On the Execution of Ambients

Successfully harnessing multi-threaded programming has recently received renewed attention. The GHz war of the last years has been replaced with a parallelism war, each manufacturer seeking to produce CPUs supporting a greater number of threads in parallel execution. The Ambient calculus offers a simple yet powerful means to model communication, distributed computation and mobility. However, given its first class support for concurrency, we sought to investigate the utility of the Ambient calculus for practical programming purposes. Although too low-level to be considered as a general-purpose programming language itself, the Ambient calculus is nevertheless a suitable virtual machine for the execution of mobile and distributed higher-level languages. We present the Glint Virtual Machine: an interpreter for the Safe Boxed Ambient calculus. The GlintVM provides an effective platform for mobile, distributed and parallel computation and should ease some of the difficulties of writing compilers for languages that can exploit the new thread-parallel architectures

Inner Classes and Virtual Types

This paper studies the interplay between inner classes and virtual types. The combination of these two concepts can be observed in object-oriented languages like Beta or Scala. This study is based on a calculus of classes and objects composed of a very limited number of constructs. For example the calculus has neither methods nor class constructors. Instead it has a more general concept of abstract inheritance which lets a class extend an arbitrary object. Thanks to an interpretation of terms as types the calculus also unifies type fields and term fields. The main contribution of this work is to show that typing virtual types in the presence of inner classes requires some kind of alias analysis and to formalize this mechanism with a simple calculus

Kan extensions and the calculus of modules for ∞\infty-categories

Various models of $(\infty,1)$-categories, including quasi-categories, complete Segal spaces, Segal categories, and naturally marked simplicial sets can be considered as the objects of an $\infty$-cosmos. In a generic $\infty$-cosmos, whose objects we call $\infty$-categories, we introduce modules (also called profunctors or correspondences) between $\infty$-categories, incarnated as as spans of suitably-defined fibrations with groupoidal fibers. As the name suggests, a module from $A$ to $B$ is an $\infty$-category equipped with a left action of $A$ and a right action of $B$, in a suitable sense. Applying the fibrational form of the Yoneda lemma, we develop a general calculus of modules, proving that they naturally assemble into a multicategory-like structure called a virtual equipment, which is known to be a robust setting in which to develop formal category theory. Using the calculus of modules, it is straightforward to define and study pointwise Kan extensions, which we relate, in the case of cartesian closed $\infty$-cosmoi, to limits and colimits of diagrams valued in an $\infty$-category, as introduced in previous work.Comment: 84 pages; a sequel to arXiv:1506.05500; v2. new results added, axiom circularity removed; v3. final journal version to appear in Alg. Geom. To

Towards a General Framework for Formal Reasoning about Java Bytecode Transformation

Program transformation has gained a wide interest since it is used for several purposes: altering semantics of a program, adding features to a program or performing optimizations. In this paper we focus on program transformations at the bytecode level. Because these transformations may introduce errors, our goal is to provide a formal way to verify the update and establish its correctness. The formal framework presented includes a definition of a formal semantics of updates which is the base of a static verification and a scheme based on Hoare triples and weakest precondition calculus to reason about behavioral aspects in bytecode transformationComment: In Proceedings SCSS 2012, arXiv:1307.802

Moduli space and structure of noncommutative 3-spheres

We analyse the moduli space and the structure of noncommutative 3-spheres. We develop the notion of central quadratic form for quadratic algebras, and prove a general algebraic result which considerably refines the classical homomorphism from a quadratic algebra to a cross-product algebra associated to the characteristic variety and lands in a richer cross-product. It allows to control the $C^\ast$-norm on involutive quadratic algebras and to construct the differential calculus in the desired generality. The moduli space of noncommutative 3-spheres is identified with equivalence classes of pairs of points in a symmetric spaceof unitary unimodular symmetric matrices. The scaling foliation of the moduli space is identified to the gradient flow of the character of a virtual representation of SO(6). Its generic orbits are connected components of real parts of elliptic curves which form a net of biquadratic curves with 8 points in common. We show that generically these curves are the same as the characteristic variety of the associated quadratic algebra. We then apply the general theory of central quadratic forms to show that the noncommutative 3-spheres admit a natural ramified covering $\pi$ by a noncommutative 3-dimensional nilmanifold. This yields the differential calculus. We then compute the Jacobian of the ramified covering $\pi$ by pairing the direct image of the fundamental class of the noncommutative 3--dimensional nilmanifold with the Chern character of the defining unitary and obtain the answer as the product of a period (of an elliptic integral) by a rational function...Comment: 50 pages. References adde