Resource modalities in game semantics

The description of resources in game semantics has never achieved the simplicity and precision of linear logic, because of a misleading conception: the belief that linear logic is more primitive than game semantics. We advocate instead the contrary: that game semantics is conceptually more primitive than linear logic. Starting from this revised point of view, we design a categorical model of resources in game semantics, and construct an arena game model where the usual notion of bracketing is extended to multi- bracketing in order to capture various resource policies: linear, affine and exponential

A theory of distributed aspects

International audienceOver the last five years, several systems have been proposed to take distribution into account in Aspect-Oriented Programming. While they appeared to be fruitful to develop or improve distributed component infrastructures or application servers, those systems are not underpinned with a formal semantics and so do not permit to establish properties on the code to be executed. This paper introduces the aspect join calculus -- an aspect-oriented and distributed language based on the join calculus, a member of the pi-calculus family of process calculi suitable as a programming language. It provides a first formal theory of distributed AOP as well as a base language in which many features of previous distributed AOP systems can be formalized. The semantics of the aspect join calculus is given by a (chemical) operational semantics and a type system is developed to ensure properties satisfied by aspects during the execution of a process. We also give a translation of the aspect join calculus into the core join calculus. The translation is proved to be correct by a bisimilarity argument. In this way, we provide a well-defined version of a weaving algorithm which constitutes the main step towards an implementation of the aspect join calculus directly in JoCaml. We conclude this paper by showing that despite its minimal definition, the aspect join calculus is a convenient language in which existing distributed AOP languages can be formalized. Indeed, many features (such as remote pointcut, distributed advice, migration of aspects, asynchronous and synchronous aspects, re-routing of messages and distributed control flow) can be defined in this simple language

A Monadic Interpretation of Execution Levels and Exceptions for AOP

International audienceAspect-Oriented Programming (AOP) started ten years ago with the remark that modularization of so-called crosscutting functionalities is a fundamental problem for the engineering of large-scale applications. Originating at Xerox PARC, this observation has sparked the development of a new style of programming featured that is gradually gaining traction. However, AOP lacks theoretical foundations to clarify new ideas showing up in its wake. This paper proposes to put a bridge between AOP and the notion of 2-category to enhance the conceptual understanding of AOP. Starting from the connection between the λ-calculus and the theory of categories, we provide an internal language for 2-categories and show how it can be used to define the first categorical semantics for a realistic functional AOP language, called MinAML. We then take advantage of this new categorical framework to introduce the notion of computational 2-monads for AOP. We illustrate their conceptual power by defining a 2-monad for Éric Tanter's execution levels--which constitutes the first algebraic semantics for execution levels--and then introducing the first exception monad transformer specific to AOP that gives rise to a non-flat semantics for exceptions by taking levels into account

Contraction analysis of nonlinear random dynamical systems

In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \cite{Lohmiller98} to random differential equations. We propose new definitions of contraction (almost sure contraction and contraction in mean square) which allow to master the evolution of a stochastic system in two manners. The first one guarantees eventual exponential convergence of the system for almost all draws, whereas the other guarantees the exponential convergence in $L_2$ of to a unique trajectory. We then illustrate the relative simplicity of this extension by analyzing usual deterministic properties in the presence of noise. Specifically, we analyze stochastic gradient descent, impact of noise on oscillators synchronization and extensions of combination properties of contracting systems to the stochastic case. This is a first step towards combining the interesting and simplifying properties of contracting systems with the probabilistic approach.Comment: No. RR-8368 (2013

The Journey of Biorthogonal Logical Relations to the Realm of Assembly Code

Logical relations appeared to be very fruitful for the development of modular proofs of compiler correctness. In this field, logical relations are parametrized by a high-level type system, and are even sometimes directly relating low level pieces of code to high-level programs. All those works rely crucially on biorthogonality to get extensionality and compositionality properties. But the use of biorthogonality in the definitions also complicates matters when it comes to operational correctness. Most of the time, such correctness results amount to show an unfolding lemma that makes reduction more explicit than in a biorthogonal definition. Unfortunately, unfolding lemmas are not easy to derive for rich languages and in particular for assembly code. In this paper, we focus on three different situations that enable to reach step-by-step the assembly code universe: the use of Curry-style polymorphism, the presence of syntactical equality in the language and finally an ideal assembly code with a notion of code pointer

Univalence for free

We present an internalization of the 2-groupoid interpretation of the calculus of construction that allows to realize the univalence axiom, proof irrelevance and reasoning modulo. As an example, we show that in our setting, the type of Church integers is equal to the inductive type of natural numbers

Krivine realizability for compiler correctness

We propose a semantic type soundness result, formalized in the Coq proof assistant, for a compiler from a simple functional language to SECD machine code. Our result is quite independent from the source language as it uses Krivine's realizability to give a denotational semantics to SECD machine code using only the type system of the source language. We use realizability to prove the correctness of both a call-by-name (CBN) and a call-by-value (CBV) compiler with the same notion of orthogonality. We abstract over the notion of observation (e.g. divergence or termination) and derive an operational correctness result that relates the reduction of a term with the execution of its compiled SECD machine code