A coinductive semantics of the Unlimited Register Machine

We exploit (co)inductive specifications and proofs to approach the evaluation of low-level programs for the Unlimited Register Machine (URM) within the Coq system, a proof assistant based on the Calculus of (Co)Inductive Constructions type theory. Our formalization allows us to certify the implementation of partial functions, thus it can be regarded as a first step towards the development of a workbench for the formal analysis and verification of both converging and diverging computations

A formally verified compiler back-end

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well

LF+ in Coq for fast-and-loose reasoning

We develop the metatheory and the implementation, in Coq, of the novel logical framework LF+ and discuss several of its applications. LF+ generalises research work, carried out by the authors over more than a decade, on Logical Frameworks conservatively extending LF and featuring lock-type constructors L-P(N:sigma)[center dot]. Lock-types capture monadically the concept of inhabitability up-to. They were originally introduced for factoring-out, postponing, or delegating to external tools the verification of time-consuming judgments, which are morally proof-irrelevant, thus allowing for integrating different sources of epistemic evidence in a unique Logical Framework. Besides introducing LF+ and its "shallow" implementation in Coq, the main novelty of the paper is to show that lock-types are also a very flexible tool for expressing in Type Theory several diverse cognitive attitudes and mental strategies used in ordinary reasoning, which essentially amount to reasoning up-to, as in e.g. Typical Ambiguity provisos or co-inductive Coq proofs. In particular we address the encoding of the emerging paradigm of fast-and-loose reasoning, which trades off efficiency for correctness. This paradigm, implicitly used normally in naive Set Theory, is producing considerable impact also in computer architecture and distributed systems, when branch prediction and optimistic concurrency control are implemented

Client-Server Sessions in Linear Logic

We introduce coexponentials, a new set of modalities for Classical Linear Logic. As duals to exponentials, the coexponentials codify a distributed form of the structural rules of weakening and contraction. This makes them a suitable logical device for encapsulating the pattern of a server receiving requests from an arbitrary number of clients on a single channel. Guided by this intuition we formulate a system of session types based on Classical Linear Logic with coexponentials, which is suited to modelling client-server interactions. We also present a session-typed functional programming language for server-client programming, which we translate to our system of coexponentials

A definitional implementation of the LAX logical framework LLFP in CoQ, for supporting fast and loose reasoning

The Lax Logical Framework, LLFP, was introduced, by a team including the last two authors, to provide a conceptual framework for integrating different proof development tools, thus allowing for external evidence and for postponing, delegating, or factoring-out side conditions. In particular, LLFP allows for reducing the number of times a proof-irrelevant check is performed. In this paper we give a shallow, actually definitional, implementation of LLFP in Coq, i.e. we use Coq both as host framework and oracle for LLFP. This illuminates the principles underpinning the mechanism of Lock-types and also suggests how to possibly extend Coq with the features of LLFP. The derived proof editor is then put to use for developing case-studies on an emerging paradigm, both at logical and implementation level, which we call fast and loose reasoning following Danielsson et alii [6]. This paradigm trades off efficiency for correctness and amounts to postponing, or running in parallel, tedious or computationally demanding checks, until we are really sure that the intended goal can be achieved. Typical examples are branch-prediction in CPUs and optimistic concurrency control

Congruent Weak Conformance

This research addresses the problem of verifying implementations against specifications through an innovative logic approach. Congruent weak conformance, a formal relationship between agents and specifications, has been developed and proven to be a congruent partial order. This property arises from a set of relations called weak conformations. The largest, called weak conformance, is analogous to Milner\u27s observational equivalence. Weak conformance is not an equivalence, however, but rather an ordering relation among processes. Weak conformance allows behaviors in the implementation that are unreachable in the specification. Furthermore, it exploits output concurrencies and allows interleaving of extraneous output actions in the implementation. Finally, reasonable restrictions in CCS syntax strengthen weak conformance to a congruence, called congruent weak conformance. At present, congruent weak conformance is the best known formal relation for verifying implementations against specifications. This precongruence derives maximal flexibility and embodies all weaknesses in input, output, and no-connect signals while retaining a fully replaceable conformance to the specification. Congruent weak conformance has additional utility in verifying transformations between systems of incompatible semantics. This dissertation describes a hypothetical translator from the informal simulation semantics of VHDL to the bisimulation semantics of CCS. A second translator is described from VHDL to a broadcast-communication version of CCS. By showing that they preserve congruent weak conformance, both translators are verified

Proceedings of the Sixth NASA Langley Formal Methods (LFM) Workshop

Today's verification techniques are hard-pressed to scale with the ever-increasing complexity of safety critical systems. Within the field of aeronautics alone, we find the need for verification of algorithms for separation assurance, air traffic control, auto-pilot, Unmanned Aerial Vehicles (UAVs), adaptive avionics, automated decision authority, and much more. Recent advances in formal methods have made verifying more of these problems realistic. Thus we need to continually re-assess what we can solve now and identify the next barriers to overcome. Only through an exchange of ideas between theoreticians and practitioners from academia to industry can we extend formal methods for the verification of ever more challenging problem domains. This volume contains the extended abstracts of the talks presented at LFM 2008: The Sixth NASA Langley Formal Methods Workshop held on April 30 - May 2, 2008 in Newport News, Virginia, USA. The topics of interest that were listed in the call for abstracts were: advances in formal verification techniques; formal models of distributed computing; planning and scheduling; automated air traffic management; fault tolerance; hybrid systems/hybrid automata; embedded systems; safety critical applications; safety cases; accident/safety analysis

Programming Languages and Systems

This open access book constitutes the proceedings of the 31st European Symposium on Programming, ESOP 2022, which was held during April 5-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 21 regular papers presented in this volume were carefully reviewed and selected from 64 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Programming Languages and Systems

This open access book constitutes the proceedings of the 31st European Symposium on Programming, ESOP 2022, which was held during April 5-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 21 regular papers presented in this volume were carefully reviewed and selected from 64 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems