290 research outputs found
The foundational legacy of ASL
Abstract. We recall the kernel algebraic specification language ASL and outline its main features in the context of the state of research on algebraic specification at the time it was conceived in the early 1980s. We discuss the most significant new ideas in ASL and the influence they had on subsequent developments in the field and on our own work in particular.
Abstraction and Invariance for Algebraically Indexed Types
Reynolds’ relational parametricity provides a powerful way to reason about programs in terms of invariance under changes of data representation. A dazzling array of applications of Reynolds’ theory exists, exploiting invariance to yield “free theorems”, non-inhabitation results, and encodings of algebraic datatypes. Outside computer science, invariance is a common theme running through many areas of mathematics and physics. For example, the area of a triangle is unaltered by rotation or flipping. If we scale a triangle, then we scale its area, maintaining an invariant relationship be-tween the two. The transformations under which properties are in-variant are often organised into groups, with the algebraic structure reflecting the composability and invertibility of transformations. In this paper, we investigate programming languages whose types are indexed by algebraic structures such as groups of geometric transformations. Other examples include types indexed by principals–for information flow security–and types indexed by distances–for analysis of analytic uniform continuity properties. Following Reynolds, we prove a general Abstraction Theorem that covers all these instances. Consequences of our Abstraction Theorem include free theorems expressing invariance properties of programs, type isomorphisms based on invariance properties, and non-definability results indicating when certain algebraically indexed types are uninhabited or only inhabited by trivial programs. We have fully formalized our framework and most examples in Coq
Probabilistic Programming Interfaces for Random Graphs::Markov Categories, Graphons, and Nominal Sets
We study semantic models of probabilistic programming languages over graphs, and establish a connection to graphons from graph theory and combinatorics. We show that every well-behaved equational theory for our graph probabilistic programming language corresponds to a graphon, and conversely, every graphon arises in this way.We provide three constructions for showing that every graphon arises from an equational theory. The first is an abstract construction, using Markov categories and monoidal indeterminates. The second and third are more concrete. The second is in terms of traditional measure theoretic probability, which covers 'black-and-white' graphons. The third is in terms of probability monads on the nominal sets of Gabbay and Pitts. Specifically, we use a variation of nominal sets induced by the theory of graphs, which covers Erdős-Rényi graphons. In this way, we build new models of graph probabilistic programming from graphons
Search for Program Structure
The community of programming language research loves the Curry-Howard correspondence between proofs and programs. Cut-elimination as computation, theorems for free, \u27call/cc\u27 as excluded middle, dependently typed languages as proof assistants, etc.
Yet we have, for all these years, missed an obvious observation: "the structure of programs corresponds to the structure of proof search". For pure programs and intuitionistic logic, more is known about the latter than the former. We think we know what programs are, but logicians know better!
To motivate the study of proof search for program structure, we retrace recent research on applying focusing to study the canonical structure of simply-typed lambda-terms. We then motivate the open problem of extending canonical forms to support richer type systems, such as polymorphism, by discussing a few enticing applications of more canonical program representations
Automated Unbounded Verification of Stateful Cryptographic Protocols with Exclusive OR
International audienceExclusive-or (XOR) operations are common in cryptographic protocols, in particular in RFID protocols and electronic payment protocols. Although there are numerous applications , due to the inherent complexity of faithful models of XOR, there is only limited tool support for the verification of cryptographic protocols using XOR.The TAMARIN prover is a state-of-the-art verification tool for cryptographic protocols in the symbolic model. In this paper, we improve the underlying theory and the tool to deal with an equational theory modeling XOR operations. The XOR theory can be freely combined with all equational theories previously supported, including user-defined equational theories. This makes TAMARIN the first tool to support simultaneously this large set of equational theories, protocols with global mutable state, an unbounded number of sessions, and complex security properties including observational equivalence. We demonstrate the effectiveness of our approach by analyzing several protocols that rely on XOR, in particular multiple RFID-protocols, where we can identify attacks as well as provide proofs
Full Abstraction for the Resource Lambda Calculus with Tests, through Taylor Expansion
We study the semantics of a resource-sensitive extension of the lambda
calculus in a canonical reflexive object of a category of sets and relations, a
relational version of Scott's original model of the pure lambda calculus. This
calculus is related to Boudol's resource calculus and is derived from Ehrhard
and Regnier's differential extension of Linear Logic and of the lambda
calculus. We extend it with new constructions, to be understood as implementing
a very simple exception mechanism, and with a "must" parallel composition.
These new operations allow to associate a context of this calculus with any
point of the model and to prove full abstraction for the finite sub-calculus
where ordinary lambda calculus application is not allowed. The result is then
extended to the full calculus by means of a Taylor Expansion formula. As an
intermediate result we prove that the exception mechanism is not essential in
the finite sub-calculus
Verification of Stateful Cryptographic Protocols with Exclusive OR
International audienceIn cryptographic protocols, in particular RFID protocols, exclusive-or (XOR) operations are common. Due to the inherent complexity of faithful models of XOR, there is only limited tool support for the verification of cryptographic protocols using XOR. In this paper, we improve the TAMARIN prover and its underlying theory to deal with an equational theory modeling XOR operations. The XOR theory can be combined with all equational theories previously supported, including user-defined equational theories. This makes TAMARIN the first verification tool for cryptographic protocols in the symbolic model to support simultaneously this large set of equational theories, protocols with global mutable state, an unbounded number of sessions, and complex security properties including observational equivalence. We demonstrate the effectiveness of our approach by analyzing several protocols that rely on XOR, in particular multiple RFID-protocols, where we can identify attacks as well as provide proofs
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
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