Transforming data by calculation

Thispaperaddressesthefoundationsofdata-modeltransformation.A catalog of data mappings is presented which includes abstraction and representa- tion relations and associated constraints. These are justified in an algebraic style via the pointfree-transform, a technique whereby predicates are lifted to binary relation terms (of the algebra of programming) in a two-level style encompassing both data and operations. This approach to data calculation, which also includes transformation of recursive data models into “flat” database schemes, is offered as alternative to standard database design from abstract models. The calculus is also used to establish a link between the proposed transformational style and bidi- rectional lenses developed in the context of the classical view-update problem.Fundação para a Ciência e a Tecnologia (FCT

A functional specification of effects

This dissertation is about effects and type theory. Functional programming languages such as Haskell illustrate how to encapsulate side effects using monads. Haskell compilers provide a handful of primitive effectful functions. Programmers can construct larger computations using the monadic return and bind operations. These primitive effectful functions, however, have no associated definition. At best, their semantics are specified separately on paper. This can make it difficult to test, debug, verify, or even predict the behaviour of effectful computations. This dissertation provides pure, functional specifications in Haskell of several different effects. Using these specifications, programmers can test and debug effectful programs. This is particularly useful in tandem with automatic testing tools such as QuickCheck. The specifications in Haskell are not total. This makes them unsuitable for the formal verification of effectful functions. This dissertation overcomes this limitation, by presenting total functional specifications in Agda, a programming language with dependent types. There have been alternative approaches to incorporating effects in a dependently typed programming language. Most notably, recent work on Hoare Type Theory proposes to extend type theory with axioms that postulate the existence of primitive effectful functions. This dissertation shows how the functional specifications implement these axioms, unifying the two approaches. The results presented in this dissertation may be used to write and verify effectful programs in the framework of type theory

A functional specification of effects

This dissertation is about effects and type theory. Functional programming languages such as Haskell illustrate how to encapsulate side effects using monads. Haskell compilers provide a handful of primitive effectful functions. Programmers can construct larger computations using the monadic return and bind operations. These primitive effectful functions, however, have no associated definition. At best, their semantics are specified separately on paper. This can make it difficult to test, debug, verify, or even predict the behaviour of effectful computations. This dissertation provides pure, functional specifications in Haskell of several different effects. Using these specifications, programmers can test and debug effectful programs. This is particularly useful in tandem with automatic testing tools such as QuickCheck. The specifications in Haskell are not total. This makes them unsuitable for the formal verification of effectful functions. This dissertation overcomes this limitation, by presenting total functional specifications in Agda, a programming language with dependent types. There have been alternative approaches to incorporating effects in a dependently typed programming language. Most notably, recent work on Hoare Type Theory proposes to extend type theory with axioms that postulate the existence of primitive effectful functions. This dissertation shows how the functional specifications implement these axioms, unifying the two approaches. The results presented in this dissertation may be used to write and verify effectful programs in the framework of type theory

Construcción de programas que manejan dinámicamente la memoria

Tesis (Doctor en Cs. de la Computación)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía y Física, 2015.En este trabajo abordamos diferentes aspectos de la verificación de programas que manejan dinámicamente la memoria, y más en general, al razonamiento formal sobre ellos. Por un lado, proponemos un marco conceptual para considerar cuestiones ontológicas y epistemológicas de la propia tarea de verificación formal, a través de una generalización del concepto de intérprete, que nos permite relacionar los aspectos abstractos y concretos de la computación. En el plano metodológico, la principal contribución es la introducción de la Sharing Logic, que permite especificar de forma precisa estructuras dinámicas complejas y las relaciones entre ellas, de manera compatible con los principios de abstracción e information hiding. En el plano práctico, abordamos la decidibilidad del problema de validez de un fragmento de nuestra Sharing Logic que permite caracterizar estructuras de datos como listas enlazadas y segmentos de ellas. Además presentamos un análisis estático, que verifica automáticamente programas que manipulan estructuras de datos no lineales

Inductive representation, proofs and refinement of pointer structures

Cette thèse s'intègre dans le domaine général des méthodes formelles qui donnent une sémantique aux programmes pour vérifier formellement des propriétés sur ceux-ci. Sa motivation originale provient d'un besoin de certification des systèmes industriels souvent développés à l'aide de l'Ingénierie Dirigée par les Modèles (IDM) et de langages orientés objets (OO). Pour transformer efficacement des modèles (ou graphes), il est avantageux de les représenter à l'aide de structures de pointeurs, économisant le temps et la mémoire grâce au partage qu'ils permettent. Cependant la vérification de propriétés sur des programmes manipulant des pointeurs est encore complexe. Pour la simplifier, nous proposons de démarrer le développement par une implémentation haut-niveau sous la forme de programmes fonctionnels sur des types de données inductifs facilement vérifiables dans des assistants à la preuve tels que Isabelle/HOL. La représentation des structures de pointeurs est faite à l'aide d'un arbre couvrant contenant des références additionnelles. Ces programmes fonctionnels sont ensuite raffinés si nécessaire vers des programmes impératifs à l'aide de la bibliothèque Imperative_HOL. Ces programmes sont en dernier lieu extraits vers du code Scala (OO). Cette thèse décrit la méthodologie de représentation et de raffinement et fournit des outils pour la manipulation et la preuve de programmes OO dans Isabelle/HOL. L'approche est éprouvée par de nombreux exemples dont notamment l'algorithme de Schorr-Waite et la construction de Diagrammes de Décision Binaires (BDDs).This thesis stands in the general domain of formal methods that gives semantics to programs to formally prove properties about them. It originally draws its motivation from the need for certification of systems in an industrial context where Model Driven Engineering (MDE) and object-oriented (OO) languages are common. In order to obtain efficient transformations on models (graphs), we can represent them as pointer structures, allowing space and time savings through the sharing of nodes. However verification of properties on programs manipulating pointer structures is still hard. To ease this task, we propose to start the development with a high-level implementation embodied by functional programs manipulating inductive data-structures, that are easily verified in proof assistants such as Isabelle/HOL. Pointer structures are represented by a spanning tree adorned with additional references. These functional programs are then refined - if necessary - to imperative programs thanks to the library Imperative_HOL. These programs are finally extracted to Scala code (OO). This thesis describes this kind of representation and refinement and provides tools to manipulate and prove OO programs in Isabelle/HOL. This approach is put in practice with several examples, and especially with the Schorr-Waite algorithm and the construction of Binary Decision Diagrams (BDDs)

FUNCTIONAL PEARL Unfolding pointer algorithms

A fair amount has been written on the subject of reasoning about pointer algorithms. There was a peak about 1980 when everyone seemed to be tackling the formal verication of the Schorr{Waite marking algorithm, including Gries (1979, Morris (1982) and Topor (1979). Bornat (2000) writes: \The Schorr{Waite algorithm is the rst mountain that any formalism for pointer aliasing should climb". Then it went more or less quiet for a while, but in the last few years there has been a resurgence of interest, driven by new ideas in relational algebras (M¨oeller, 1993), in data renement Butler (1999), in type theory (Hofmann, 2000; Walker and Morrisett, 2000), in novel kinds of assertion (Reynolds, 2000), and by the demands of mechanised reasoning (Bornat, 2000). Most approaches end up being based in the Floyd{Dijkstra{Hoare tradition with loops and invariant assertions. To be sure, when dealing with any recursively-dened linked structure some declarative notation has to be brought in to specify the problem, but no one to my knowledge has advocated a purely functional approach throughout. Mason (1988) comes close, but his Lisp expressions can be very impure. M¨oller (1999) also exploits an algebraic approach, and the structure of his paper has much in common with what follows. This pearl explores the possibility of a simple functional approach to pointer manipulation algorithms

FUNCTIONAL PEARL Unfolding pointer algorithms

A fair amount has been written on the subject of reasoning about pointer algorithms. There was a peak about 1980 when everyone seemed to be tackling the formal verication of the Schorr{Waite marking algorithm, including Gries (1979, Morris (1982) and Topor (1979). Bornat (2000) writes: \The Schorr{Waite algorithm is the rst mountain that any formalism for pointer aliasing should climb". Then it went more or less quiet for a while, but in the last few years there has been a resurgence of interest, driven by new ideas in relational algebras (M¨oeller, 1993), in data renement Butler (1999), in type theory (Hofmann, 2000; Walker and Morrisett, 2000), in novel kinds of assertion (Reynolds, 2000), and by the demands of mechanised reasoning (Bornat, 2000). Most approaches end up being based in the Floyd{Dijkstra{Hoare tradition with loops and invariant assertions. To be sure, when dealing with any recursively-dened linked structure some declarative notation has to be brought in to specify the problem, but no one to my knowledge has advocated a purely functional approach throughout. Mason (1988) comes close, but his Lisp expressions can be very impure. M¨oller (1999) also exploits an algebraic approach, and the structure of his paper has much in common with what follows. This pearl explores the possibility of a simple functional approach to pointer manipulation algorithms

Functional pearl: Unfolding pointer algorithms

A fair amount has been written on the subject of reasoning about pointer algorithms. There was a peak about 1980 when everyone seemed to be tackling the formal verification of the Schorr–Waite marking algorithm, including Gries (1979, Morris (1982) and Topor (1979). Bornat (2000) writes: “The Schorr–Waite algorithm is th