Capsules and Separation

We study a formulation of separation logic using capsules, a representation of the state of a computation in higher-order programming languages with mutable variables. We prove soundness of the frame rule in this context and investigate alternative formulations with weaker side conditions

Footprints in Local Reasoning

Local reasoning about programs exploits the natural local behaviour common in programs by focussing on the footprint - that part of the resource accessed by the program. We address the problem of formally characterising and analysing the footprint notion for abstract local functions introduced by Calcagno, O Hearn and Yang. With our definition, we prove that the footprints are the only essential elements required for a complete specification of a local function. We formalise the notion of small specifications in local reasoning and show that for well-founded resource models, a smallest specification always exists that only includes the footprints, and also present results for the non-well-founded case. Finally, we use this theory of footprints to investigate the conditions under which the footprints correspond to the smallest safe states. We present a new model of RAM in which, unlike the standard model, the footprints of every program correspond to the smallest safe states, and we also identify a general condition on the primitive commands of a programming language which guarantees this property for arbitrary models.Comment: LMCS 2009 (FOSSACS 2008 special issue

Separation Logic

Separation logic is a key development in formal reasoning about programs, opening up new lines of attack on longstanding problems

Undecidability of Propositional Separation Logic and Its Neighbours

n this article, we investigate the logical structure of memory models of theoretical and practical interest. Our main interest is in “the logic behind a fixed memory model”, rather than in “a model of any kind behind a given logical system”. As an effective language for reasoning about such memory models, we use the formalism of separation logic. Our main result is that for any concrete choice of heap-like memory model, validity in that model is undecidable even for purely propositional formulas in this language. The main novelty of our approach to the problem is that we focus on validity in specific, concrete memory models, as opposed to validity in general classes of models. Besides its intrinsic technical interest, this result also provides new insights into the nature of their decidable fragments. In particular, we show that, in order to obtain such decidable fragments, either the formula language must be severely restricted or the valuations of propositional variables must be constrained. In addition, we show that a number of propositional systems that approximate separation logic are undecidable as well. In particular, this resolves the open problems of decidability for Boolean BI and Classical BI. Moreover, we provide one of the simplest undecidable propositional systems currently known in the literature, called “Minimal Boolean BI”, by combining the purely positive implication-conjunction fragment of Boolean logic with the laws of multiplicative *-conjunction, its unit and its adjoint implication, originally provided by intuitionistic multiplicative linear logic. Each of these two components is individually decidable: the implication-conjunction fragment of Boolean logic is co-NP-complete, and intuitionistic multiplicative linear logic is NP-complete. All of our undecidability results are obtained by means of a direct encoding of Minsky machines

Understanding and evolving the Rust programming language

Rust is a young systems programming language that aims to fill the gap between high-level languages—which provide strong static guarantees like memory and thread safety—and low-level languages—which give the programmer fine-grained control over data layout and memory management. This dissertation presents two projects establishing the first formal foundations for Rust, enabling us to better understand and evolve this important language: RustBelt and Stacked Borrows. RustBelt is a formal model of Rust’s type system, together with a soundness proof establishing memory and thread safety. The model is designed to verify the safety of a number of intricate APIs from the Rust standard library, despite the fact that the implementations of these APIs use unsafe language features. Stacked Borrows is a proposed extension of the Rust specification, which enables the compiler to use the strong aliasing information in Rust’s types to better analyze and optimize the code it is compiling. The adequacy of this specification is evaluated not only formally, but also by running real Rust code in an instrumented version of Rust’s Miri interpreter that implements the Stacked Borrows semantics. RustBelt is built on top of Iris, a language-agnostic framework, implemented in the Coq proof assistant, for building higher-order concurrent separation logics. This dissertation begins by giving an introduction to Iris, and explaining how Iris enables the derivation of complex high-level reasoning principles from a few simple ingredients. In RustBelt, this technique is exploited crucially to introduce the lifetime logic, which provides a novel separation-logic account of borrowing, a key distinguishing feature of the Rust type system.Rust ist eine junge systemnahe Programmiersprache, die es sich zum Ziel gesetzt hat, die Lücke zu schließen zwischen Sprachen mit hohem Abstraktionsniveau, die vor Speicher- und Nebenläufigkeitsfehlern schützen, und Sprachen mit niedrigem Abstraktionsniveau, welche dem Programmierer detaillierte Kontrolle über die Repräsentation von Daten und die Verwaltung des Speichers ermöglichen. Diese Dissertation stellt zwei Projekte vor, welche die ersten formalen Grundlagen für Rust zum Zwecke des besseren Verständnisses und der weiteren Entwicklung dieser wichtigen Sprache legen: RustBelt und Stacked Borrows. RustBelt ist ein formales Modell des Typsystems von Rust einschließlich eines Korrektheitsbeweises, welcher die Sicherheit von Speicherzugriffen und Nebenläufigkeit zeigt. Das Modell ist darauf ausgerichtet, einige komplexe Komponenten der Standardbibliothek von Rust zu verifizieren, obwohl die Implementierung dieser Komponenten unsichere Sprachkonstrukte verwendet. Stacked Borrows ist eine Erweiterung der Spezifikation von Rust, die es dem Compiler ermöglicht, den Quelltext mit Hilfe der im Typsystem kodierten Alias-Informationen besser zu analysieren und zu optimieren. Die Tauglichkeit dieser Spezifikation wird nicht nur formal belegt, sondern auch an echten Programmen getestet, und zwar mit Hilfe einer um Stacked Borrows erweiterten Version des Interpreters Miri. RustBelt basiert auf Iris, welches die Konstruktion von Separationslogiken für beliebige Programmiersprachen im Beweisassistenten Coq ermöglicht. Diese Dissertation beginnt mit einer Einführung in Iris und erklärt, wie komplexe Beweismethoden mit Hilfe weniger einfacher Bausteine hergeleitet werden können. In RustBelt wird diese Technik für die Umsetzung der „Lebenszeitlogik“ verwendet, einer Erweiterung der Separationslogik mit dem Konzept von „Leihgaben“ (borrows), welche eine wichtige Rolle im Typsystem von Rust spielen.This research was supported in part by a European Research Council (ERC) Consolidator Grant for the project "RustBelt", funded under the European Union’s Horizon 2020 Framework Programme (grant agreement no. 683289)