Interpolation in local theory extensions

In this paper we study interpolation in local extensions of a base theory. We identify situations in which it is possible to obtain interpolants in a hierarchical manner, by using a prover and a procedure for generating interpolants in the base theory as black-boxes. We present several examples of theory extensions in which interpolants can be computed this way, and discuss applications in verification, knowledge representation, and modular reasoning in combinations of local theories.Comment: 31 pages, 1 figur

Consistency and Completeness of Rewriting in the Calculus of Constructions

Adding rewriting to a proof assistant based on the Curry-Howard isomorphism, such as Coq, may greatly improve usability of the tool. Unfortunately adding an arbitrary set of rewrite rules may render the underlying formal system undecidable and inconsistent. While ways to ensure termination and confluence, and hence decidability of type-checking, have already been studied to some extent, logical consistency has got little attention so far. In this paper we show that consistency is a consequence of canonicity, which in turn follows from the assumption that all functions defined by rewrite rules are complete. We provide a sound and terminating, but necessarily incomplete algorithm to verify this property. The algorithm accepts all definitions that follow dependent pattern matching schemes presented by Coquand and studied by McBride in his PhD thesis. It also accepts many definitions by rewriting, containing rules which depart from standard pattern matching.Comment: 20 page

Mechanical verification of a schematic Byzantine clock synchronization algorithm

Schneider generalizes a number of protocols for Byzantine fault tolerant clock synchronization and presents a uniform proof for their correctness. The authors present a machine checked proof of this schematic protocol that revises some of the details in Schneider's original analysis. The verification was carried out with the EHDM system developed at the SRI Computer Science Laboratory. The mechanically checked proofs include the verification that the egocentric mean function used in Lamport and Melliar-Smith's Interactive Convergence Algorithm satisfies the requirements of Schneider's protocol

SimCheck: An Expressive Type System for Simulink

MATLAB Simulink is a member of a class of visual languages that are used for modeling and simulating physical and cyber-physical systems. A Simulink model consists of blocks with input and output ports connected using links that carry signals. We extend the type system of Simulink with annotations and dimensions/units associated with ports and links. These types can capture invariants on signals as well as relations between signals. We define a type-checker that checks the wellformedness of Simulink blocks with respect to these type annotations. The type checker generates proof obligations that are solved by SRI's Yices solver for satisfiability modulo theories (SMT). This translation can be used to detect type errors, demonstrate counterexamples, generate test cases, or prove the absence of type errors. Our work is an initial step toward the symbolic analysis of MATLAB Simulink models

SOTER: A Runtime Assurance Framework for Programming Safe Robotics Systems

The recent drive towards achieving greater autonomy and intelligence in robotics has led to high levels of complexity. Autonomous robots increasingly depend on third party off-the-shelf components and complex machine-learning techniques. This trend makes it challenging to provide strong design-time certification of correct operation. To address these challenges, we present SOTER, a robotics programming framework with two key components: (1) a programming language for implementing and testing high-level reactive robotics software and (2) an integrated runtime assurance (RTA) system that helps enable the use of uncertified components, while still providing safety guarantees. SOTER provides language primitives to declaratively construct a RTA module consisting of an advanced, high-performance controller (uncertified), a safe, lower-performance controller (certified), and the desired safety specification. The framework provides a formal guarantee that a well-formed RTA module always satisfies the safety specification, without completely sacrificing performance by using higher performance uncertified components whenever safe. SOTER allows the complex robotics software stack to be constructed as a composition of RTA modules, where each uncertified component is protected using a RTA module. To demonstrate the efficacy of our framework, we consider a real-world case-study of building a safe drone surveillance system. Our experiments both in simulation and on actual drones show that the SOTER-enabled RTA ensures the safety of the system, including when untrusted third-party components have bugs or deviate from the desired behavior

Abstract Datatypes in PVS

PVS (Prototype Verification System) is a general-purpose environment for developing specifications and proofs. This document deals primarily with the abstract datatype mechanism in PVS which generates theories containing axioms and definitions for a class of recursive datatypes. The concepts underlying the abstract datatype mechanism are illustrated using ordered binary trees as an example. Binary trees are described by a PVS abstract datatype that is parametric in its value type. The type of ordered binary trees is then presented as a subtype of binary trees where the ordering relation is also taken as a parameter. We define the operations of inserting an element into, and searching for an element in an ordered binary tree; the bulk of the report is devoted to PVS proofs of some useful properties of these operations. These proofs illustrate various approaches to proving properties of abstract datatype operations. They also describe the built-in capabilities of the PVS proof checker for simplifying abstract datatype expressions

Extracting Programs from Constructive HOL Proofs via IZF Set-Theoretic<br> Semantics

Church's Higher Order Logic is a basis for influential proof assistants -- HOL and PVS. Church's logic has a simple set-theoretic semantics, making it trustworthy and extensible. We factor HOL into a constructive core plus axioms of excluded middle and choice. We similarly factor standard set theory, ZFC, into a constructive core, IZF, and axioms of excluded middle and choice. Then we provide the standard set-theoretic semantics in such a way that the constructive core of HOL is mapped into IZF. We use the disjunction, numerical existence and term existence properties of IZF to provide a program extraction capability from proofs in the constructive core. We can implement the disjunction and numerical existence properties in two different ways: one using Rathjen's realizability for IZF and the other using a new direct weak normalization result for IZF by Moczydlowski. The latter can also be used for the term existence property.Comment: 17 page

Modeling the pneumatic relay valve of an s-cam air brake

Statistics indicate that defects in brake system contribute significantly to fatal crashes involving commercial vehicles. Hence there is a need for developing preventive and active safety measures for assessing the performance of an air brake system in trucks. Existing techniques for assessing the performance of brakes are infrastructure intensive, time and labor intensive. The premise of this thesis is that model-based diagnostic techniques can be employed to overcome these limitations of existing tech- niques. The design of a model-based diagnostic system requires the development and experimental corroboration of a mathematical model of the evolution of pressure in each brake chamber of a truck in response to the application of brake pedal input by the driver, when there are no faults or defects in the brake system. This thesis is aimed at modeling and experimentally corroborating a subsystem of an air brake system, namely the pneumatic relay valve. The pneumatic relay valve takes a input signal from the primary delivery of a treadle valve and meters air from a storage reservoir to Type 30 rear brake chambers. A description of the development of the model, the experimental setup and corroborating experimental results are provided

CREATING A LEGAL COLLABORATIVE EXPERIENCE

Techniques are described for adding trust/reliability quotients to video conversation recordings by creating a secure ledger-based legal recording mechanism. The legal recording mechanism is tamper proof, faster than documenting the agreement, and legally binding