{SCL} with Theory Constraints

We lift the SCL calculus for first-order logic without equality to the SCL(T) calculus for first-order logic without equality modulo a background theory. In a nutshell, the SCL(T) calculus describes a new way to guide hierarchic resolution inferences by a partial model assumption instead of an a priori fixed order as done for instance in hierarchic superposition. The model representation consists of ground background theory literals and ground foreground first-order literals. One major advantage of the model guided approach is that clauses generated by SCL(T) enjoy a non-redundancy property that makes expensive testing for tautologies and forward subsumption completely obsolete. SCL(T) is a semi-decision procedure for pure clause sets that are clause sets without first-order function symbols ranging into the background theory sorts. Moreover, SCL(T) can be turned into a decision procedure if the considered combination of a first-order logic modulo a background theory enjoys an abstract finite model property

SCL with Theory Constraints

We lift the SCL calculus for first-order logic without equality to the SCL(T) calculus for first-order logic without equality modulo a background theory. In a nutshell, the SCL(T) calculus describes a new way to guide hierarchic resolution inferences by a partial model assumption instead of an a priori fixed order as done for instance in hierarchic superposition. The model representation consists of ground background theory literals and ground foreground first-order literals. One major advantage of the model guided approach is that clauses generated by SCL(T) enjoy a non-redundancy property that makes expensive testing for tautologies and forward subsumption completely obsolete. SCL(T) is a semi-decision procedure for pure clause sets that are clause sets without first-order function symbols ranging into the background theory sorts. Moreover, SCL(T) can be turned into a decision procedure if the considered combination of a first-order logic modulo a background theory enjoys an abstract finite model property.Comment: 22 page

SCL with Theory Constraints

22 pagesWe lift the SCL calculus for first-order logic without equality to the SCL(T) calculus for first-order logic without equality modulo a background theory. In a nutshell, the SCL(T) calculus describes a new way to guide hierarchic resolution inferences by a partial model assumption instead of an a priori fixed order as done for instance in hierarchic superposition. The model representation consists of ground background theory literals and ground foreground first-order literals. One major advantage of the model guided approach is that clauses generated by SCL(T) enjoy a non-redundancy property that makes expensive testing for tautologies and forward subsumption completely obsolete. SCL(T) is a semi-decision procedure for pure clause sets that are clause sets without first-order function symbols ranging into the background theory sorts. Moreover, SCL(T) can be turned into a decision procedure if the considered combination of a first-order logic modulo a background theory enjoys an abstract finite model property

MAC-in-the-Box: Verifying a Minimalistic Hardware Design for MAC Computation

We study the verification of security properties at the state machine level of a minimalistic device, called the MAC-in-the-Box (MITB). This device computes a message authentication code based on the SHA-3 hash function and a key that is stored on device, but never output directly. It is designed for secure password storage, but may also be used for secure key-exchange and second-factor authentication. We formally verify, in the HOL4 theorem prover, that no outside observer can distinguish this device from an ideal functionality that provides only access to a hashing oracle. Furthermore, we propose protocols for the MITB’s use in password storage, key-exchange and second-factor authentication, and formally show that it improves resistance against host-compromise in these three application scenarios

Nominal Recursors as Epi-Recursors: Extended Technical Report

We study nominal recursors from the literature on syntax with bindings and compare them with respect to expressiveness. The term "nominal" refers to the fact that these recursors operate on a syntax representation where the names of bound variables appear explicitly, as in nominal logic. We argue that nominal recursors can be viewed as epi-recursors, a concept that captures abstractly the distinction between the constructors on which one actually recurses, and other operators and properties that further underpin recursion.We develop an abstract framework for comparing epi-recursors and instantiate it to the existing nominal recursors, and also to several recursors obtained from them by cross-pollination. The resulted expressiveness hierarchies depend on how strictly we perform this comparison, and bring insight into the relative merits of different axiomatizations of syntax. We also apply our methodology to produce an expressiveness hierarchy of nominal corecursors, which are principles for defining functions targeting infinitary non-well-founded terms (which underlie lambda-calculus semantics concepts such as B\"ohm trees). Our results are validated with the Isabelle/HOL theorem prover

Diagnostic distribué de systèmes respectant la confidentialité

Dans cette thèse, nous nous intéressons à diagnostiquer des systèmes intrinsèquement distribués (comme les systèmes pairs-à-pairs) où chaque pair n'a accès qu'à une sous partie de la description d'un système global. De plus, en raison d'une politique d'accès trop restrictive, il sera pourra qu'aucun pair ne puisse expliquer le comportement du système global. Dans ce contexte, le challenge du diagnostic distribué est le suivant: expliquer le comportement global d'un système distribué par un ensemble de pairs ayant chacun une vision limitée, tout comme l'aurait fait un unique pair diagnostiqueur ayant, lui, une vision globale du système.D'un point de vue théorique, nous montrons que tout nouveau système, logiquement équivalent au système pair-à-pairs initialement observé, garantit que tout diagnostic local d'un pair pourra être prolongé par un diagnostic global (dans ce cas, le nouveau système est dit correct pour le diagnostic distribué).Nous montrons aussi que si ce nouveau système est structuré (c-à-d: il contient un arbre couvrant pour lequel tous les pairs contenant une même variable forme un graphe connecté) alors il garantit que tout diagnostic global pourra être retrouvé à travers un ensemble de diagnostics locaux des pairs (dans ce cas le nouveau système est dit complet pour le diagnostic distribué).Dans un souci de représentation succincte et afin de respecter la politique de confidentialité du vocabulaire de chacun des pairs, nous présentons un nouvel algorithme Token Elimination (TE), qui décompose le système de pairs initial vers un système structuré.Nous montrons expérimentalement que TE produit des décompositions de meilleurs qualité (c-à-d: de plus petites largeurs arborescentes) que les méthodes envisagées dans un contexte distribué. À partir du système structuré construit par TE, nous transformons chaque description locale en une Forme Normale Disjonctive (FND) globalement cohérente.Nous montrons que ce dernier système garantit effectivement un diagnostic distribué correct et complet. En plus, nous exhibons un algorithme capable de vérifier efficacement que tout diagnostic local fait partie d'un diagnostic minimal global, faisant du système structuré de FNDs un système compilé pour le diagnostic distribué.In this thesis, we focus on diagnosing inherently distributed systems such as peer-to-peer, where each peer has access to only a sub-part of the description of an overall system.In addition, due to a too restrictive access control policy, it can be possible that neither peer nor supervisor is able to explain the behaviour of the overall system.The goal of distributed diagnosis is to explain the behaviour of a distributed system by a set of peers (each having a limited local view) as a single diagnosis engine having a global view of the overall system.First, we show that any new system logically equivalent to the initially observed peer-to-peer setting ensures that all diagnosis of a peer may be extended to a global diagnosis (in this case the new system ensures correctness of the distributed diagnosis).Moreover, we prove that if the new system is structured (i.e.it contains a spanning tree for which all peers containing the same variable form a connected graph) then it ensures that any global diagnosis can be found through a set of local diagnoses (in this case the new system ensures the completeness of the distributed diagnoses).For a succinct representation and in order to comply with the privacy policy of the vocabulary of each peer, we present a new algorithm Token Elimination (TE), which decomposes the original peer system to a structured one.We experimentally show that TE produces better quality decompositions (i.e. smaller tree widths) than proposed methods in a distributed context.From the structured system built by TE, we transform each local description into globally consistent DNF.We demonstrate that the latter system is correct and complete for the distributed diagnosis.Finally, we present an algorithm that can effectively check that any local diagnosis is part of a global minimal diagnosis, turning the structured system of DNFs into a compiled system for distributed diagnosis.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

Formal verification of the equivalence of system F and the pure type system L2

We develop a formal proof of the equivalence of two different variants of System F. The first is close to the original presentation where expressions are separated into distinct syntactic classes of types and terms. The second, L2 (also written as λ2), is a particular pure type system (PTS) where the notions of types and terms, and the associated expressions are unified in a single syntactic class. The employed notion of equivalence is a bidirectional reduction of the respective typing relations. A machine-verified proof of this result turns out to be surprisingly intricate, since the two variants noticeably differ in their expression languages, their type systems and the binding of local variables. Most of this work is executed in the Coq theorem prover and encompasses a general development of the PTS metatheory, an equivalence result for a stratified and a PTS variant of the simply typed λ-calculus as well as the subsequent extension to the full equivalence result for System F. We utilise nameless de Bruijn syntax with parallel substitutions for the representation of variable binding and develop an extended notion of context morphism lemmas as a structured proof method for this setting. We also provide two developments of the equivalence result in the proof systems Abella and Beluga, where we rely on higher-order abstract syntax (HOAS). This allows us to compare the three proof systems, as well as HOAS and de Bruijn for the purpose of developing formal metatheory.Wir präsentieren einen maschinell verifizierten Beweis der Äquivalenz zweier Darstellungen des Lambda-Kalküls System F. Die erste unterscheidet syntaktisch zwischen Termen und Typen und entspricht somit der geläufigen Form. Die zweite, L2 bzw. λ2, ist ein sog. Pure Type System (PTS), bei welchem alle Ausdrücke in einer syntaktischen Klasse zusammen fallen. Unser Äquivalenzbegriff ist eine bidirektionale Reduktion der jeweiligen Typrelationen. Ein formaler Beweis dieser Eigenschaft ist aufgrund der Unterschiede der Ausdruckssprachen, der Typrelationen und der Bindung lokaler Variablen überraschend anspruchsvoll. Der Hauptteil dieser Arbeit wurde in dem Beweisassistenten Coq entwickelt und umfasst eine Abhandlung der PTS Metatheorie, sowie einen Äquivalenzbeweis für das einfach getypte Lambda-Kalkül, welcher dann zu dem vollen Ergebnis für System F skaliert wird. Für die Darstellung lokaler Variablenbindung verwenden wir de Bruijn Syntax, gepaart mit parallelen Substitutionen. Außerdem entwickeln wir eine generalisierte Form von Kontext-Morphismen Lemmas, welche eine strukturierte Beweismethodik in diesem Umfeld liefern. Darüber hinaus betrachten wir zwei weitere Formalisierungen des Äquivalenzresultats in den Beweissystemen Abella und Beluga, welche beide höherstufige abstrakte Syntax (HOAS) zur Darstellung lokaler Bindung verwenden. Dies ermöglicht es uns, sowohl die drei Beweissysteme, als auch den HOAS und den de Bruijn Ansatz mit Hinblick auf die Entwicklung formaler Metatheorie zu vergleichen