Adaptable processes

We propose the concept of adaptable processes as a way of overcoming the limitations that process calculi have for describing patterns of dynamic process evolution. Such patterns rely on direct ways of controlling the behavior and location of running processes, and so they are at the heart of the adaptation capabilities present in many modern concurrent systems. Adaptable processes have a location and are sensible to actions of dynamic update at runtime; this allows to express a wide range of evolvability patterns for concurrent processes. We introduce a core calculus of adaptable processes and propose two verification problems for them: bounded and eventual adaptation. While the former ensures that the number of consecutive erroneous states that can be traversed during a computation is bound by some given number k, the latter ensures that if the system enters into a state with errors then a state without errors will be eventually reached. We study the (un)decidability of these two problems in several variants of the calculus, which result from considering dynamic and static topologies of adaptable processes as well as different evolvability patterns. Rather than a specification language, our calculus intends to be a basis for investigating the fundamental properties of evolvable processes and for developing richer languages with evolvability capabilities

Environmental Bisimulations for Delimited-Control Operators

International audienceWe present a theory of environmental bisimilarity for the delimited-control operators shift and reset. We consider two different notions of contextual equivalence: one that does not require the presence of a top-level control delimiter when executing tested terms, and another one, fully compatible with the original CPS semantics of shift and reset, that does. For each of them, we develop sound and complete environmental bisimilarities, and we discuss up-to techniques

Environmental Bisimulations for Delimited-Control Operators with Dynamic Prompt Generation

International audienceWe present sound and complete environmental bisimilarities for a variant of Dybvig et al.'s calculus of multi-prompted delimited-control operators with dynamic prompt generation. The reasoning principles that we obtain generalize and advance the existing techniques for establishing program equivalence in calculi with single-prompted delimited control. The basic theory that we develop is presented using Madiot et al.'s framework that allows for smooth integration and composition of up-to techniques facilitating bisimulation proofs. We also generalize the framework in order to express environmental bisimulations that support equivalence proofs of evaluation contexts representing continuations. This change leads to a novel and powerful up-to technique enhancing bisimulation proofs in the presence of control operators

Bisimulations for Delimited-Control Operators

We present a comprehensive study of the behavioral theory of an untyped $\lambda$-calculus extended with the delimited-control operators shift and reset. To that end, we define a contextual equivalence for this calculus, that we then aim to characterize with coinductively defined relations, called bisimilarities. We consider different styles of bisimilarities (namely applicative, normal-form, and environmental) within a unifying framework, and we give several examples to illustrate their respective strengths and weaknesses. We also discuss how to extend this work to other delimited-control operators

Environmental bisimulations for probabilistic higher-order languages

Environmental bisimulations for probabilistic higher-order languages are studied. In contrastwith applicative bisimulations, environmental bisimulations are known to be more robust and do not require sophisticated techniques such as Howe's in the proofs of congruence. As representative calculi, call-by-name and call-by-value λ-calculus, and a (call-by-value) λ-calculus extended with references (i.e., a store) are considered. In each case, full abstraction results are derived for probabilistic environmental similarity and bisimilarity with respect to contextual preorder and contextual equivalence, respectively. Some possible enhancements of the (bi)simulations, as "up-to techniques," are also presented. Probabilities force a number of modifications to the definition of environmental bisimulations in nonprobabilistic languages. Some of thesemodifications are specific to probabilities, others may be seen as general refinements of environmental bisimulations, applicable also to non-probabilistic languages. Several examples are presented, to illustrate the modifications and the differences

Environmental Bisimulations for Probabilistic Higher-Order Languages

International audienceEnvironmental bisimulations for probabilistic higher-order languages are studied. In contrast with applicative bisimulations, environmental bisimulations are known to be more robust and do not require sophisticated techniques such as Howe's in the proofs of congruence. As representative calculi, call-by-name and call-by-value λ-calculus, and a (call-by-value) λ-calculus extended with references (i.e., a store) are considered. In each case full abstraction results are derived for probabilistic environmental similarity and bisimilarity with respect to contextual preorder and contextual equivalence, respectively. Some possible enhancements of the (bi)simulations, as 'up-to techniques', are also presented. Probabilities force a number of modifications to the definition of environmental bisimulations in non-probabilistic languages. Some of these modifications are specific to probabilities, others may be seen as general refinements of environmental bisimulations, applicable also to non-probabilistic languages. Several examples are presented, to illustrate the modifications and the differences

A Higher-Order Distributed Calculus with Name Creation

Abstract—This paper introduces HOπPn, the higher-order π-calculus with passivation and name creation, and develops an equivalence theory for this calculus. Passivation [Schmitt and Stefani] is a language construct that elegantly models higherorder distributed behaviours like failure, migration, or duplication (e.g. when a running process or virtual machine is copied), and name creation consists in generating a fresh name instead of hiding one. Combined with higher-order distribution, name creation leads to different semantics from name hiding, and is closer to implementations of distributed systems. We define for this new calculus a theory of sound and complete environmental bisimulation to prove reduction-closed barbed equivalence and (a reasonable form of) congruence. We furthermore define environmental simulations to prove behavioural approximation, and use these theories to show non-trivial examples of equivalence or approximation. Those examples could not be proven with previous theories, which were either unsound or incomplete under the presence of process duplication and name restriction, or else required universal quantification over general contexts. I