487 research outputs found
Global semantic typing for inductive and coinductive computing
Inductive and coinductive types are commonly construed as ontological
(Church-style) types, denoting canonical data-sets such as natural numbers,
lists, and streams. For various purposes, notably the study of programs in the
context of global semantics, it is preferable to think of types as semantical
properties (Curry-style). Intrinsic theories were introduced in the late 1990s
to provide a purely logical framework for reasoning about programs and their
semantic types. We extend them here to data given by any combination of
inductive and coinductive definitions. This approach is of interest because it
fits tightly with syntactic, semantic, and proof theoretic fundamentals of
formal logic, with potential applications in implicit computational complexity
as well as extraction of programs from proofs. We prove a Canonicity Theorem,
showing that the global definition of program typing, via the usual (Tarskian)
semantics of first-order logic, agrees with their operational semantics in the
intended model. Finally, we show that every intrinsic theory is interpretable
in a conservative extension of first-order arithmetic. This means that
quantification over infinite data objects does not lead, on its own, to
proof-theoretic strength beyond that of Peano Arithmetic. Intrinsic theories
are perfectly amenable to formulas-as-types Curry-Howard morphisms, and were
used to characterize major computational complexity classes Their extensions
described here have similar potential which has already been applied
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Automated verification of refinement laws
Demonic refinement algebras are variants of Kleene algebras. Introduced by von Wright as a light-weight variant of the refinement calculus, their intended semantics are positively disjunctive predicate transformers, and their calculus is entirely within first-order equational logic. So, for the first time, off-the-shelf automated theorem proving (ATP) becomes available for refinement proofs. We used ATP to verify a toolkit of basic refinement laws. Based on this toolkit, we then verified two classical complex refinement laws for action systems by ATP: a data refinement law and Back's atomicity refinement law. We also present a refinement law for infinite loops that has been discovered through automated analysis. Our proof experiments not only demonstrate that refinement can effectively be automated, they also compare eleven different ATP systems and suggest that program verification with variants of Kleene algebras yields interesting theorem proving benchmarks. Finally, we apply hypothesis learning techniques that seem indispensable for automating more complex proofs
Extending the Real-Time Maude Semantics of Ptolemy to Hierarchical DE Models
This paper extends our Real-Time Maude formalization of the semantics of flat
Ptolemy II discrete-event (DE) models to hierarchical models, including modal
models. This is a challenging task that requires combining synchronous
fixed-point computations with hierarchical structure. The synthesis of a
Real-Time Maude verification model from a Ptolemy II DE model, and the formal
verification of the synthesized model in Real-Time Maude, have been integrated
into Ptolemy II, enabling a model-engineering process that combines the
convenience of Ptolemy II DE modeling and simulation with formal verification
in Real-Time Maude.Comment: In Proceedings RTRTS 2010, arXiv:1009.398
Checking Zenon Modulo Proofs in Dedukti
Dedukti has been proposed as a universal proof checker. It is a logical
framework based on the lambda Pi calculus modulo that is used as a backend to
verify proofs coming from theorem provers, especially those implementing some
form of rewriting. We present a shallow embedding into Dedukti of proofs
produced by Zenon Modulo, an extension of the tableau-based first-order theorem
prover Zenon to deduction modulo and typing. Zenon Modulo is applied to the
verification of programs in both academic and industrial projects. The purpose
of our embedding is to increase the confidence in automatically generated
proofs by separating untrusted proof search from trusted proof verification.Comment: In Proceedings PxTP 2015, arXiv:1507.0837
CafeOBJ: Logical Foundations and Methodologies
CafeOBJ is an executable industrial strength multi-logic algebraic specification language which is a modern successor of OBJ and incorporates several new algebraic specification paradigms. In this paper we survey its logical foundations and present some of its methodologies
Rule-based Methodologies for the Specification and Analysis of Complex Computing Systems
Desde los orígenes del hardware y el software hasta la época actual, la complejidad
de los sistemas de cálculo ha supuesto un problema al cual informáticos, ingenieros
y programadores han tenido que enfrentarse. Como resultado de este esfuerzo han
surgido y madurado importantes áreas de investigación. En esta disertación abordamos
algunas de las líneas de investigación actuales relacionada con el análisis y
la verificación de sistemas de computación complejos utilizando métodos formales y
lenguajes de dominio específico.
En esta tesis nos centramos en los sistemas distribuidos, con un especial interés por
los sistemas Web y los sistemas biológicos. La primera parte de la tesis está dedicada
a aspectos de seguridad y técnicas relacionadas, concretamente la certificación del
software. En primer lugar estudiamos sistemas de control de acceso a recursos y proponemos
un lenguaje para especificar políticas de control de acceso que están fuertemente
asociadas a bases de conocimiento y que proporcionan una descripción sensible
a la semántica de los recursos o elementos a los que se accede. También hemos desarrollado
un marco novedoso de trabajo para la Code-Carrying Theory, una metodología
para la certificación del software cuyo objetivo es asegurar el envío seguro de código
en un entorno distribuido. Nuestro marco de trabajo está basado en un sistema de
transformación de teorías de reescritura mediante operaciones de plegado/desplegado.
La segunda parte de esta tesis se concentra en el análisis y la verificación de sistemas
Web y sistemas biológicos. Proponemos un lenguaje para el filtrado de información
que permite la recuperación de informaciones en grandes almacenes de datos. Dicho
lenguaje utiliza información semántica obtenida a partir de ontologías remotas
para re nar el proceso de filtrado. También estudiamos métodos de validación para
comprobar la consistencia de contenidos web con respecto a propiedades sintácticas
y semánticas. Otra de nuestras contribuciones es la propuesta de un lenguaje que
permite definir y comprobar automáticamente restricciones semánticas y sintácticas
en el contenido estático de un sistema Web. Finalmente, también consideramos los
sistemas biológicos y nos centramos en un formalismo basado en lógica de reescritura
para el modelado y el análisis de aspectos cuantitativos de los procesos biológicos.
Para evaluar la efectividad de todas las metodologías propuestas, hemos prestado
especial atención al desarrollo de prototipos que se han implementado utilizando
lenguajes basados en reglas.Baggi ., M. (2010). Rule-based Methodologies for the Specification and Analysis of Complex Computing Systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8964Palanci
Term rewriting systems from Church-Rosser to Knuth-Bendix and beyond
Term rewriting systems are important for computability theory of abstract data types, for automatic theorem proving, and for the foundations of functional programming. In this short survey we present, starting from first principles, several of the basic notions and facts in the area of term rewriting. Our treatment, which often will be informal, covers abstract rewriting, Combinatory Logic, orthogonal systems, strategies, critical pair completion, and some extended rewriting formats
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