On CSP and the Algebraic Theory of Effects

We consider CSP from the point of view of the algebraic theory of effects, which classifies operations as effect constructors or effect deconstructors; it also provides a link with functional programming, being a refinement of Moggi's seminal monadic point of view. There is a natural algebraic theory of the constructors whose free algebra functor is Moggi's monad; we illustrate this by characterising free and initial algebras in terms of two versions of the stable failures model of CSP, one more general than the other. Deconstructors are dealt with as homomorphisms to (possibly non-free) algebras. One can view CSP's action and choice operators as constructors and the rest, such as concealment and concurrency, as deconstructors. Carrying this programme out results in taking deterministic external choice as constructor rather than general external choice. However, binary deconstructors, such as the CSP concurrency operator, provide unresolved difficulties. We conclude by presenting a combination of CSP with Moggi's computational {\lambda}-calculus, in which the operators, including concurrency, are polymorphic. While the paper mainly concerns CSP, it ought to be possible to carry over similar ideas to other process calculi

Deterministic Pomsets

This paper is about partially ordered multisets (pomsets for short). We investigate a particular class of pomsets that we call deterministic, properly including all partially ordered sets, which satisfies a number of interesting properties: among other things, it forms a distributive lattice under pomset prefix (hence prefix closed sets of deterministic pomsets are prime algebraic), and it constitutes a reflective subcategory of the category of all pomsets. For the deterministic pomsets we develop an algebra with a sound and (ω-)complete equational theory. The operators in the algebra are concatenation and join, the latter being a variation on the more usual disjoint union of pomsets with the special property that it yields the least upper bound with respect to pomset prefix.\ud \ud This theory is then extended in several ways. We capture refinement of pomsets by incorporating homomorphisms between models as objects in the algebra and homomorphism application as a new operator. This in turn allows to formulate distributed termination and sequential composition of pomsets, where the latter is different from concatenation in that it is right-distributive over union. To contrast this we also formulate a notion of global termination. Each variation is captured equationally by a sound and ω-complete theory.\u

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

Universal Quantitative Algebra for Fuzzy Relations and Generalised Metric Spaces

We present a generalisation of the theory of quantitative algebras of Mardare, Panangaden and Plotkin where (i) the carriers of quantitative algebras are not restricted to be metric spaces and can be arbitrary fuzzy relations or generalised metric spaces, and (ii) the interpretations of the algebraic operations are not required to be nonexpansive. Our main results include: a novel sound and complete proof system, the proof that free quantitative algebras always exist, the proof of strict monadicity of the induced Free-Forgetful adjunction, the result that all monads (on fuzzy relations) that lift finitary monads (on sets) admit a quantitative equational presentation.Comment: Appendix remove

A categorical foundation for structured reversible flowchart languages: Soundness and adequacy

Structured reversible flowchart languages is a class of imperative reversible programming languages allowing for a simple diagrammatic representation of control flow built from a limited set of control flow structures. This class includes the reversible programming language Janus (without recursion), as well as more recently developed reversible programming languages such as R-CORE and R-WHILE. In the present paper, we develop a categorical foundation for this class of languages based on inverse categories with joins. We generalize the notion of extensivity of restriction categories to one that may be accommodated by inverse categories, and use the resulting decisions to give a reversible representation of predicates and assertions. This leads to a categorical semantics for structured reversible flowcharts, which we show to be computationally sound and adequate, as well as equationally fully abstract with respect to the operational semantics under certain conditions

A formal framework for model management

El Desarrollo de Software Dirigido por Modelos es una rama de la Ingeniería del Software en la que los artefactos software se representan como modelos para incrementar la productividad, calidady eficiencia económica en el proceso de desarrollo de software, donde un modelo proporciona una representación abstracta del código final de una aplicación. En este campo, la iniciativa Model-Driven Architecture (MDA), patrocinada por la OMG, está constituida por una familia de estándares industriales, entre los que se destacan: Meta-Object Facility (MOF), Unified Modeling Language (UML), Object Constraint Language (OCL), XML Metadata Interchange (XMI), y Query/Views/Transformations (QVT). Estos estándares proporcionan unas directrices comunes para herramientas basadas en modelos y para procesos de desarrollo de software dirigidos por modelos. Su objetivo consiste en mejorar la interoperabilidad entre marcos de trabajo ejecutables, en automatizar el proceso desarrollo de software de software y en proporcionar técnicas que eviten errores durante ese proceso. El estándar MOF describe un marco de trabajo genérico que permite definir la sintaxis abstracta de lenguajes de modelado. Este estándar persigue la definición de los conceptos básicos que son utilizados en procesos de desarrollo de software dirigidos por modelos: que es un modelo, que es un metamodelo, qué es reflexión en un marco de trabajo basado en MOF, etc. Sin embargo, la mayoría de estos conceptos carecen de una semántica formal en la versión actual del estándar MOF. Además, OCL se utiliza como un lenguage de definición de restricciones que permite añadir semántica a un metamodelo MOF. Desafortunadamente, la relación entre un metamodelo y sus restricciones OCL también carece de una semántica formal. Este hecho es debido, en parte, a que los metamodelos solo pueden ser definidos como dato en un marco de trabajo basado en MOF. El estándar MOF también proporciona las llamadas facilidades de reflexión de MOF (MOF ReflectiBoronat Moll, A. (2007). A formal framework for model management [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/1964Palanci

Characterising Testing Preorders for Finite Probabilistic Processes

In 1992 Wang & Larsen extended the may- and must preorders of De Nicola and Hennessy to processes featuring probabilistic as well as nondeterministic choice. They concluded with two problems that have remained open throughout the years, namely to find complete axiomatisations and alternative characterisations for these preorders. This paper solves both problems for finite processes with silent moves. It characterises the may preorder in terms of simulation, and the must preorder in terms of failure simulation. It also gives a characterisation of both preorders using a modal logic. Finally it axiomatises both preorders over a probabilistic version of CSP.Comment: 33 page