Extending Nunchaku to Dependent Type Theory

Nunchaku is a new higher-order counterexample generator based on a sequence of transformations from polymorphic higher-order logic to first-order logic. Unlike its predecessor Nitpick for Isabelle, it is designed as a stand-alone tool, with frontends for various proof assistants. In this short paper, we present some ideas to extend Nunchaku with partial support for dependent types and type classes, to make frontends for Coq and other systems based on dependent type theory more useful.Comment: In Proceedings HaTT 2016, arXiv:1606.0542

TEMPOS: A Platform for Developing Temporal Applications on Top of Object DBMS

This paper presents TEMPOS: a set of models and languages supporting the manipulation of temporal data on top of object DBMS. The proposed models exploit object-oriented technology to meet some important, yet traditionally neglected design criteria related to legacy code migration and representation independence. Two complementary ways for accessing temporal data are offered: a query language and a visual browser. The query language, namely TempOQL, is an extension of OQL supporting the manipulation of histories regardless of their representations, through fully composable functional operators. The visual browser offers operators that facilitate several time-related interactive navigation tasks, such as studying a snapshot of a collection of objects at a given instant, or detecting and examining changes within temporal attributes and relationships. TEMPOS models and languages have been formalized both at the syntactical and the semantical level and have been implemented on top of an object DBMS. The suitability of the proposals with regard to applications' requirements has been validated through concrete case studies

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

AsterixDB: A Scalable, Open Source BDMS

AsterixDB is a new, full-function BDMS (Big Data Management System) with a feature set that distinguishes it from other platforms in today's open source Big Data ecosystem. Its features make it well-suited to applications like web data warehousing, social data storage and analysis, and other use cases related to Big Data. AsterixDB has a flexible NoSQL style data model; a query language that supports a wide range of queries; a scalable runtime; partitioned, LSM-based data storage and indexing (including B+-tree, R-tree, and text indexes); support for external as well as natively stored data; a rich set of built-in types; support for fuzzy, spatial, and temporal types and queries; a built-in notion of data feeds for ingestion of data; and transaction support akin to that of a NoSQL store. Development of AsterixDB began in 2009 and led to a mid-2013 initial open source release. This paper is the first complete description of the resulting open source AsterixDB system. Covered herein are the system's data model, its query language, and its software architecture. Also included are a summary of the current status of the project and a first glimpse into how AsterixDB performs when compared to alternative technologies, including a parallel relational DBMS, a popular NoSQL store, and a popular Hadoop-based SQL data analytics platform, for things that both technologies can do. Also included is a brief description of some initial trials that the system has undergone and the lessons learned (and plans laid) based on those early "customer" engagements

A functional approach for in line analytical processing

This paper describes an approach to On Line Analytical Processing (OLAP), expresed in the declarative programming paradigm. We define a collection of functions that capture some of the functionality currently provided by multidimensional database product. This is done by defining operations which allow for classifying and reducing relations (tables). Suitably combined, these operations will make possible to carry out the multidimensional analysis of a relational database, and make possible the declarative specification and optimization of multidimensional database queries. The library works over an abstract model of the relational database calculus as defined by Maier, written in the style of model-oriented formal specification in the functional language HaskellEste paper describe una aproximación al Procesamiento Analítico On Line (OLAP), desarrollado en el paradigma de la programación declarativa. Definimos un conjunto de funciones que capturan algunas de las funcionalidades actualmente provistas por las bases de datos multidimensionales existentes. Esto es realizado definiendo operaciones que permiten clasificar y reducir relaciones (tablas). Dichas operaciones, convenientemente combinadas, permitirían llevar a cabo el análisis multidimensional de una base de datos relacional, junto con la especificación declarativa y optimización de las correspondientes consultas multidimensionales sobre dicha base. La biblioteca provista trabaja sobre un modelo abstracto del cálculo de base de datos relacionales tal como ha sido definido por Maier, escrito en un estilo de especificación formal orientada al modelo en el lenguaje funcional HaskellIII Workshop de Ingeniería de Software y Bases de Datos (WISBD)Red de Universidades con Carreras en Informática (RedUNCI

Refactoring pattern matching

Defining functions by pattern matching over the arguments is advantageous for understanding and reasoning, but it tends to expose the implementation of a datatype. Significant effort has been invested in tackling this loss of modularity; however, decoupling patterns from concrete representations while maintaining soundness of reasoning has been a challenge. Inspired by the development of invertible programming, we propose an approach to program refactoring based on a right-invertible language rinv—every function has a right (or pre-) inverse. We show how this new design is able to permit a smooth incremental transition from programs with algebraic datatypes and pattern matching, to ones with proper encapsulation, while maintaining simple and sound reasoning

Strategic term rewriting and its application to a VDM-SL to SQL conversion

We constructed a tool, called VooDooM, which converts datatypes in Vdm-sl into Sql relational data models. The conversion involves transformation of algebraic types to maps and products, and pointer introduction. The conversion is specified as a theory of refinement by calculation. The implementation technology is strategic term rewriting in Haskell, as supported by the Strafunski bundle. Due to these choices of theory and technology, the road from theory to practise is straightforward.Fundação para a Ciência e a Tecnologia (FCT) - POSI/ICHS/44304/2002Agência de Inovação (ADI) - ∑!223

Towards a Convenient Category of Topological Domains

We propose a category of topological spaces that promises to be convenient for the purposes of domain theory as a mathematical theory for modelling computation. Our notion of convenience presupposes the usual properties of domain theory, e.g. modelling the basic type constructors, fixed points, recursive types, etc. In addition, we seek to model parametric polymorphism, and also to provide a flexible toolkit for modelling computational effects as free algebras for algebraic theories. Our convenient category is obtained as an application of recent work on the remarkable closure conditions of the category of quotients of countably-based topological spaces. Its convenience is a consequence of a connection with realizability models