Computation in director string calculus

In this thesis we introduce a modified version of Director String Calculus (MDSC) which preserves the applicative structure of the original lambda terms and captures the strong reduction as opposed to weak reduction of the original Director String Calculus (DSC). Furthermore, our reduction system provides an environment which supports the nonatomic nature of substitution operation and hence can lend itself to parallel and optimal reduction. We shall compare our reduction method with other reduction methods, and discuss some of the advantages and disadvantages of our method

Bounded Refinement Types

We present a notion of bounded quantification for refinement types and show how it expands the expressiveness of refinement typing by using it to develop typed combinators for: (1) relational algebra and safe database access, (2) Floyd-Hoare logic within a state transformer monad equipped with combinators for branching and looping, and (3) using the above to implement a refined IO monad that tracks capabilities and resource usage. This leap in expressiveness comes via a translation to "ghost" functions, which lets us retain the automated and decidable SMT based checking and inference that makes refinement typing effective in practice.Comment: 14 pages, International Conference on Functional Programming, ICFP 201

Multifocal: a strategic bidirectional transformation language for XML schemas

Lenses are one of the most popular approaches to define bidirectional transformations between data models. However, writing a lens transformation typically implies describing the concrete steps that convert values in a source schema to values in a target schema. In contrast, many XML-based languages allow writing structure-shy programs that manipulate only specific parts of XML documents without having to specify the behavior for the remaining structure. In this paper, we propose a structure-shy bidirectional two-level transformation language for XML Schemas, that describes generic type-level transformations over schema representations coupled with value-level bidirectional lenses for document migration. When applying these two-level programs to particular schemas, we employ an existing algebraic rewrite system to optimize the automatically-generated lens transformations, and compile them into Haskell bidirectional executables. We discuss particular examples involving the generic evolution of recursive XML Schemas, and compare their performance gains over non-optimized definitions.Fundação para a Ciência e a Tecnologi

Categorical combinators

Our main aim is to present the connection between λ-calculus and Cartesian closed categories both in an untyped and purely syntactic setting. More specifically we establish a syntactic equivalence theorem between what we call categorical combinatory logic and λ-calculus with explicit products and projections, with β and η-rules as well as with surjective pairing. “Combinatory logic” is of course inspired by Curry's combinatory logic, based on the well-known S, K, I. Our combinatory logic is “categorical” because its combinators and rules are obtained by extracting untyped information from Cartesian closed categories (looking at arrows only, thus forgetting about objects). Compiling λ-calculus into these combinators happens to be natural and provokes only n log n code expansion. Moreover categorical combinatory logic is entirely faithful to β-reduction where combinatory logic needs additional rather complex and unnatural axioms to be. The connection easily extends to the corresponding typed calculi, where typed categorical combinatory logic is a free Cartesian closed category where the notion of terminal object is replaced by the explicit manipulation of applying (a function to its argument) and coupling (arguments to build datas in products). Our syntactic equivalences induce equivalences at the model level. The paper is intended as a mathematical foundation for developing implementations of functional programming languages based on a “categorical abstract machine,” as developed in a companion paper (Cousineau, Curien, and Mauny, in “Proceedings, ACM Conf. on Functional Programming Languages and Computer Architecture,” Nancy, 1985)

On strong reduction in director string calculus

An algebra is presented which is used in conjunction with a modified version of director string calculus (MDSC). The algebra simplifies the implementation of the MDSC while preserving the applicative structure of the originalexpression, and capturing strong reduction

Security-Policy Analysis with eXtended Unix Tools

During our fieldwork with real-world organizations---including those in Public Key Infrastructure (PKI), network configuration management, and the electrical power grid---we repeatedly noticed that security policies and related security artifacts are hard to manage. We observed three core limitations of security policy analysis that contribute to this difficulty. First, there is a gap between policy languages and the tools available to practitioners. Traditional Unix text-processing tools are useful, but practitioners cannot use these tools to operate on the high-level languages in which security policies are expressed and implemented. Second, practitioners cannot process policy at multiple levels of abstraction but they need this capability because many high-level languages encode hierarchical object models. Finally, practitioners need feedback to be able to measure how security policies and policy artifacts that implement those policies change over time. We designed and built our eXtended Unix tools (XUTools) to address these limitations of security policy analysis. First, our XUTools operate upon context-free languages so that they can operate upon the hierarchical object models of high-level policy languages. Second, our XUTools operate on parse trees so that practitioners can process and analyze texts at multiple levels of abstraction. Finally, our XUTools enable new computational experiments on multi-versioned structured texts and our tools allow practitioners to measure security policies and how they change over time. Just as programmers use high-level languages to program more efficiently, so can practitioners use these tools to analyze texts relative to a high-level language. Throughout the historical transmission of text, people have identified meaningful substrings of text and categorized them into groups such as sentences, pages, lines, function blocks, and books to name a few. Our research interprets these useful structures as different context-free languages by which we can analyze text. XUTools are already in demand by practitioners in a variety of domains and articles on our research have been featured in various news outlets that include ComputerWorld, CIO Magazine, Communications of the ACM, and Slashdot

A Theory of Explicit Substitutions with Safe and Full Composition

Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the first part of this paper. Then, very simple technology in named variable-style notation is used to establish a theory of explicit substitutions for the lambda-calculus which enjoys a whole set of useful properties such as full composition, simulation of one-step beta-reduction, preservation of beta-strong normalisation, strong normalisation of typed terms and confluence on metaterms. Normalisation of related calculi is also discussed.Comment: 29 pages Special Issue: Selected Papers of the Conference "International Colloquium on Automata, Languages and Programming 2008" edited by Giuseppe Castagna and Igor Walukiewic