67 research outputs found
Unifying type systems for mobile processes
We present a unifying framework for type systems for process calculi. The
core of the system provides an accurate correspondence between essentially
functional processes and linear logic proofs; fragments of this system
correspond to previously known connections between proofs and processes. We
show how the addition of extra logical axioms can widen the class of typeable
processes in exchange for the loss of some computational properties like
lock-freeness or termination, allowing us to see various well studied systems
(like i/o types, linearity, control) as instances of a general pattern. This
suggests unified methods for extending existing type systems with new features
while staying in a well structured environment and constitutes a step towards
the study of denotational semantics of processes using proof-theoretical
methods
Quantitative testing semantics for non-interleaving
This paper presents a non-interleaving denotational semantics for the
?-calculus. The basic idea is to define a notion of test where the outcome is
not only whether a given process passes a given test, but also in how many
different ways it can pass it. More abstractly, the set of possible outcomes
for tests forms a semiring, and the set of process interpretations appears as a
module over this semiring, in which basic syntactic constructs are affine
operators. This notion of test leads to a trace semantics in which traces are
partial orders, in the style of Mazurkiewicz traces, extended with readiness
information. Our construction has standard may- and must-testing as special
cases
Realizability with constants
We extend Krivine's classical realizability to a simply typed calculus with some constants and primitives and a call-with-current-continuation construct similar to Felleisen's C operator. We show how the theory extends smoothly by associating an appropriate truth value to concrete types. As a consequence, results and methods from realizability still hold in this new context; this is especially interesting in the case of specification theorems because they hold a significant meaning from the programmer's point of view
A proof-theoretic view on scheduling in concurrency
This paper elaborates on a new approach of the question of the
proof-theoretic study of concurrent interaction called "proofs as schedules".
Observing that proof theory is well suited to the description of confluent
systems while concurrency has non-determinism as a fundamental feature, we
develop a correspondence where proofs provide what is needed to make concurrent
systems confluent, namely scheduling. In our logical system, processes and
schedulers appear explicitly as proofs in different fragments of the proof
language and cut elimination between them does correspond to execution of a
concurrent system. This separation of roles suggests new insights for the
denotational semantics of processes and new methods for the translation of
pi-calculi into prefix-less formalisms (like solos) as the operational
counterpart of translations between proof systems
Order algebras: a quantitative model of interaction
International audienceA quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This algebraic structure is shown to provide faithful interpretations of finitary process algebras, for an extension of the standard notion of testing semantics, leading to a model that is both denotational (in the sense that the internal workings of processes are ignored) and non-interleaving. Constructions on algebras and their subspaces enjoy a good structure that make them (nearly) a model of differential linear logic, showing that the underlying approach to the representation of non-determinism as linear combinations is the same
Verification of Timed Automata Using Rewrite Rules and Strategies
ELAN is a powerful language and environment for specifying and prototyping
deduction systems in a language based on rewrite rules controlled by
strategies. Timed automata is a class of continuous real-time models of
reactive systems for which efficient model-checking algorithms have been
devised. In this paper, we show that these algorithms can very easily be
prototyped in the ELAN system. This paper argues through this example that
rewriting based systems relying on rules and strategies are a good framework to
prototype, study and test rather efficiently symbolic model-checking
algorithms, i.e. algorithms which involve combination of graph exploration
rules, deduction rules, constraint solving techniques and decision procedures
Concurrent Realizability on Conjunctive Structures
This work aims at exploring the algebraic structure of concurrent processes and their behavior independently of a particular formalism used to define them. We propose a new algebraic structure called conjunctive involutive monoidal algebra (CIMA) as a basis for an algebraic presentation of concurrent realizability, following ideas of the algebrization program already developed in the realm of classical and intuitionistic realizability. In particular, we show how any CIMA provides a sound interpretation of multiplicative linear logic. This new structure involves, in addition to the tensor and the orthogonal map, a parallel composition. We define a reference model of this structure as induced by a standard process calculus and we use this model to prove that parallel composition cannot be defined from the conjunctive structure alone
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