Verifying object-oriented programs with higher-order separation logic in Coq

We present a shallow Coq embedding of a higher-order separation logic with nested triples for an object-oriented programming language. Moreover, we develop novel specification and proof patterns for reasoning in higher-order separation logic with nested triples about programs that use interfaces and interface inheritance. In particular, we show how to use the higher-order features of the Coq formalisation to specify and reason modularly about programs that (1) depend on some unknown code satisfying a specification or that (2) return objects conforming to a certain specification. All of our results have been formally verified in the interactive theorem prover Coq

Automating Deductive Verification for Weak-Memory Programs

Writing correct programs for weak memory models such as the C11 memory model is challenging because of the weak consistency guarantees these models provide. The first program logics for the verification of such programs have recently been proposed, but their usage has been limited thus far to manual proofs. Automating proofs in these logics via first-order solvers is non-trivial, due to reasoning features such as higher-order assertions, modalities and rich permission resources. In this paper, we provide the first implementation of a weak memory program logic using existing deductive verification tools. We tackle three recent program logics: Relaxed Separation Logic and two forms of Fenced Separation Logic, and show how these can be encoded using the Viper verification infrastructure. In doing so, we illustrate several novel encoding techniques which could be employed for other logics. Our work is implemented, and has been evaluated on examples from existing papers as well as the Facebook open-source Folly library.Comment: Extended version of TACAS 2018 publicatio

History-based verification of functional behaviour of concurrent programs

Modular verification of the functional behaviour of a concurrent program remains a challenge. We propose a new way to achieve this, using histories, modelled as process algebra terms, to keep track of local changes. When threads terminate or synchronise in some other way, local histories are combined into global histories, and by resolving the global histories, the reachable state properties can be determined. Our logic is an extension of permission-based separation logic, which supports expressive and intuitive specifications. We discuss soundness of the approach, and illustrate it on several examples

Structural Refinement for the Modal nu-Calculus

We introduce a new notion of structural refinement, a sound abstraction of logical implication, for the modal nu-calculus. Using new translations between the modal nu-calculus and disjunctive modal transition systems, we show that these two specification formalisms are structurally equivalent. Using our translations, we also transfer the structural operations of composition and quotient from disjunctive modal transition systems to the modal nu-calculus. This shows that the modal nu-calculus supports composition and decomposition of specifications.Comment: Accepted at ICTAC 201

Towards Scientific Incident Response

A scientific incident analysis is one with a methodical, justifiable approach to the human decision-making process. Incident analysis is a good target for additional rigor because it is the most human-intensive part of incident response. Our goal is to provide the tools necessary for specifying precisely the reasoning process in incident analysis. Such tools are lacking, and are a necessary (though not sufficient) component of a more scientific analysis process. To reach this goal, we adapt tools from program verification that can capture and test abductive reasoning. As Charles Peirce coined the term in 1900, “Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea.” We reference canonical examples as paradigms of decision-making during analysis. With these examples in mind, we design a logic capable of expressing decision-making during incident analysis. The result is that we can express, in machine-readable and precise language, the abductive hypotheses than an analyst makes, and the results of evaluating them. This result is beneficial because it opens up the opportunity of genuinely comparing analyst processes without revealing sensitive system details, as well as opening an opportunity towards improved decision-support via limited automation

Lambda Definability with Sums via Grothendieck Logical Relations

. We introduce a notion of Grothendieck logical relation and use it to characterise the definability of morphisms in stable bicartesian closed categories by terms of the simply-typed lambda calculus with finite products and finite sums. Our techniques are based on concepts from topos theory, however our exposition is elementary. Introduction The use of logical relations as a tool for characterising the -definable elements in a model of the simply-typed -calculus originated in the work of Plotkin [10], who obtained such a characterisation of the definable elements in the full type hierarchy using a notion of Kripke logical relation. Subsequently, the more general notion of a Kripke logical relation of varying arity was developed by Jung and Tiuryn, and shown to characterise the definable elements in any Henkin model [4]. Although not emphasised in [4], relations of varying arity are powerful enough to characterise relative definability with respect to any given set of elements consider..

Automatic Verification of Parameterized Data Structures

Abstract. Verifying correctness of programs operating on data structures has become an integral part of software verification. A method is a program that acts on an input data structure (modeled as a graph) and produces an output data structure. The parameterized correctness problem for such methods can be defined as follows: Given a method and a property of the input graphs, we wish to verify that for all input graphs, parameterized by their size, the output graphs also satisfy the property. We present an automated approach to verify that a given method preserves a given property for a large class of methods. Examples include reversals of linked lists, insertion, deletion and iterative modification of nodes in directed graphs. Our approach draws on machinery from automata theory and temporal logic. For a useful class of data structures and properties, our solution is polynomial in the size of the method and size of the property specification

Verifying Class Invariants in Concurrent Programs

Class invariants are a highly useful feature for the verification of object-oriented programs, because they can be used to capture all valid object states. In a sequential program setting, the validity of class invariants is typically described in terms of a visible state semantics, i.e., invariants only have to hold whenever a method begins or ends execution, and they may be broken inside a method body. However, in a concurrent setting, this restriction is no longer usable, because due to thread interleavings, any program state is potentially a visible state. In this paper we present a new approach for reasoning about class invariants in multithreaded programs. We allow a thread to explicitly break an invariant at specific program locations, while ensuring that no other thread can observe the broken invariant. We develop our technique in a permission-based separation logic environment. However, we deviate from separation logic's standard rules and allow a class invariant to express properties over shared memory locations (the invariant footprint), independently of the permissions on these locations. In this way, a thread may break or reestablish an invariant without holding permissions to all locations in its footprint. To enable modular verification, we adopt the restrictions of Muller's ownership-based type system