Pierre-Louis Curien

L-Nets, strategies and proof-nets

We consider the setting of L-nets, recently introduced by Faggian and Maurel as a game model of concurrent interaction and based on Girards Ludics. We show how L-nets satisfying an additional condition, which we call logical L-nets, can be sequentialized into traditional tree-like strategies, and vice-versa.

Symmetry and interactivity in programming

We recall some of the early occurrences of the notions of interactivity and symmetry in the operational and denotational semantics of programming languages. We suggest some connections with ludics.

A theory of effects and resources: adjunction models and polarised calculi

We consider the Curry-Howard-Lambek correspondence for effectful computation and resource management, specifically proposing polarised calculi together with presheaf-enriched adjunction models as the starting point for a comprehensive semantic theory relating logical systems, typed calculi, and categorical models in this context. Our thesis is that the combination of effects and resources should be considered orthogonally. Model theoretically, this leads to an understanding of our categorical models from two complementary perspectives: (i) as a linearisation of CBPV (Call-by-Push-Value) adjunction models, and (ii) as an extension of linear/non-linear adjunction models with an adjoint resolution of computational effects. When the linear structure is cartesian and the resource structure is trivial we recover Levy’s notion of CBPV adjunction model, while when the effect structure is trivial we have Benton’s linear/non-linear adjunction models. Further instances of our model theory include the dialogue categories with a resource modality of Melliès and Tabareau, and the [E]EC ([Enriched] Effect Calculus) models of Egger, Møgelberg and Simpson. Our development substantiates the approach by providing a lifting theorem of linear models into cartesian ones. To each of our categorical models we systematically associate a typed term calculus, each of which corresponds to a variant of the sequent calculi LJ (Intuitionistic Logic) or ILL (Intuitionistic Linear Logic). The adjoint resolution of effects corresponds to polarisation whereby, syntactically, types locally determine a strict or lazy evaluation order and, semantically, the associativity of cuts is relaxed. In particular, our results show that polarisation provides a computational interpretation of CBPV in direct style. Further, we characterise depolarised models: those where the cut is associative, and where the evaluation order is unimportant. We explain possible advantages of this style of calculi for the operational semantics of effects.

Combinators and Functional Programming Languages

Introduction The Amber language embeds many recent ideas in programming language design, and tries to introduce all the features in their minimal, essential, form. One of its main goals is to safely blend static typing with the dynamic requirements of a system programming language. For this purpose, multiple inheritance and persistent objects are integrated in a strongly typed language. Other features include graphics, higher-order functions, modules and concurrency. Amber is a spin-off of the ML programming language [Milner 84]. The ML language is now being standardized, and as such is not very suitable for experimentation. Amber is intended as a tool for trying out new ideas in language implementation, language design, and language environments, while being deeply influenced by the ML experience. As a programming language, Amber was defined to experiment with a new style of polymorphism [Cardelli 84b] which, unlike the ML-style parametric polymorphism [Milner 78], is based on a notion of type inclusion, and can be used to interpret many programming concepts found in object-oriented languages [Goldberg Robson 83]. In this view, the main features of functional and object-oriented languages can be naturally integrated, and the combination of higher-order functions and multiple inheritance can be strongly typed. Some typechecking anomalies are still present in Amber, and current research is aimed at solving them and integrating inclusion polymorphism with parametric polymorphism. Type inclusion also plays an important role in modularization. Amber programs can be partitioned into modules and separately compiled. Modules have import-export lists for types and values. When a type is imported, its actual definition is not accessible: this is a form of data abstraction realized through the module mechanism, and implies that modules can be compiled in any order. It is possible to specify that two imported types, although unknown, are one a subtype of the other, so that inheritance can be made to work across module boundaries. At the programming system level, the implementation is heavily based on the ability to export and import arbitrary values to/from persistent storage. This feature is provided at the lowest level, and guarantees the preservation of any circularity or sharing present in the

Playful, Streamlike Computation

We offer a short tour into the interactive interpretation of sequential programs. We emphasize streamlike computation — that is, computation of successive bits of information upon request. The core of the approach surveyed here dates back to the work of Berry and the author on sequential algorithms on concrete data structures in the late seventies, culminating in the design of the programming language CDS, in which the semantics of programs of any type can be explored interactively. Around one decade later, two major insights of Cartwright and Felleisen on one hand, and of Lamarche on the other hand gave new, decisive impulses to the study of sequentiality. Cartwright and Felleisen observed that sequential algorithms give a direct semantics to control operators like call-cc and proposed to include explicit errors both in the syntax and in the semantics of the language PCF. Lamarche (unpublished) connected sequential algorithms to linear logic and games. The successful program of games semantics has spanned over the nineties until now, starting with syntax-independent characterizations of the term model of PCF by Abramsky, Jagadeesan, and Malacaria on one hand, and by Hyland and Ong on the other hand.