On coinduction and quantum lambda calculi

© Yuxin Deng, Yuan Feng, and Ugo Dal Lago; licensed under Creative Commons License CC-BY. In the ubiquitous presence of linear resources in quantum computation, program equivalence in linear contexts, where programs are used or executed once, is more important than in the classical setting. We introduce a linear contextual equivalence and two notions of bisimilarity, a state-based and a distribution-based, as proof techniques for reasoning about higher-order quantum programs. Both notions of bisimilarity are sound with respect to the linear contextual equivalence, but only the distribution-based one turns out to be complete. The completeness proof relies on a characterisation of the bisimilarity as a testing equivalence

Pi-Calculus: A Unifying Framework for Programming Paradigms

π-calculus is a calculus for modeling dynamically changing configurations of a network of communicating agents. This paper studies the suitability of π-calculus as a unifying framework to model the operational semantics of the three paradigms of programming: functional, logic and imperative paradigms. In doing so, the attempt is to demonstrate that π-calculus models a primitive that is pervasive in the three paradigms and to illustrate that the three forms of sequential computing are special instances of concurrent computing

A behavioral analysis tool for models of software systems

Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia InformáticaProcess calculi are simple languages which permit modeling of concurrent systems so that they can be verified for correctness. We can analyze concurrent systems based on process calculi by either comparing a representation of the actual implementation with a simpler specification for equivalence, or by verifying whether desired properties described in an adequate logic hold. Strong bisimulation equivalence is one of many equivalence relations defined on process calculi to aid in the verification of concurrent software. This equivalence relation relates processes which exhibit the same behavior, i.e. perform the same transitions, as equivalent regardless of internal implementation details. Logics to reason about processes range from those which describe temporal properties – how properties evolve during the course of a process’ life – behavioral properties – which actions a process is capable of performing – and spatial properties – what components compose a process and how are they connected. Model checking consists of verifying if a model, in our case a process, satisfies a given property. Model checking techniques are quite popular in conjunction with process calculi to aid in the verification of the correctness of concurrent systems. In this thesis we address the problems of checking bisimilarity between processess using characteristic formulae, which are formulae used to fully describe a process’ behavior. We implement some facilities to allow bisimilarity verification in the Spatial Logic Model Checker tool. As a result of adding these facilities we also extend the SLMC tool with an extra modality in the logic it uses to reason about processes. We have also added the possibility to define mutually recursive properties in the tool and enhanced the model checking algorithm with a cache to prevent redundant, time-consuming checks to be performed

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

A network-conscious π-calculus and its coalgebraic semantics

Traditional process calculi usually abstract away from network details, modeling only communication over shared channels. They, however, seem inadequate to describe new network architectures, such as Software Defined Networks, where programs are allowed to manipulate the infrastructure. In this paper we present the Network Conscious @p-calculus ( NCPi), a proper extension of the @p-calculus with an explicit notion of network: network links and nodes are represented as names, in full analogy with ordinary @p-calculus names, and observations are routing paths through which data is transported. However, restricted links do not appear in the observations, which thus can possibly be as abstract as in the @p-calculus. Then we construct a presheaf-based coalgebraic semantics for NCPi along the lines of Turi-Plotkin's approach, by indexing processes with the network resources they use: we give a model for observational equivalence in this context, and we prove that it admits an equivalent nominal automaton (HD-automaton), suitable for verification. Finally, we give a concurrent semantics for NCPi where observations are multisets of routing paths. We show that bisimilarity for this semantics is a congruence, and this property holds also for the concurrent version of the @p-calculus