SPIKE, an automatic theorem prover -- revisited

International audienceSPIKE, an induction-based theorem prover built to reason on conditional theories with equality, is one of the few formal tools able to perform automatically mutual and lazy induction. Designed at the beginning of 1990s, it has been successfully used in many non-trivial applications and served as a prototype for different proof experiments and extensions. The first paper introducing SPIKE is [14], published shortly after the tool was created. The goal of this paper is to highlight and bring together in one spot the major changes supported by SPIKE since then

Reasoning on Schemata of Formulae

A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists, the trees etc.). A proof procedure is proposed to relate the satisfiability problem for schemata to that of finite disjunctions of base formulae. It is shown that this procedure is sound, complete and terminating, hence the basic computational properties of the base language can be carried over to schemata

Analysis of Composite Web Services using Logging Facilities

Web services are becoming more and more complex, involving numerous interacting business objects within considerable processes. In order to fully explore Web service business opportunities while ensuring a correct and reliable modelling and execution, analyzing and tracking Web services interactions will enable them to be well understood and controlled. Then, given the resulting event log we want to verify certain specified properties, to provide knowledge about the context of and the reasons for discrepancies between services'behaviours and related instances. This paper advocates a novel technique to log composite Web services and a formal approach, based on an algeabric specification of the discrete event calculus language DEC, to check behavioural properties of composite Web services regarding their execution log. An automated induction-based theorem prover SPIKE is used as verification back-end

ARC: An Educational Project on Automated Reasoning in the Class

International audienceThe international Erasmus+ European Project: "ARC-Automated Reasoning in the Class", running from 2019 to 2022 is a partnership of universities from Austria, France, Germany, Hungary, and Romania, and has the purpose of developing advanced material for teaching subjects related to Computational Logic by using Automated Reasoning. The material includes a comprehensive textbook treating the necessary theoretical background (selected topics in Mathematical Logic), but mostly the practical methods from Automated Theorem Proving, as well as the description of the basic programming paradigms and the associated languages, in relation to their logical aspects. Furthermore, we address the most important applications, like program verification and testing, semantic representation of information, algorithm synthesis, etc. One of the main goals of the approach is to improve the logical background of the software professionals in order to motivate them to use formal methods for certification of complex systems and thus to avoid costly failures

Récurrence noethérienne pour le raisonnement de premier ordre

National audienceLa récurrence nœthérienne est un des principes les plus généraux de raisonnement formel. Dans le cadre du raisonnement de premier ordre, nous présentons une classification de ses instances pouvant être partagées en instances basées sur des termes et des formules. Nous donnons un aperçu du raisonnement par récurrence nœthérienne basée sur des termes et sur des formules, puis nous établissons des relations entre eux. Enfin, nous présentons une méthodologie pour la certification du raisonnement basé sur des formules à l’aide de l’assistant de preuve Coq

Strategic Issues, Problems and Challenges in Inductive Theorem Proving

Abstract(Automated) Inductive Theorem Proving (ITP) is a challenging field in automated reasoning and theorem proving. Typically, (Automated) Theorem Proving (TP) refers to methods, techniques and tools for automatically proving general (most often first-order) theorems. Nowadays, the field of TP has reached a certain degree of maturity and powerful TP systems are widely available and used. The situation with ITP is strikingly different, in the sense that proving inductive theorems in an essentially automatic way still is a very challenging task, even for the most advanced existing ITP systems. Both in general TP and in ITP, strategies for guiding the proof search process are of fundamental importance, in automated as well as in interactive or mixed settings. In the paper we will analyze and discuss the most important strategic and proof search issues in ITP, compare ITP with TP, and argue why ITP is in a sense much more challenging. More generally, we will systematically isolate, investigate and classify the main problems and challenges in ITP w.r.t. automation, on different levels and from different points of views. Finally, based on this analysis we will present some theses about the state of the art in the field, possible criteria for what could be considered as substantial progress, and promising lines of research for the future, towards (more) automated ITP

Narrowing Based Inductive Proof Search

Premiere version en 2005, en l'honneur de Harald GanzingerVersion finale envoyé a SpringerWe present in this paper a narrowing-based proof search method for inductive theorems. It has the specificity to be grounded on deduction modulo and to yield a direct translation from a successful proof search derivation to a proof in the sequent calculus. The method is shown to be sound and refutationally correct in a proof theoretical way

Méthodologie de conception d'un modèle comportemental pour la vérification formelle

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal