Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs最新文献

Proofs in conflict-driven theory combination 冲突驱动理论组合中的证明

Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs Pub Date : 2018-01-08 DOI: 10.1145/3167096

M. P. Bonacina, Stéphane Lengrand, N. Shankar

{"title":"Proofs in conflict-driven theory combination","authors":"M. P. Bonacina, Stéphane Lengrand, N. Shankar","doi":"10.1145/3167096","DOIUrl":"https://doi.org/10.1145/3167096","url":null,"abstract":"Search-based satisfiability procedures try to construct a model of the input formula by simultaneously proposing candidate models and deriving new formulae implied by the input. When the formulae are satisfiable, these procedures generate a model as a witness. Dually, it is desirable to have a proof when the formulae are unsatisfiable. Conflict-driven procedures perform nontrivial inferences only when resolving conflicts between the formulae and assignments representing the candidate model. CDSAT (Conflict-Driven SATisfiability) is a method for conflict-driven reasoning in combinations of theories. It combines solvers for individual theories as theory modules within a solver for the union of the theories. In this paper we endow CDSAT with lemma learning and proof generation. For the latter, we present two techniques. The first one produces proof objects in memory: it assumes that all theory modules produce proof objects and it accommodates multiple proof formats. The second technique adapts the LCF approach to proofs from interactive theorem proving to conflict-driven SMT-solving and theory combination, by defining a small kernel of reasoning primitives that guarantees that CDSAT proofs are correct by construction.","PeriodicalId":273972,"journal":{"name":"Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127872370","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

Binder aware recursion over well-scoped de Bruijn syntax 绑定器感知递归在范围良好的de Bruijn语法上

Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs Pub Date : 2018-01-08 DOI: 10.1145/3167098

Jonas Kaiser, S. Schäfer, Kathrin Stark

引用次数: 12

Generic derivation of induction for impredicative encodings in Cedille Cedille中不可预知编码归纳的一般推导

Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs Pub Date : 2018-01-08 DOI: 10.1145/3167087

Denis Firsov, Aaron Stump

引用次数: 18

A constructive formalisation of Semi-algebraic sets and functions 半代数集和函数的构造形式化

Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs Pub Date : 2018-01-08 DOI: 10.1145/3167099

Boris Djalal

引用次数: 1

A formal proof in Coq of a control function for the inverted pendulum 倒立摆控制函数的Coq形式证明

Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs Pub Date : 2018-01-08 DOI: 10.1145/3167101

Damien Rouhling

引用次数: 13

Triangulating context lemmas 三角化上下文引理

Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs Pub Date : 2018-01-08 DOI: 10.1145/3167081

Craig McLaughlin, J. McKinna, I. Stark

{"title":"Triangulating context lemmas","authors":"Craig McLaughlin, J. McKinna, I. Stark","doi":"10.1145/3167081","DOIUrl":"https://doi.org/10.1145/3167081","url":null,"abstract":"The idea of a context lemma spans a range of programming-language models: from Milner’s original through the CIU theorem to ‘CIU-like’ results for multiple language features. Each shows that to prove observational equivalence between program terms it is enough to test only some restricted class of contexts: applicative, evaluation, reduction, etc. We formally reconstruct a distinctive proof method for context lemmas based on cyclic inclusion of three program approximations: by triangulating between ‘applicative’ and ‘logical’ relations we prove that both match the observational notion, while being simpler to compute. Moreover, the observational component of the triangle condenses a series of approximations covering variation in the literature around what variable-capturing structure qualifies as a ‘context’. Although entirely concrete, our approach involves no term dissection or inspection of reduction sequences; instead we draw on previous context lemmas using operational logical relations and biorthogonality. We demonstrate the method for a fine-grained call-by-value presentation of the simply-typed lambda-calculus, and extend to a CIU result formulated with frame stacks. All this is formalised and proved in Agda: building on work of Allais et al., we exploit dependent types to specify lambda-calculus terms as well-typed and well-scoped by construction. By doing so, we seek to dispel any lingering anxieties about the manipulation of concrete contexts when reasoning about bound variables, capturing substitution, and observational equivalences.","PeriodicalId":273972,"journal":{"name":"Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123891848","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

Mechanising blockchain consensus 机械化区块链共识

Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs Pub Date : 2018-01-08 DOI: 10.1145/3167086

George Pîrlea, Ilya Sergey

{"title":"Mechanising blockchain consensus","authors":"George Pîrlea, Ilya Sergey","doi":"10.1145/3167086","DOIUrl":"https://doi.org/10.1145/3167086","url":null,"abstract":"We present the first formalisation of a blockchain-based distributed consensus protocol with a proof of its consistency mechanised in an interactive proof assistant. Our development includes a reference mechanisation of the block forest data structure, necessary for implementing provably correct per-node protocol logic. We also define a model of a network, implementing the protocol in the form of a replicated state-transition system. The protocol's executions are modeled via a small-step operational semantics for asynchronous message passing, in which packages can be rearranged or duplicated. In this work, we focus on the notion of global system safety, proving a form of eventual consistency. To do so, we provide a library of theorems about a pure functional implementation of block forests, define an inductive system invariant, and show that, in a quiescent system state, it implies a global agreement on the state of per-node transaction ledgers. Our development is parametric with respect to implementations of several security primitives, such as hash-functions, a notion of a proof object, a Validator Acceptance Function, and a Fork Choice Rule. We precisely characterise the assumptions, made about these components for proving the global system consensus, and discuss their adequacy. All results described in this paper are formalised in Coq.","PeriodicalId":273972,"journal":{"name":"Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117295294","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: 52

A two-level logic perspective on (simultaneous) substitutions (同时)替换的两级逻辑视角

Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs Pub Date : 2018-01-08 DOI: 10.1145/3167093

Kaustuv Chaudhuri

{"title":"A two-level logic perspective on (simultaneous) substitutions","authors":"Kaustuv Chaudhuri","doi":"10.1145/3167093","DOIUrl":"https://doi.org/10.1145/3167093","url":null,"abstract":"Lambda-tree syntax (λTS), also known as higher-order abstract syntax (HOAS), is a representational technique where the pure λ-calculus in a meta-language is used to represent binding constructs in an object language. A key feature of λTS is that capture-avoiding substitution in the object language is represented by β-reduction in the meta language. However, to reason about the meta-theory of (simultaneous) substitutions, it may seem that λTS gets in the way: not only does iterated β-reduction not capture simultaneity, but also β-redexes are not first-class constructs. This paper proposes a representation of (simultaneous) substitutions in the two-level logic approach (2LLA), where properties of a specification language are established in a strong reasoning meta-logic that supports inductive reasoning. A substitution, which is a partial map from variables to terms, is represented in a form similar to typing contexts, which are partial maps from variables to types; both are first-class in 2LLA. The standard typing rules for substitutions are then just a kind of context relation that are already well-known in 2LLA. This representation neither changes the reasoning kernel, nor requires any modification of existing type systems, and does not sacrifice any expressivity.","PeriodicalId":273972,"journal":{"name":"Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114316678","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

Completeness and decidability of converse PDL in the constructive type theory of Coq Coq构造型理论中逆PDL的完备性和可判定性

Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs Pub Date : 2018-01-08 DOI: 10.1145/3167088

C. Doczkal, Joachim Bard

引用次数: 5

Efficient certification of complexity proofs: formalizing the Perron–Frobenius theorem (invited talk paper) 复杂性证明的有效认证:Perron-Frobenius定理的形式化(特邀演讲论文)

Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs Pub Date : 2018-01-08 DOI: 10.1145/3167103

Jose Divasón, Sebastiaan J. C. Joosten, Ondrej Kuncar, René Thiemann, A. Yamada

引用次数: 8