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11
Session Types as Intuitionistic Linear Propositions
"... Several type disciplines for πcalculi have been proposed in which linearity plays a key role, even if their precise relationship with pure linear logic is still not well understood. In this paper, we introduce a type system for the πcalculus that exactly corresponds to the standard sequent calculu ..."
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Cited by 26 (14 self)
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Several type disciplines for πcalculi have been proposed in which linearity plays a key role, even if their precise relationship with pure linear logic is still not well understood. In this paper, we introduce a type system for the πcalculus that exactly corresponds to the standard sequent calculus proof system for dual intuitionistic linear logic. Our type system is based on a new interpretation of linear propositions as session types, and provides the first purely logical account of all (both shared and linear) features of session types. We show that our type discipline is useful from a programming perspective, and ensures session fidelity, absence of deadlocks, and a tight operational correspondence between πcalculus reductions and cut elimination steps. 1
Dependent Session Types via Intuitionistic Linear Type Theory
"... We develop an interpretation of linear type theory as dependent session types for a term passing extension of the πcalculus. The type system allows us to express rich constraints on sessions, such as interface contracts and proofcarrying certification, which go beyond existing session type systems ..."
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Cited by 12 (10 self)
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We develop an interpretation of linear type theory as dependent session types for a term passing extension of the πcalculus. The type system allows us to express rich constraints on sessions, such as interface contracts and proofcarrying certification, which go beyond existing session type systems, and are here justified on purely logical grounds. We can further refine our interpretation using proof irrelevance to eliminate communication overhead for proofs between trusted parties. Our technical results include type preservation and global progress, which in our setting naturally imply compliance to all properties declared in interface contracts expressed by dependent types.
Lolliproc: to Concurrency from Classical Linear Logic via CurryHoward and Control
"... While many type systems based on the intuitionistic fragment of linear logic have been proposed, applications in programming languages of the full power of linear logic—including doublenegation elimination—have remained elusive. Meanwhile, linearity has been used in many type systems for concurrent ..."
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Cited by 5 (0 self)
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While many type systems based on the intuitionistic fragment of linear logic have been proposed, applications in programming languages of the full power of linear logic—including doublenegation elimination—have remained elusive. Meanwhile, linearity has been used in many type systems for concurrent programs—e.g., session types—which suggests applicability to the problems of concurrent programming, but the ways in which linearity has interacted with concurrency primitives in lambda calculi have remained somewhat adhoc. In this paper we connect classical linear logic and concurrent functional programming in the language Lolliproc, which provides simple primitives for concurrency that have a direct logical interpretation and that combine to provide the functionality of session types. Lolliproc features a simple process calculus “under the hood ” but hides the machinery of processes from programmers. We illustrate Lolliproc by example and prove soundness, strong normalization, and confluence results, which, among other things, guarantees freedom from deadlocks and race conditions.
An algebraic process calculus
 In Proceedings of the twentythird annual IEEE symposium on logic in computer science (LICS
, 2008
"... We present an extension of the πIcalculus with formal sums of terms. The 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 ..."
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Cited by 5 (3 self)
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We present an extension of the πIcalculus with formal sums of terms. The 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 a fully abstract trace semantics for testing of πI processes. 1.
Relational Parametricity for Polymorphic Session Types
"... We introduce a theory of polymorphic concurrent processes, which arises from an interpretation of secondorder intuitionistic linear logic propositions as polymorphic session types, in the style of the GirardReynolds polymorphic λcalculus. The interpretation naturally generalizes recent discover ..."
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Cited by 4 (3 self)
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We introduce a theory of polymorphic concurrent processes, which arises from an interpretation of secondorder intuitionistic linear logic propositions as polymorphic session types, in the style of the GirardReynolds polymorphic λcalculus. The interpretation naturally generalizes recent discoveries on the correspondence between linear logic propositions and session types. In our proposed theory, polymorphism accounts for the exchange of abstract communication protocols, and dynamic instantiation of heterogeneous interfaces. Welltyped processes enjoy a strong form of subject reduction (type preservation) and global progress, but also termination (strong normalization) and relational parametricity (representation independence). The latter two properties are obtained by adapting proof techniques in the functional setting to linear session types.
Functions as proofs as processes
 CoRR
"... Abstract. This paper presents a logical approach to the translation of functional calculi into concurrent process calculi. The starting point is a type system for the πcalculus closely related to linear logic. Decompositions of intuitionistic and classical logics into this system provide typeprese ..."
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Abstract. This paper presents a logical approach to the translation of functional calculi into concurrent process calculi. The starting point is a type system for the πcalculus closely related to linear logic. Decompositions of intuitionistic and classical logics into this system provide typepreserving translations of the λ and λµcalculus, both for callbyname and callbyvalue evaluation strategies. Previously known encodings of the λcalculus are shown to correspond to particular cases of this logical embedding. The realisability interpretation of types in the πcalculus provides systematic soundness arguments for these translations and allows for the definition of typesafe extensions of functional calculi. 1
A Concurrent Interpretation of Intuitionistic Linear Logic
"... Several type disciplines for πcalculi have been proposed, in which linearity frequently plays a key role. In this paper, we introduce a type system for the πcalculus that exactly corresponds to the standard sequent calculus proof system for dual intuitionistic linear logic, based on an interpretat ..."
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Cited by 1 (0 self)
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Several type disciplines for πcalculi have been proposed, in which linearity frequently plays a key role. In this paper, we introduce a type system for the πcalculus that exactly corresponds to the standard sequent calculus proof system for dual intuitionistic linear logic, based on an interpretation of linear propositions as session types. Perhaps surprisingly, the induced type discipline reveals a close connection between intuitionistic linear logic, linear and session types for mobile processes, and forms of concurrent functional evaluation. We also show that our type system ensures session fidelity and the absence of deadlocks, and a tight operational correspondence between πcalculus reductions and cut elimination steps. 1
Proofs as executions
, 2012
"... Abstract. 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 c ..."
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Abstract. 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 lockavoiding 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. 1
Cut Reduction in Linear Logic as Asynchronous SessionTyped Communication ∗
"... Prior work has shown that intuitionistic linear logic can be seen as a sessiontype discipline for the πcalculus, where cut reduction in the sequent calculus corresponds to synchronous process reductions. In this paper, we exhibit a new process assignment from the asynchronous, polyadic πcalculus ..."
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Cited by 1 (1 self)
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Prior work has shown that intuitionistic linear logic can be seen as a sessiontype discipline for the πcalculus, where cut reduction in the sequent calculus corresponds to synchronous process reductions. In this paper, we exhibit a new process assignment from the asynchronous, polyadic πcalculus to exactly the same proof rules. Prooftheoretically, the difference between these interpretations can be understood through permutations of inference rules that preserve observational equivalence of closed processes in the synchronous case. We also show that, under this new asynchronous interpretation, cut reductions correspond to a natural asynchronous buffered session semantics, where each session is allocated a separate communication buffer.
unknown title
"... B2 – Description du projet et résultats attendus (8 pages maximum en Arial 11, simple interligne) L’originalité et le caractère ambitieux du projet devront être explicités. L’interdisciplinarité et l’ouverture à diverses collaborations seront à justifier en accord avec l’orientation du projet. La ca ..."
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B2 – Description du projet et résultats attendus (8 pages maximum en Arial 11, simple interligne) L’originalité et le caractère ambitieux du projet devront être explicités. L’interdisciplinarité et l’ouverture à diverses collaborations seront à justifier en accord avec l’orientation du projet. La capacité de ou des équipes « porteuse(s) » devra être attestée par la qualification et les productions scientifiques antérieures de leurs membres. Leurs rôles dans les différentes phases du projet devront être précisés et la valeur ajoutée des collaborations entre les différentes équipes sera argumentée. On décrira le déroulement prévisionnel et les diverses phases intermédiaires ainsi que les méthodologies employées. Les moyens demandés devront être en accord avec les objectifs scientifiques du projet. Uniquement dans le domaine des sciences humaines et sociales, les projets de recherche peuvent impliquer la production de données statistiques. Dans ce cas l'accès au financement de l'ANR implique l'obligation de déposer ces données, documentées, dans un centre d'archivage et de diffusion auprès des chercheurs, et de les mettre à disposition de la communauté scientifique (éventuellement au terme d'un embargo de durée déterminée). 1