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Tom Hirschowitz

Publications and source records attributed to Tom Hirschowitz.

25 records · Page 2Linked to original sources
arXiv2009

Encapsulation and Dynamic Modularity in the Pi-Calculus

We describe a process calculus featuring high level constructs for component-oriented programming in a distributed setting. We propose an extension of the higher-order pi-calculus intended to capture several important mechanisms related to component-based programming, such as dynamic update, reconfiguration and code migration. In this paper, we are primarily concerned with the possibility to build a distributed implementation of our calculus. Accordingly, we define a low-level calculus, that describes how the high-level constructs are implemented, as well as details of the data structures manipulated at runtime. We also discuss current and future directions of research in relation to our analysis of component-based programming.

cs.PL↗
arXiv2009

Binding bigraphs as symmetric monoidal closed theories

Milner's bigraphs are a general framework for reasoning about distributed and concurrent programming languages. Notably, it has been designed to encompass both the pi-calculus and the Ambient calculus. This paper is only concerned with bigraphical syntax: given what we here call a bigraphical signature K, Milner constructs a (pre-) category of bigraphs BBig(K), whose main features are (1) the presence of relative pushouts (RPOs), which makes them well-behaved w.r.t. bisimulations, and that (2) the so-called structural equations become equalities. Examples of the latter include, e.g., in pi and Ambient, renaming of bound variables, associativity and commutativity of parallel composition, or scope extrusion for restricted names. Also, bigraphs follow a scoping discipline ensuring that, roughly, bound variables never escape their scope. Here, we reconstruct bigraphs using a standard categorical tool: symmetric monoidal closed (SMC) theories. Our theory enforces the same scoping discipline as bigraphs, as a direct property of SMC structure. Furthermore, it elucidates the slightly mysterious status of so-called links in bigraphs. Finally, our category is also considerably larger than the category of bigraphs, notably encompassing in the same framework terms and a flexible form of higher-order contexts.

cs.LO↗
arXiv2009

Variable binding, symmetric monoidal closed theories, and bigraphs

This paper investigates the use of symmetric monoidal closed (SMC) structure for representing syntax with variable binding, in particular for languages with linear aspects. In our setting, one first specifies an SMC theory T, which may express binding operations, in a way reminiscent from higher-order abstract syntax. This theory generates an SMC category S(T) whose morphisms are, in a sense, terms in the desired syntax. We apply our approach to Jensen and Milner's (abstract binding) bigraphs, which are linear w.r.t. processes. This leads to an alternative category of bigraphs, which we compare to the original.

cs.LO↗
arXiv2009

Contraction-free proofs and finitary games for Linear Logic

In the standard sequent presentations of Girard's Linear Logic (LL), there are two "non-decreasing" rules, where the premises are not smaller than the conclusion, namely the cut and the contraction rules. It is a universal concern to eliminate the cut rule. We show that, using an admissible modification of the tensor rule, contractions can be eliminated, and that cuts can be simultaneously limited to a single initial occurrence. This view leads to a consistent, but incomplete game model for LL with exponentials, which is finitary, in the sense that each play is finite. The game is based on a set of inference rules which does not enjoy cut elimination. Nevertheless, the cut rule is valid in the model.

cs.LO↗
arXiv2009

Compilation of extended recursion in call-by-value functional languages

This paper formalizes and proves correct a compilation scheme for mutually-recursive definitions in call-by-value functional languages. This scheme supports a wider range of recursive definitions than previous methods. We formalize our technique as a translation scheme to a lambda-calculus featuring in-place update of memory blocks, and prove the translation to be correct.

cs.PL↗
arXiv2008

Topological Observations on Multiplicative Additive Linear Logic

As an attempt to uncover the topological nature of composition of strategies in game semantics, we present a ``topological'' game for Multiplicative Additive Linear Logic without propositional variables, including cut moves. We recast the notion of (winning) strategy and the question of cut elimination in this context, and prove a cut elimination theorem. Finally, we prove soundness and completeness. The topology plays a crucial role, in particular through the fact that strategies form a sheaf.

cs.LO↗