Emmanuel Beffara

A Concurrent Model for Linear Logic

We build a realizability model for linear logic using a name-passing process calculus. The construction is based on testing semantics for processes, drawing ideas from spatial and modal logics, and yields a new type system for process calculi that ensures termination while allowing significantly concurrent behaviours. Then we study how embeddings of intuitionistic and classical logics into linear logic induce typed translations of @l and @[emailxa0protected] calculi in which new concurrent instructions can be introduced, thus sketching the basis for a Curry-Howard interpretation of linear and classical proofs in terms of concurrent interaction.

ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming

All classical ?-terms typable with disjunctive normal forms are shown to share a common computational behavior: they implement a local exception handling mechanism whose exact workings depend on the tautology. Equivalent and more efficient control combinators are described through a specialized sequent calculus and shown to be correct.

Proofs as executions

This paper proposes a new interpretation of the logical contents of programs in the context of concurrent interaction, wherein proofs correspond to valid executions of a processes. A type system based on linear logic is used, in which a given process has many different types, each typing corresponding to a particular way of interacting with its environment and cut elimination corresponds to executing the process in a given interaction scenario. A completeness result is established, stating that every lock-avoiding execution of a process in some environment corresponds to a particular typing. Besides traces, types contain precise information about the flow of control between a process and its environment, and proofs are interpreted as composable schedulings of processes. In this interpretation, logic appears as a way of making explicit the flow of causality between interacting processes.

An Algebraic Process Calculus

We present an extension of the piI-calculus with formal sums of terms. A study of the properties of this sum reveals that its neutral element can be used to make assumptions about the behaviour of the environment of a process. Furthermore, the formal sum appears as a fundamental construct that can be used to decompose both internal and external choice. From these observations, we derive an enriched calculus that enjoys a confluent reduction which preserves the testing semantics of processes. This system is shown to be strongly normalising for terms without replication, and the study of its normal forms provides fully abstract trace semantics for testing of piI processes.

Disjunctive normal forms and local exceptions

All classical ?-terms typable with disjunctive normal forms are shown to share a common computational behavior: they implement a local exception handling mechanism whose exact workings depend on the tautology. Equivalent and more efficient control combinators are described through a specialized sequent calculus and shown to be correct.

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.

Concurrent Nets

We introduce the calculus of concurrent nets as an extension of the fusion calculus in which usual prefixing is replaced by arbitrary monotonic guards. Then we use this formalism to describe the prefixing policy of standard calculi as a particular form of communication. By developing a graphical syntax, we sharpen the geometric intuition and finally we provide an encoding of these guards as causality in the prefix-free fragment, in the spirit of the encoding of the fusion calculus into solos by Laneve and Victor, proving that communication by fusion is expressive enough to implement arbitrary monotonic guards.

Disjunctive Normal Forms and Local Exceptions

All classical ?-terms typable with disjunctive normal forms are shown to share a common computational behavior: they implement a local exception handling mechanism whose exact workings depend on the tautology. Equivalent and more efficient control combinators are described through a specialized sequent calculus and shown to be correct.