Coinductive Formal Reasoning in Exact Real Arithmetic

In this article we present a method for formally proving the correctness of the lazy algorithms for computing homographic and quadratic transformations -- of which field operations are special cases-- on a representation of real numbers by coinductive streams. The algorithms work on coinductive stream of M\"{o}bius maps and form the basis of the Edalat--Potts exact real arithmetic. We use the machinery of the Coq proof assistant for the coinductive types to present the formalisation. The formalised algorithms are only partially productive, i.e., they do not output provably infinite streams for all possible inputs. We show how to deal with this partiality in the presence of syntactic restrictions posed by the constructive type theory of Coq. Furthermore we show that the type theoretic techniques that we develop are compatible with the semantics of the algorithms as continuous maps on real numbers. The resulting Coq formalisation is available for public download.Comment: 40 page

Analytical methods and simulation models to assess innovative operational measures and technologies for rail port terminals: the case of Valencia Principe Felipe terminal

The topic of freight transport by rail is a complex theme and, in recent years, a main issue of European policy. The legislation evolution and the White Paper 2011 have demonstrated the European intention to re-launch this sector. The challenge is to promote the intermodal transport system to the detriment of road freight transport. In this context intermodal freight terminals, play a primary role for the supply chain, they are the connection point between the various transport nodes and the nodal points where the freight are handled, stored and transferred between different modes to final customer. To achieve the purpose, it is strengthen the improvement of existing intermodal freight terminals and the development of innovative intermodal freight terminals towards higher performance (ERRAC, 2012). Many terminal performances improvements have been proposed and sometime experimented. They are normally basing on combinations of operational measures and innovative technologies (e.g. automatic horizontal and parallel storage and handling, automated gate and sensors for tracking systems data exchange) tested in various terminals, with often-contradictory results. The research work described in this paper (developed within the Capacity4Rail EU project) focusses on the assessment of effects that these innovations can have in the intermodal freight terminals combined in various alternative consistent effective scenarios. The methodological framework setup to assess these innovations is basing on a combination of analytical methods based on sequential algorithms and discrete events simulation models. The output of this assessment method are key performance indicators (KPIs) selected according to terminals typologies and related to different aspects (e.g. management, operation and organization). The present paper illustrates the application of the methodological framework, tuned on the operation of various intermodal terminals, for the validation on today operation and the assessment of possible future scenarios to the case study of the Principe Felipe sea-rail terminal in Valencia

Reasoning about modular datatypes with Mendler induction

In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof assistants that are based on type theory, like Coq. The reason is that it involves type definitions, such as those of type-level fixpoint operators, that are not strictly positive. The known work-around of impredicative encodings is problematic, insofar as it impedes conventional inductive reasoning. Weak induction principles can be used instead, but they considerably complicate proofs. This paper proposes a novel and simpler technique to reason inductively about impredicative encodings, based on Mendler-style induction. This technique involves dispensing with dependent induction, ensuring that datatypes can be lifted to predicates and relying on relational formulations. A case study on proving subject reduction for structural operational semantics illustrates that the approach enables modular proofs, and that these proofs are essentially similar to conventional ones.Comment: In Proceedings FICS 2015, arXiv:1509.0282

A Generic Formalised Framework for Reasoning About Weak Memory Models

This paper describes Coq libraries devoted to the semantic of relaxed memory models. These libraries formalise a framework which covers a large class of industrial models. Implementing this framework inside a proof assistant has significantly helped improving its design and crafting the most concise and relevant specifications. Similarly the use of a proof assistant has been instrumental in the study of the semantic of synchronisation primitives, which we illustrate by the formal proof of a barrier placement theorem. We explain the choices we made to re-design our Coq libraries, and in particular what we gained from adopting a small-scale reflection methodology

Leveraging service-oriented business applications to a rigorous rule-centric dynamic behavioural architecture.

Today’s market competitiveness and globalisation are putting pressure on organisations to join their efforts, to focus more on cooperation and interaction and to add value to their businesses. That is, most information systems supporting these cross-organisations are characterised as service-oriented business applications, where all the emphasis is put on inter-service interactions rather than intra-service computations. Unfortunately for the development of such inter-organisational service-oriented business systems, current service technology proposes only ad-hoc, manual and static standard web-service languages such as WSDL, BPEL and WS-CDL [3, 7]. The main objective of the work reported in this thesis is thus to leverage the development of service-oriented business applications towards more reliability and dynamic adaptability, placing emphasis on the use of business rules to govern activities, while composing services. The best available software-engineering techniques for adaptability, mainly aspect-oriented mechanisms, are also to be integrated with advanced formal techniques. More specifically, the proposed approach consists of the following incremental steps. First, it models any business activity behaviour governing any service-oriented business process as Event-Condition-Action (ECA) rules. Then such informal rules are made more interaction-centric, using adapted architectural connectors. Third, still at the conceptual-level, with the aim of adapting such ECA-driven connectors, this approach borrows aspect-oriented ideas and mechanisms, and proposes to intercept events, select the properties required for interacting entities, explicitly and separately execute such ECA-driven behavioural interactions and finally dynamically weave the results into the entities involved. To ensure compliance and to preserve the implementation of this architectural conceptualisation, the work adopts the Maude language as an executable operational formalisation. For that purpose, Maude is first endowed with the notions of components and interfaces. Further, the concept of ECA-driven behavioural interactions are specified and implemented as aspects. Finally, capitalising on Maude reflection, the thesis demonstrates how to weave such interaction executions into associated services

Web Service Discovery in a Semantically Extended UDDI Registry: the Case of FUSION

Service-oriented computing is being adopted at an unprecedented rate, making the effectiveness of automated service discovery an increasingly important challenge. UDDI has emerged as a de facto industry standard and fundamental building block within SOA infrastructures. Nevertheless, conventional UDDI registries lack means to provide unambiguous, semantically rich representations of Web service capabilities, and the logic inference power required for facilitating automated service discovery. To overcome this important limitation, a number of approaches have been proposed towards augmenting Web service discovery with semantics. This paper discusses the benefits of semantically extending Web service descriptions and UDDI registries, and presents an overview of the approach put forward in project FUSION, towards semantically-enhanced publication and discovery of services based on SAWSDL

On the Formalisation of the Metatheory of the Lambda Calculus and Languages with Binders

Este trabajo trata sobre el razonamiento formal veri cado por computadora involucrando lenguajes con operadores de ligadura. Comenzamos presentando el Cálculo Lambda, para el cual utilizamos la sintaxis histórica, esto es, sintaxis de primer orden con sólo un tipo de nombres para las variables ligadas y libres. Primeramente trabajamos con términos concretos, utilizando la operación de sustitución múltiple de nida por Stoughton como la operación fundamental sobre la cual se de nen las conversiones alfa y beta. Utilizando esta sintaxis desarrollamos los principales resultados metateóricos del cálculo: los lemas de sustitución, el teorema de Church-Rosser y el teorema de preservación de tipo (Subject Reduction) para el sistema de asignación de tipos simples. En una segunda formalización reproducimos los mismos resultados, esta vez basando la conversion alfa sobre una operación más sencilla, que es la de permutación de nombres. Utilizando este mecanismo, derivamos principios de inducción y recursión que permiten trabajar identificando términos alfa equivalentes, de modo tal de reproducir la llamada convención de variables de Barendregt. De este modo, podemos imitar las demostraciones al estilo lápiz y papel dentro del riguroso entorno formal de un asistente de demostración. Como una generalización de este último enfoque, concluimos utilizando técnicas de programación genérica para definir una base para razonar sobre estructuras genéricas con operadores de ligadura. Definimos un universo de tipos de datos regulares con información de variables y operadores de ligadura, y sobre éstos definimos operadores genéricos de formación, eliminación e inducción. También introducimos una relación de alfa equivalencia basada en la operación de permutación y derivamos un principio de iteración/inducción que captura la convención de variables anteriormente mencionada. A modo de ejemplo, mostramos cómo definir el Cálculo Lambda y el sistema F en nuestro universo, ilustrando no sólo la reutilización de las pruebas genéricas, sino también cuán sencillo es el desarrollo de nuevas pruebas en estos casos. Todas las formalizaciones de esta tesis fueron realizadas en Teoría Constructiva de Tipos y verificadas utilizando el asistente de pruebas AgdaThis work is about formal, machine-checked reasoning on languages with name binders. We start by considering the ʎ-calculus using the historical ( rst order) syntax with only one sort of names for both bound and free variables. We rst work on the concrete terms taking Stoughton's multiple substitution operation as the fundamental operation upon which the ά and ß-conversion are de ned. Using this syntax we reach well-known meta-theoretical results, namely the Substitution lemmas, the Church-Rosser theorem and the Subject Reduction theorem for the system of assignment of simple types. In a second formalisation we reproduce the same results, this time using an approach in which -conversion is de ned using the simpler operation of name permutation. Using this we derive induction and recursion principles that allow us to work by identifying terms up to -conversion and to reproduce the so-called Barendregt's variable convention [4]. Thus, we are able to mimic pencil and paper proofs inside the rigorous formal setting of a proof assistant. As a generalisation of the latter, we conclude by using generic programming techniques to de ne a framework for reasoning over generic structures with binders. We de ne a universe of regular datatypes with variables and binders information, and over these we de ne generic formation, elimination, and induction operations. We also introduce an ά equivalence relation based on the swapping operation, and are able to derive an -iteration/induction principle that captures Barendregt's variable convention. As an example, we show how to de ne the ʎ calculus and System F in our universe, and thereby we are able to illustrate not only the reuse of the generic proofs but also how simple the development of new proofs becomes in these instances. All formalisations in this thesis have been made in Constructive Type Theory and completely checked using the Agda proof assistan

Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support

A framework and methodology---termed LogiKEy---for the design and engineering of ethical reasoners, normative theories and deontic logics is presented. The overall motivation is the development of suitable means for the control and governance of intelligent autonomous systems. LogiKEy's unifying formal framework is based on semantical embeddings of deontic logics, logic combinations and ethico-legal domain theories in expressive classic higher-order logic (HOL). This meta-logical approach enables the provision of powerful tool support in LogiKEy: off-the-shelf theorem provers and model finders for HOL are assisting the LogiKEy designer of ethical intelligent agents to flexibly experiment with underlying logics and their combinations, with ethico-legal domain theories, and with concrete examples---all at the same time. Continuous improvements of these off-the-shelf provers, without further ado, leverage the reasoning performance in LogiKEy. Case studies, in which the LogiKEy framework and methodology has been applied and tested, give evidence that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure