Mechanized semantics

The goal of this lecture is to show how modern theorem provers---in this case, the Coq proof assistant---can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and over generic program transformations, as typically found in compilers. The topics covered include: operational semantics (small-step, big-step, definitional interpreters); a simple form of denotational semantics; axiomatic semantics and Hoare logic; generation of verification conditions, with application to program proof; compilation to virtual machine code and its proof of correctness; an example of an optimizing program transformation (dead code elimination) and its proof of correctness

Certified compilation for cryptography: Extended x86 instructions and constant-time verification

We present a new tool for the generation and verification of high-assurance high-speed machine-level cryptography implementations: a certified C compiler supporting instruction extensions to the x86. We demonstrate the practical applicability of our tool by incorporating it into supercop: a toolkit for measuring the performance of cryptographic software, which includes over 2000 different implementations. We show i. that the coverage of x86 implementations in supercop increases significantly due to the added support of instruction extensions via intrinsics and ii. that the obtained verifiably correct implementations are much closer in performance to unverified ones. We extend our compiler with a specialized type system that acts at pre-assembly level; this is the first constant-time verifier that can deal with extended instruction sets. We confirm that, by using instruction extensions, the performance penalty for verifiably constant-time code can be greatly reduced.This work is financed by National Funds through the FCT - Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) within the project PTDC/CCI-INF/31698/2017, and by the Norte Portugal Regional Operational Programme (NORTE 2020) under the Portugal 2020 Partnership Agreement, through the European Regional Development Fund (ERDF) and also by national funds through the FCT, within project NORTE-01-0145-FEDER-028550 (REASSURE)

Compiler verification meets cross-language linking via data abstraction

Many real programs are written in multiple different programming languages, and supporting this pattern creates challenges for formal compiler verification. We describe our Coq verification of a compiler for a high-level language, such that the compiler correctness theorem allows us to derive partial-correctness Hoare-logic theorems for programs built by linking the assembly code output by our compiler and assembly code produced by other means. Our compiler supports such tricky features as storable cross-language function pointers, without giving up the usual benefits of being able to verify different compiler phases (including, in our case, two classic optimizations) independently. The key technical innovation is a mixed operational and axiomatic semantics for the source language, with a built-in notion of abstract data types, such that compiled code interfaces with other languages only through axiomatically specified methods that mutate encapsulated private data, represented in whatever formats are most natural for those languages.National Science Foundation (U.S.) (Grant CCF-1253229)United States. Defense Advanced Research Projects Agency (Agreement FA8750-12-2-0293)United States. Dept. of Energy. Office of Science (Award DE-SC0008923

Extensible Technology-Agnostic Runtime Verification

With numerous specialised technologies available to industry, it has become increasingly frequent for computer systems to be composed of heterogeneous components built over, and using, different technologies and languages. While this enables developers to use the appropriate technologies for specific contexts, it becomes more challenging to ensure the correctness of the overall system. In this paper we propose a framework to enable extensible technology agnostic runtime verification and we present an extension of polyLarva, a runtime-verification tool able to handle the monitoring of heterogeneous-component systems. The approach is then applied to a case study of a component-based artefact using different technologies, namely C and Java.Comment: In Proceedings FESCA 2013, arXiv:1302.478

Applying Formal Methods to Networking: Theory, Techniques and Applications

Despite its great importance, modern network infrastructure is remarkable for the lack of rigor in its engineering. The Internet which began as a research experiment was never designed to handle the users and applications it hosts today. The lack of formalization of the Internet architecture meant limited abstractions and modularity, especially for the control and management planes, thus requiring for every new need a new protocol built from scratch. This led to an unwieldy ossified Internet architecture resistant to any attempts at formal verification, and an Internet culture where expediency and pragmatism are favored over formal correctness. Fortunately, recent work in the space of clean slate Internet design---especially, the software defined networking (SDN) paradigm---offers the Internet community another chance to develop the right kind of architecture and abstractions. This has also led to a great resurgence in interest of applying formal methods to specification, verification, and synthesis of networking protocols and applications. In this paper, we present a self-contained tutorial of the formidable amount of work that has been done in formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial

Formal Verification vs. Quantum Uncertainty

Quantum programming is hard: Quantum programs are necessarily probabilistic and impossible to examine without disrupting the execution of a program. In response to this challenge, we and a number of other researchers have written tools to verify quantum programs against their intended semantics. This is not enough. Verifying an idealized semantics against a real world quantum program doesn\u27t allow you to confidently predict the program\u27s output. In order to have verification that works, you need both an error semantics related to the hardware at hand (this is necessarily low level) and certified compilation to the that same hardware. Once we have these two things, we can talk about an approach to quantum programming where we start by writing and verifying programs at a high level, attempt to verify properties of the compiled code, and repeat as necessary

Verified compilation and optimization of floating-point kernels

When verifying safety-critical code on the level of source code, we trust the compiler to produce machine code that preserves the behavior of the source code. Trusting a verified compiler is easy. A rigorous machine-checked proof shows that the compiler correctly translates source code into machine code. Modern verified compilers (e.g. CompCert and CakeML) have rich input languages, but only rudimentary support for floating-point arithmetic. In fact, state-of-the-art verified compilers only implement and verify an inflexible one-to-one translation from floating-point source code to machine code. This translation completely ignores that floating-point arithmetic is actually a discrete representation of the continuous real numbers. This thesis presents two extensions improving floating-point arithmetic in CakeML. First, the thesis demonstrates verified compilation of elementary functions to floating-point code in: Dandelion, an automatic verifier for polynomial approximations of elementary functions; and libmGen, a proof-producing compiler relating floating-point machine code to the implemented real-numbered elementary function. Second, the thesis demonstrates verified optimization of floating-point code in: Icing, a floating-point language extending standard floating-point arithmetic with optimizations similar to those used by unverified compilers, like GCC and LLVM; and RealCake, an extension of CakeML with Icing into the first fully verified optimizing compiler for floating-point arithmetic.Bei der Verifizierung von sicherheitsrelevantem Quellcode vertrauen wir dem Compiler, dass er Maschinencode ausgibt, der sich wie der Quellcode verhält. Man kann ohne weiteres einem verifizierten Compiler vertrauen. Ein rigoroser maschinen-ü}berprüfter Beweis zeigt, dass der Compiler Quellcode in korrekten Maschinencode übersetzt. Moderne verifizierte Compiler (z.B. CompCert und CakeML) haben komplizierte Eingabesprachen, aber unterstützen Gleitkommaarithmetik nur rudimentär. De facto implementieren und verifizieren hochmoderne verifizierte Compiler für Gleitkommaarithmetik nur eine starre eins-zu-eins Übersetzung von Quell- zu Maschinencode. Diese Übersetzung ignoriert vollständig, dass Gleitkommaarithmetik eigentlich eine diskrete Repräsentation der kontinuierlichen reellen Zahlen ist. Diese Dissertation präsentiert zwei Erweiterungen die Gleitkommaarithmetik in CakeML verbessern. Zuerst demonstriert die Dissertation verifizierte Übersetzung von elementaren Funktionen in Gleitkommacode mit: Dandelion, einem automatischen Verifizierer für Polynomapproximierungen von elementaren Funktionen; und libmGen, einen Beweis-erzeugenden Compiler der Gleitkommacode in Relation mit der implementierten elementaren Funktion setzt. Dann demonstriert die Dissertation verifizierte Optimierung von Gleitkommacode mit: Icing, einer Gleitkommasprache die Gleitkommaarithmetik mit Optimierungen erweitert die ähnlich zu denen in unverifizierten Compilern, wie GCC und LLVM, sind; und RealCake, eine Erweiterung von CakeML mit Icing als der erste vollverifizierte Compiler für Gleitkommaarithmetik

Proceedings of the Third International Workshop on Proof-Carrying Code and Software Certification

This NASA conference publication contains the proceedings of the Third International Workshop on Proof-Carrying Code and Software Certification, held as part of LICS in Los Angeles, CA, USA, on August 15, 2009. Software certification demonstrates the reliability, safety, or security of software systems in such a way that it can be checked by an independent authority with minimal trust in the techniques and tools used in the certification process itself. It can build on existing validation and verification (V&V) techniques but introduces the notion of explicit software certificates, Vvilich contain all the information necessary for an independent assessment of the demonstrated properties. One such example is proof-carrying code (PCC) which is an important and distinctive approach to enhancing trust in programs. It provides a practical framework for independent assurance of program behavior; especially where source code is not available, or the code author and user are unknown to each other. The workshop wiII address theoretical foundations of logic-based software certification as well as practical examples and work on alternative application domains. Here "certificate" is construed broadly, to include not just mathematical derivations and proofs but also safety and assurance cases, or any fonnal evidence that supports the semantic analysis of programs: that is, evidence about an intrinsic property of code and its behaviour that can be independently checked by any user, intermediary, or third party. These guarantees mean that software certificates raise trust in the code itself, distinct from and complementary to any existing trust in the creator of the code, the process used to produce it, or its distributor. In addition to the contributed talks, the workshop featured two invited talks, by Kelly Hayhurst and Andrew Appel. The PCC 2009 website can be found at http://ti.arc.nasa.gov /event/pcc 091

Function extraction

AbstractLow-level imperative programming languages typically have complex operational semantics (e.g. derived from an underlying processor architecture). In this paper, we describe an automatic method for extracting recursive functions from such low-level programs. The functions are derived by formal deduction from the semantics of the programming language. For each function extracted, a proof of correspondence to the original program is automatically constructed. Subsequent program verification can then be done without referring to the details of the low-level programming language semantics at all: it suffices to prove properties of the extracted function. The technique is explained for simple while programs and also for the machine code of a widely used processor. We show how heuristics can enhance the output from the function extractor/decompiler and how the technique aids implementation of a trustworthy compiler. Our tools have been implemented in the HOL4 theorem prover