs and sledgehammer. Heuristic automation builds in a lot of implicit knowledge, which is potentially unpredictable, but in combination with structured proofs any breakages (caused by updates to the system) are localised and easily fixed. Sledgehammer (which uses powerful external automation to solve subgoals) can frequently complete an argument without requiring a precise reproduction of the original HOL Light proof. Sledgehammer also encourages a style in which the user reaches the desired result by suggesting a series of intermediate claims. Such proofs are genuinely human-oriented. And only such proofs will attract mathematicians; even a guarantee of correctness will not impress them unless the system lets them understand and tinker with their formal proofs.","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"47-48 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":"114468974","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

Formally verified differential dynamic logic 正式验证差分动态逻辑

Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018616

Rose Bohrer, Vincent Rahli, I. Vukotic, M. Völp, André Platzer

引用次数: 52

Lifting proof-relevant unification to higher dimensions 将证明相关的统一提升到更高的维度

Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018612

Jesper Cockx, Dominique Devriese

{"title":"Lifting proof-relevant unification to higher dimensions","authors":"Jesper Cockx, Dominique Devriese","doi":"10.1145/3018610.3018612","DOIUrl":"https://doi.org/10.1145/3018610.3018612","url":null,"abstract":"In a dependently typed language such as Coq or Agda, unification can be used to discharge equality constraints and detect impossible cases automatically. By nature of dependent types, it is necessary to use a proof-relevant unification algorithm where unification rules are functions manipulating equality proofs. This ensures their correctness but simultaneously sets a high bar for new unification rules. In particular, so far no-one has given a satisfactory proof-relevant version of the injectivity rule for indexed datatypes. In this paper, we describe a general technique for solving equations between constructors of indexed datatypes. We handle the main technical problem—generalization over equality proofs in the indices—by introducing new equations between equality proofs. Borrowing terminology from homotopy type theory, we call them higher-dimensional equations. To apply existing one-dimensional unifiers to these higher-dimensional equations, we show how unifiers can be lifted to a higher dimension. We show the usefulness of this idea by applying it to the unification algorithm used by Agda, though it can also be applied in languages that support identity types but not general indexed datatypes.","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"106 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":"115768269","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

A reflexive tactic for polynomial positivity using numerical solvers and floating-point computations 使用数值求解器和浮点计算的多项式正性的反射策略

Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018622

Érik Martin-Dorel, P. Roux

{"title":"A reflexive tactic for polynomial positivity using numerical solvers and floating-point computations","authors":"Érik Martin-Dorel, P. Roux","doi":"10.1145/3018610.3018622","DOIUrl":"https://doi.org/10.1145/3018610.3018622","url":null,"abstract":"Polynomial positivity over the real field is known to be decidable but even the best algorithms remain costly. An incomplete but often efficient alternative consists in looking for positivity witnesses as sum of squares decompositions. Such decompositions can in practice be obtained through convex optimization. Unfortunately, these methods only yield approximate solutions. Hence the need for formal verification of such witnesses. State of the art methods rely on heuristic roundings to exact solutions in the rational field. These solutions are then easy to verify in a proof assistant. However, this verification often turns out to be very costly, as rational coefficients may blow up during computations. Nevertheless, overapproximations with floating-point arithmetic can be enough to obtain proofs at a much lower cost. Such overapproximations being non trivial, it is mandatory to formally prove that rounding errors are correctly taken into account. We develop a reflexive tactic for the Coq proof assistant allowing one to automatically discharge polynomial positivity proofs. The tactic relies on heavy computation involving multivariate polynomials, matrices and floating-point arithmetic. Benchmarks indicate that we are able to formally address positivity problems that would otherwise be untractable with other state of the art methods.","PeriodicalId":262665,"journal":{"name":"Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs","volume":"19 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":"114630845","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: 16

Type-and-scope safe programs and their proofs 类型和作用域安全的程序及其证明

Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018613

Guillaume Allais, James Chapman, Conor McBride, J. McKinna

引用次数: 33

Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs 第六届ACM SIGPLAN认证程序和证明会议论文集

Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610

Yves Bertot, Viktor Vafeiadis

引用次数: 0

Verified compilation of CakeML to multiple machine-code targets 经过验证的CakeML编译到多个机器码目标

Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs Pub Date : 2017-01-16 DOI: 10.1145/3018610.3018621

A. Fox, Magnus O. Myreen, Yong Kiam Tan, Ramana Kumar

引用次数: 21