Relational Parametricity and Control

We study the equational theory of Parigot's second-order λμ-calculus in connection with a call-by-name continuation-passing style (CPS) translation into a fragment of the second-order λ-calculus. It is observed that the relational parametricity on the target calculus induces a natural notion of equivalence on the λμ-terms. On the other hand, the unconstrained relational parametricity on the λμ-calculus turns out to be inconsistent with this CPS semantics. Following these facts, we propose to formulate the relational parametricity on the λμ-calculus in a constrained way, which might be called ``focal parametricity''.Comment: 22 pages, for Logical Methods in Computer Scienc

On the relative expressiveness of higher-order session processes

By integrating constructs from the λ-calculus and the π-calculus, in higher-order process calculi exchanged values may contain processes. This paper studies the relative expressiveness of HOπ, the higher-order π-calculus in which communications are governed by session types. Our main discovery is that HO, a subcalculus of HOπ which lacks name-passing and recursion, can serve as a new core calculus for session-typed higher-order concurrency. By exploring a new bisimulation for HO, we show that HO can encode HOπ fully abstractly (up to typed contextual equivalence) more precisely and efficiently than the first-order session π-calculus (π). Overall, under session types, HOπ, HO, and π are equally expressive; however, HOπ and HO are more tightly related than HOπ and π

Application of a stochastic name-­passing calculus to representation and simulation of molecular processes

We describe a novel application of a stochastic name passing calculus for the study of biomolecular systems. We specify the structure and dynamics of biochemical networks in a variant of the stochastic P-­calculus, yielding a model which is mathematically well­defined and biologically faithful. We adapt the operational semantics of the calculus to account for both the time and probability of biochemical reactions, and present a computer implementation of the calculus for biochemical simulations

An Approach to Call-by-Name Delimited Continuations

International audienceWe show that a variant of Parigot's λμ-calculus, originally due to de Groote and proved to satisfy Böhm's theorem by Saurin, is canonically interpretable as a call-by-name calculus of delim- ited control. This observation is expressed using Ariola et al's call-by-value calculus of delimited control, an extension of λμ-calculus with delimited control known to be equationally equivalent to Danvy and Filinski's calculus with shift and reset. Our main result then is that de Groote and Saurin's variant of λμ-calculus is equivalent to a canonical call-by-name variant of Ariola et al's calculus. The rest of the paper is devoted to a comparative study of the call-by-name and call-by-value variants of Ariola et al's calculus, covering in particular the questions of simple typing, operational semantics, and continuation-passing-style semantics. Finally, we discuss the relevance of Ariola et al's calculus as a uniform framework for representing different calculi of delimited continuations, including "lazy" variants such as Sabry's shift and lazy reset calculus

On the Relation of Interaction Semantics to Continuations and Defunctionalization

In game semantics and related approaches to programming language semantics, programs are modelled by interaction dialogues. Such models have recently been used in the design of new compilation methods, e.g. for hardware synthesis or for programming with sublinear space. This paper relates such semantically motivated non-standard compilation methods to more standard techniques in the compilation of functional programming languages, namely continuation passing and defunctionalization. We first show for the linear {\lambda}-calculus that interpretation in a model of computation by interaction can be described as a call-by-name CPS-translation followed by a defunctionalization procedure that takes into account control-flow information. We then establish a relation between these two compilation methods for the simply-typed {\lambda}-calculus and end by considering recursion

Continuation-Passing Style and Strong Normalisation for Intuitionistic Sequent Calculi

The intuitionistic fragment of the call-by-name version of Curien and Herbelin's \lambda\_mu\_{\~mu}-calculus is isolated and proved strongly normalising by means of an embedding into the simply-typed lambda-calculus. Our embedding is a continuation-and-garbage-passing style translation, the inspiring idea coming from Ikeda and Nakazawa's translation of Parigot's \lambda\_mu-calculus. The embedding strictly simulates reductions while usual continuation-passing-style transformations erase permutative reduction steps. For our intuitionistic sequent calculus, we even only need "units of garbage" to be passed. We apply the same method to other calculi, namely successive extensions of the simply-typed λ-calculus leading to our intuitionistic system, and already for the simplest extension we consider (λ-calculus with generalised application), this yields the first proof of strong normalisation through a reduction-preserving embedding. The results obtained extend to second and higher-order calculi

Strong normalisation in the π-calculus

We introduce a typed π-calculus where strong normalisation is ensured by typability. Strong normalisation is a useful property in many computational contexts, including distributed systems. In spite of its simplicity, our type discipline captures a wide class of converging name-passing interactive behaviour. The proof of strong normalisability combines methods from typed λ-calculi and linear logic with process-theoretic reasoning. It is adaptable to systems involving state, polymorphism and other extensions. Strong normalisation is shown to have significant consequences, including finite axiomatisation of weak bisimilarity, a fully abstract embedding of the simply-typed λ-calculus with products and sums and basic liveness in interaction. Strong normalisability has been extensively studied as a fundamental property in functional calculi, term rewriting and logical systems. This work is one of the first steps to extend theories and proof methods for strong normalisability to the context of name-passing processes

Core higher-order session processes: tractable equivalences and relative expressiveness

This work proposes tractable bisimulations for the higher-order - calculus with session primitives (HO ) and o ers a complete study of the expressivity of its most significant subcalculi. First we develop three typed bisimulations, which are shown to coincide with contextual equivalence. These characterisations demonstrate that observing as inputs only a specific finite set of higher-order values (which inhabit session types) su ces to reason about HO processes. Next, we identify HO, a minimal, second-order subcalculus of HO in which higher-order applications/abstractions, name-passing, and recursion are absent. We show that HO can encode HO extended with higher-order applications and abstractions and that a first-order session -calculus can encode HO . Both encodings are fully abstract. We also prove that the session -calculus with passing of shared names cannot be encoded into HO without shared names. We show that HO , HO, and are equally expressive; the expressivity of HO enables e ective reasoning about typed equivalences for higher-order processes