Unifying Classical and Intuitionistic Logics for Computational Control

International audienceWe show that control operators and other extensions of the Curry-Howard isomorphism can be achieved without collapsing all of intuitionistic logic into classical logic. For this purpose we introduce a unified propositional logic using polarized formulas. We define a Kripke semantics for this logic. Our proof system extends an intuitionistic system that already allows multiple conclusions. This arrangement reveals a greater range of computational possibilities, including a form of dynamic scoping. We demonstrate the utility of this logic by showing how it can improve the formulation of exception handling in programming languages, including the ability to distinguish between different kinds of exceptions and constraining when an exception can be thrown, thus providing more refined control over computation compared to classical logic. We also describe some significant fragments of this logic and discuss its extension to second-order logic

A CPS-semantics for a typed lambda-calculus of exception handling with fixed-point

Colloque avec actes et comité de lecture.We propose to add a fixed-point combinator to a lambda- calculus of exception handling whose type system corresponds to classical logic through the Curry-Howard isomorphism. To this end, we here give a CPS-semantics to the calculus and show that for non-exceptional terms, this semantics possesses the property of computational adequacy

Relational Parametricity for Computational Effects

According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible mathematical formulation of this idea. Relational parametricity provides a powerful tool for establishing data abstraction properties, proving equivalences of datatypes, and establishing equalities of programs. Such properties have been well studied in a pure functional setting. Many programs, however, exhibit computational effects, and are not accounted for by the standard theory of relational parametricity. In this paper, we develop a foundational framework for extending the notion of relational parametricity to programming languages with effects.Comment: 31 pages, appears in Logical Methods in Computer Scienc

Strong Normalization for HA + EM1 by Non-Deterministic Choice

We study the strong normalization of a new Curry-Howard correspondence for HA + EM1, constructive Heyting Arithmetic with the excluded middle on Sigma01-formulas. The proof-term language of HA + EM1 consists in the lambda calculus plus an operator ||_a which represents, from the viewpoint of programming, an exception operator with a delimited scope, and from the viewpoint of logic, a restricted version of the excluded middle. We give a strong normalization proof for the system based on a technique of "non-deterministic immersion".Comment: In Proceedings COS 2013, arXiv:1309.092

Adaptive Process Management in Cyber-Physical Domains

The increasing application of process-oriented approaches in new challenging cyber-physical domains beyond business computing (e.g., personalized healthcare, emergency management, factories of the future, home automation, etc.) has led to reconsider the level of flexibility and support required to manage complex processes in such domains. A cyber-physical domain is characterized by the presence of a cyber-physical system coordinating heterogeneous ICT components (PCs, smartphones, sensors, actuators) and involving real world entities (humans, machines, agents, robots, etc.) that perform complex tasks in the “physical” real world to achieve a common goal. The physical world, however, is not entirely predictable, and processes enacted in cyber-physical domains must be robust to unexpected conditions and adaptable to unanticipated exceptions. This demands a more flexible approach in process design and enactment, recognizing that in real-world environments it is not adequate to assume that all possible recovery activities can be predefined for dealing with the exceptions that can ensue. In this chapter, we tackle the above issue and we propose a general approach, a concrete framework and a process management system implementation, called SmartPM, for automatically adapting processes enacted in cyber-physical domains in case of unanticipated exceptions and exogenous events. The adaptation mechanism provided by SmartPM is based on declarative task specifications, execution monitoring for detecting failures and context changes at run-time, and automated planning techniques to self-repair the running process, without requiring to predefine any specific adaptation policy or exception handler at design-time

Optimal Union-Find in Constraint Handling Rules

Constraint Handling Rules (CHR) is a committed-choice rule-based language that was originally intended for writing constraint solvers. In this paper we show that it is also possible to write the classic union-find algorithm and variants in CHR. The programs neither compromise in declarativeness nor efficiency. We study the time complexity of our programs: they match the almost-linear complexity of the best known imperative implementations. This fact is illustrated with experimental results.Comment: 12 pages, 3 figures, to appear in Theory and Practice of Logic Programming (TPLP