Maude: specification and programming in rewriting logic

Maude is a high-level language and a high-performance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and theories. The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions. Rewriting logic is reflective, in the sense of being able to express its own metalevel at the object level. Reflection is systematically exploited in Maude endowing the language with powerful metaprogramming capabilities, including both user-definable module operations and declarative strategies to guide the deduction process. This paper explains and illustrates with examples the main concepts of Maude's language design, including its underlying logic, functional, system and object-oriented modules, as well as parameterized modules, theories, and views. We also explain how Maude supports reflection, metaprogramming and internal strategies. The paper outlines the principles underlying the Maude system implementation, including its semicompilation techniques. We conclude with some remarks about applications, work on a formal environment for Maude, and a mobile language extension of Maude

Rewriting Modulo SMT and Open System Analysis

This paper proposes rewriting modulo SMT, a new technique that combines the power of SMT solving, rewriting modulo theories, and model checking. Rewriting modulo SMT is ideally suited to model and analyze reachability properties of infinite-state open systems, i.e., systems that interact with a nondeterministic environment. Such systems exhibit both internal nondeterminism, which is proper to the system, and external nondeterminism, which is due to the environment. In a reflective formalism, such as rewriting logic, rewriting modulo SMT can be reduced to standard rewriting. Hence, rewriting modulo SMT naturally extends rewriting-based reachability analysis techniques, which are available for closed systems, to open systems. The proposed technique is illustrated with the formal analysis of: (i) a real-time system that is beyond the scope of timed-automata methods and (ii) automatic detection of reachability violations in a synchronous language developed to support autonomous spacecraft operations.NSF Grant CNS 13-19109 and NASA Research Cooperative Agreement No. NNL09AA00AOpe

Equational and Rule-Based Programming: Visualization, Reliability, and Knowledge Base Generation

This document describes developing an environment for effective use of functional/equational programs and rule-based expert systems. There are significant advantages in using these paradigms for reliability, parallelism, and accumulation of expertise in knowledge bases. The environment will make it easier to understand and use these paradigms, construct more reliable systems, and automatically enrich rule-based knowledge bases with the expertise. It will consist of the following components: (1) Visualization: for composing systems using a graphical interface and for understanding of algorithms. (2) Consistency Checking: for an equational and a rule-based language in accordance with the semantics of the languages. (3) Knowledge Base Generation and Testing: a translator that extracts expertise from existing programs and accumulates it as rules in knowledge bases; the rules are tested to enhance reliability. (4) Verification: interactive heterogeneous reasoning that consists of equational reasoning based on visual and textual information. These tools will be integrated in the proposed environment. The environment will greatly reduce the costs and increase the reliability of functional/equational and rule-based systems

Termination of Narrowing: Automated Proofs and Modularity Properties

En 1936 Alan Turing demostro que el halting problem, esto es, el problema de decidir si un programa termina o no, es un problema indecidible para la inmensa mayoria de los lenguajes de programacion. A pesar de ello, la terminacion es un problema tan relevante que en las ultimas decadas un gran numero de tecnicas han sido desarrolladas para demostrar la terminacion de forma automatica de la maxima cantidad posible de programas. Los sistemas de reescritura de terminos proporcionan un marco teorico abstracto perfecto para el estudio de la terminacion de programas. En este marco, la evaluaci on de un t ermino consiste en la aplicacion no determinista de un conjunto de reglas de reescritura. El estrechamiento (narrowing) de terminos es una generalizacion de la reescritura que proporciona un mecanismo de razonamiento automatico. Por ejemplo, dado un conjunto de reglas que denan la suma y la multiplicacion, la reescritura permite calcular expresiones aritmeticas, mientras que el estrechamiento permite resolver ecuaciones con variables. Esta tesis constituye el primer estudio en profundidad de las propiedades de terminacion del estrechamiento. Las contribuciones son las siguientes. En primer lugar, se identican clases de sistemas en las que el estrechamiento tiene un comportamiento bueno, en el sentido de que siempre termina. Muchos metodos de razonamiento automatico, como el analisis de la semantica de lenguajes de programaci on mediante operadores de punto jo, se benefician de esta caracterizacion. En segundo lugar, se introduce un metodo automatico, basado en el marco teorico de pares de dependencia, para demostrar la terminacion del estrechamiento en un sistema particular. Nuestro metodo es, por primera vez, aplicable a cualquier clase de sistemas. En tercer lugar, se propone un nuevo metodo para estudiar la terminacion del estrechamiento desde un termino particular, permitiendo el analisis de la terminacion de lenguajes de programacion. El nuevo metodo generaliza losIborra López, J. (2010). Termination of Narrowing: Automated Proofs and Modularity Properties [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/19251Palanci

A rationale for conditional equational programming

AbstractConditional equations provide a paradigm of computation that combines the clean syntax and semantics of LISP-like functional programming with Prolog-like logic programming in a uniform manner. For functional programming, equations are used as rules for left-to-right rewriting; for logic programming, the same rules are used for conditional narrowing. Together, rewriting and narrowing provide increased expressive power. We discuss some aspects of the theory of conditional rewriting, and the reasons underlying certain choices in designing a language based on them. The most important correctness property a conditional rewriting program may posses is ground confluence; this ensures that at most one value can be computed from any given (variable-free) input term. We give criteria for confluence. Reasonable conditions for ensuring the completeness of narrowing as an operational mechanism for solving goals are provided; these results are then extended to handle rewriting with existentially quantified conditions and built-in predicates. Some termination issues are also considered, including the case of rewriting with higher-order terms

Formal Models and Techniques for Analyzing Security Protocols: A Tutorial

International audienceSecurity protocols are distributed programs that aim at securing communications by the means of cryptography. They are for instance used to secure electronic payments, home banking and more recently electronic elections. Given The financial and societal impact in case of failure, and the long history of design flaws in such protocol, formal verification is a necessity. A major difference from other safety critical systems is that the properties of security protocols must hold in the presence of an arbitrary adversary. The aim of this paper is to provide a tutorial to some modern approaches for formally modeling protocols, their goals and automatically verifying them