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Register a new userAn Overview of the HFL Model Checking Project
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Publication date
2021
fields
Informatics Engineering
and research's language is
English
Authors
Naoki Kobayashi
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In this article, we give an overview of our project on higher-order program verification based on HFL (higher-order fixpoint logic) model checking. After a brief introduction to HFL, we explain how it can be applied to program verification, and summarize the current status of the project.
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Proof assistants are getting more widespread use in research and industry to provide certified and independently checkable guarantees about theories, designs, systems and implementations. However, proof assistant implementations themselves are seldom verified, although they take a major share of the trusted code base in any such certification effort. In this area, proof assistants based on Higher-Order Logic enjoy stronger guarantees, as self-certified implementations have been available for some years. One cause of this difference is the inherent complexity of dependent type theories together with their extensions with inductive types, universe polymorphism and complex sort systems, and the gap between theory on paper and practical implementations in efficient programming languages. MetaCoq is a collaborative project that aims to tackle these difficulties to provide the first fully-certified realistic implementation of a type checker for the full calculus underlying the Coq proof assistant. To achieve this, we refined the sometimes blurry, if not incorrect, specification and implementation of the system. We show how theoretical tools from this community such as bidirectional type-checking, Tait-Martin-Lof/Takahashis confluence proof technique and monadic and dependently-typed programming can help construct the following artefacts: a specification of Coqs syntax and type theory, the Polymorphic Cumulative Calculus of (Co)-Inductive Constructions (PCUIC); a monad for the manipulation of raw syntax and interaction with the Coq system; a verification of PCUICs metatheory, whose main results are the confluence of reduction, type preservation and principality of typing; a realistic, correct and complete type-checker for PCUIC; a sound type and proof erasure procedure from PCUIC to untyped lambda-calculus, i.e., the core of the extraction mechanism of Coq.
In recent work, we have developed a session types discipline for a calculus that features the usual constructs for session establishment and communication, but also two novel constructs that enable communicating processes to be stopped, duplicated, or discarded at runtime. The aim is to understand whether known techniques for the static analysis of structured communications scale up to the challenging context of context-aware, adaptable distributed systems, in which disciplined interaction and runtime adaptation are intertwined concerns. In this short note, we summarize the main features of our session-typed framework with runtime adaptation, and recall its basic correctness properties. We illustrate our framework by means of examples. In particular, we present a session representation of supervision trees, a mechanism for enforcing fault-tolerant applications in the Erlang language.
In this paper we investigate the applicability of standard model checking approaches to verifying properties in probabilistic programming. As the operational model for a standard probabilistic program is a potentially infinite parametric Markov decision process, no direct adaption of existing techniques is possible. Therefore, we propose an on-the-fly approach where the operational model is successively created and verified via a step-wise execution of the program. This approach enables to take key features of many probabilistic programs into account: nondeterminism and conditioning. We discuss the restrictions and demonstrate the scalability on several benchmarks.
This work strives to make formal verification of POSIX multithreaded programs easily accessible to general programmers. Sthread operates directly on multithreaded C/C++ programs, without the need for an intermediate formal model. Sthread is in-vivo in that it provides a drop-in replacement for the pthread library, and operates directly on the compiled target executable and application libraries. There is no compiler-generated intermediate representation. The system calls in the application remain unaltered. Optionally, the programmer can add a small amount of additional native C code to include assertions based on the users algorithm, declarations of shared memory regions, and progress/liveness conditions. The work has two important motivations: (i) It can be used to verify correctness of a concurrent algorithm being implemented with multithreading; and (ii) it can also be used pedagogically to provide immediate feedback to students learning either to employ POSIX threads system calls or to implement multithreaded algorithms. This work represents the first example of in-vivo model checking operating directly on the standard multithreaded executable and its libraries, without the aid of a compiler-generated intermediate representation. Sthread leverages the open-source SimGrid libraries, and will eventually be integrated into SimGrid. Sthread employs a non-preemptive model in which thread context switches occur only at multithreaded system calls (e.g., mutex, semaphore) or before accesses to shared memory regions. The emphasis is on finding algorithmic bugs (bugs in an original algorithm, implemented as POSIX threads and shared memory regions. This work is in contrast to Context-Bounded Analysis (CBA), which assumes a preemptive model for threads, and emphasizes implementation bugs such as buffer overruns and write-after-free for memory allocation. In particular, the Sthread in-vivo approach has strong future potential for pedagogy, by providing immediate feedback to students who are first learning the correct use of Pthreads system calls in implementation of concurrent algorithms based on multithreading.
We identify a subproblem of the model-checking problem for the epistemic mu-calculus which is decidable. Formulas in the instances of this subproblem allow free variables within the scope of epistemic modalities in a restricted form that avoids embodying any form of common knowledge. Our subproblem subsumes known decidable fragments of epistemic CTL/LTL, may express winning strategies in two-player games with one player having imperfect information and non-observable objectives, and, with a suitable encoding, decidable instances of the model-checking problem for ATLiR.
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