2011

Editors: Frank Piessens, Gilles Barthe, Andrew Gordon

We present a calculus that models a form of process interaction based on copyless message passing, in the style of Singularity OS. The calculus is equipped with a type system ensuring that well-typed processes are free from memory faults, memory leaks, and communication errors. The type system is essentially linear, but we show that linearity alone is inadequate, because it leaves room for scenarios where well-typed processes leak significant amounts of memory. We address these problems basing the type system upon an original variant of session types.

We present a static analysis by Abstract Interpretation to check for run-time errors in parallel and multi-threaded C programs. Following our work on Astrée, we focus on embedded critical programs without recursion nor dynamic memory allocation, but extend the analysis to a static set of threads communicating implicitly through a shared memory and explicitly using a finite set of mutual exclusion locks, and scheduled according to a real-time scheduling policy and fixed priorities. Our method is thread-modular. It is based on a slightly modified non-parallel analysis that, when analyzing a thread, applies and enriches an abstract set of thread interferences. An iterator then re-analyzes each thread in turn until interferences stabilize. We prove the soundness of our method with respect to the sequential consistency semantics, but also with respect to a reasonable weakly consistent memory semantics. We also show how to take into account mutual exclusion and thread priorities through a partitioning over an abstraction of the scheduler state. We present preliminary experimental results analyzing an industrial program with our prototype, Thésée, and demonstrate the scalability of our approach.

We develop and prove sound a concurrent separation logic for Pthreads-style barriers. Although Pthreads barriers are widely used in systems, and separation logic is widely used for verification, there has not been any effort to combine the two. Unlike locks and critical sections, Pthreads barriers enable simultaneous resource redistribution between multiple threads and are inherently stateful, leading to significant complications in the design of the logic and its soundness proof. We show how our logic can be applied to a specific example program in a modular way. Our proofs are machine-checked in Coq. We showcase a program verification toolset that automatically applies the logic rules and discharges the associated proof obligations.

Exchanging mutable data objects with untrusted code is a delicate matter because of the risk of creating a data space that is accessible by an attacker. Consequently, secure programming guidelines for Java stress the importance of using defensive copying before accepting or handing out references to an internal mutable object. However, implementation of a copy method (like clone()) is entirely left to the programmer. It may not provide a sufficiently deep copy of an object and is subject to overriding by a malicious sub-class. Currently no language-based mechanism supports secure object cloning. This paper proposes a type-based annotation system for defining modular copy policies for class-based object-oriented programs. A copy policy specifies the maximally allowed sharing between an object and its clone. We present a static enforcement mechanism that will guarantee that all classes fulfil their copy policy, even in the presence of overriding of copy methods, and establish the semantic correctness of the overall approach in Coq. The mechanism has been implemented and experimentally evaluated on clone methods from several Java libraries.

Nominal Isabelle is a definitional extension of the Isabelle/HOL theorem prover. It provides a proving infrastructure for reasoning about programming language calculi involving named bound variables (as opposed to de-Bruijn indices). In this paper we present an extension of Nominal Isabelle for dealing with general bindings, that means term constructors where multiple variables are bound at once. Such general bindings are ubiquitous in programming language research and only very poorly supported with single binders, such as lambda-abstractions. Our extension includes new definitions of alpha-equivalence and establishes automatically the reasoning infrastructure for alpha-equated terms. We also prove strong induction principles that have the usual variable convention already built in.

Separation logic is a concise method for specifying programs that manipulate dynamically allocated storage. Partially inspired by separation logic, Implicit Dynamic Frames has recently been proposed, aiming at first-order tool support. In this paper, we precisely connect the semantics of these two logics. We define a logic whose syntax subsumes both that of a standard separation logic, and that of implicit dynamic frames as sub-syntaxes. We define a total heap semantics for our logic, and, for the separation logic subsyntax, prove it equivalent the standard partial heaps model. In order to define a semantics which works uniformly for both subsyntaxes, we define the novel concept of a minimal state extension, which provides a different (but equivalent) definition of the semantics of separation logic implication and magic wand connectives, while also giving a suitable semantics for these connectives in implicit dynamic frames. We show that our resulting semantics agrees with the existing definition of weakest pre-condition semantics for the implicit dynamic frames fragment. Finally, we show that we can encode the separation logic fragment of our logic into the implicit dynamic frames fragment, preserving semantics. For the connectives typically supported by tools, this shows that separation logic can be faithfully encoded in a first-order automatic verification tool (Chalice).

Traditionally, transfer functions have been designed manually for each operation in a program, instruction by instruction. In such a setting, a transfer function describes the semantics of a single instruction, detailing how a given abstract input state is mapped to an abstract output state. The net effect of a sequence of instructions, a basic block, can then be calculated by composing the transfer functions of the constituent instructions. However, precision can be improved by applying a single transfer function that captures the semantics of the block as a whole. Since blocks are program-dependent, this approach necessitates automation. There has thus been growing interest in computing transfer functions automatically, most notably using techniques based on quantifier elimination. Although conceptually elegant, quantifier elimination inevitably induces a computational bottleneck, which limits the applicability of these methods to small blocks. This paper contributes a method for calculating transfer functions that finesses quantifier elimination altogether, and can thus be seen as a response to this problem. The practicality of the method is demonstrated by generating transfer functions for input and output states that are described by linear template constraints, which include intervals and octagons.

We consider the problem of computing numerical invariants of programs, for instance bounds on the values of numerical program variables. More specifically, we study the problem of performing static analysis by abstract interpretation using template linear constraint domains. Such invariants can be obtained by Kleene iterations that are, in order to guarantee termination, accelerated by widening operators. In many cases, however, applying this form of extrapolation leads to invariants that are weaker than the strongest inductive invariant that can be expressed within the abstract domain in use. Another well-known source of imprecision of traditional abstract interpretation techniques stems from their use of join operators at merge nodes in the control flow graph. The mentioned weaknesses may prevent these methods from proving safety properties. The technique we develop in this article addresses both of these issues: contrary to Kleene iterations accelerated by widening operators, it is guaranteed to yield the strongest inductive invariant that can be expressed within the template linear constraint domain in use. It also eschews join operators by distinguishing all paths of loop-free code segments. Formally speaking, our technique computes the least fixpoint within a given template linear constraint domain of a transition relation that is succinctly expressed as an existentially quantified linear real arithmetic formula. In contrast to previously published techniques that rely […]

The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables. There is a trend in machine learning towards expressing Bayesian models as probabilistic programs. As a foundation for this kind of programming, we propose a core functional calculus with primitives for sampling prior distributions and observing variables. We define measure-transformer combinators inspired by theorems in measure theory, and use these to give a rigorous semantics to our core calculus. The original features of our semantics include its support for discrete, continuous, and hybrid measures, and, in particular, for observations of zero-probability events. We compile our core language to a small imperative language that is processed by an existing inference engine for factor graphs, which are data structures that enable many efficient inference algorithms. This allows efficient approximate inference of posterior marginal distributions, treating thousands of observations per second for large instances of realistic models.