Metric Semantics and Full Abstractness for Action Refinement and Probabilistic Choice

This paper provides a case-study in the field of metric semantics for probabilistic programming. Both an operational and a denotational semantics are presented for an abstract process language L_pr, which features action refinement and probabilistic choice. The two models are constructed in the setting of complete ultrametric spaces, here based on probability measures of compact support over sequences of actions. It is shown that the standard toolkit for metric semantics works well in the probabilistic context of L_pr, e.g. in establishing the correctness of the denotational semantics with respect to the operational one. In addition, it is shown how the method of proving full abstraction --as proposed recently by the authors for a nondeterministic language with action refinement-- can be adapted to deal with the probabilistic language L_pr as well

Logical Concurrency Control from Sequential Proofs

We are interested in identifying and enforcing the isolation requirements of a concurrent program, i.e., concurrency control that ensures that the program meets its specification. The thesis of this paper is that this can be done systematically starting from a sequential proof, i.e., a proof of correctness of the program in the absence of concurrent interleavings. We illustrate our thesis by presenting a solution to the problem of making a sequential library thread-safe for concurrent clients. We consider a sequential library annotated with assertions along with a proof that these assertions hold in a sequential execution. We show how we can use the proof to derive concurrency control that ensures that any execution of the library methods, when invoked by concurrent clients, satisfies the same assertions. We also present an extension to guarantee that the library methods are linearizable or atomic

Fully abstract denotational models for nonuniform concurrent languages

AbstractThis paper investigates full abstraction of denotational model w.r.t. operational ones for two concurrent languages. The languages are nonuniform in the sense that the meaning of atomic statements generally depends on the current state. The first language, L1, has parallel composition but no communication, whereas the second one, L2, has CSP-like communications in addition. For each of Li (i = 1, 2), an operational model Oi is introduced in terms of a Plotkin-style transition system, while a denotational model Di for Li is defined compositionally using interpreted operations of the language, with meanings of recursive programs as fixed points in appropriate complete metric spaces. The full abstraction is shown by means of a context with parallel composition: Given two statements s1 and s2 with different denotational meanings, a suitable statement T is constructed such that the operational meanings of s1 ∥ T and s2 ∥ T are distinct. A combinatorial method for constructing such T is proposed. Thereby the full abstraction of D1 and D2 w.r.t. O1 and O2, respectively, is established. That is, Di is most abstract of those models C which are compositional and satisfy Oi = α ∘ C for some abstraction function α (i = 1, 2)

How to interpret and establish consistency results for semantics of concurrent programming languages

It is meaningful that a language is provided with several semantic descriptions: e.g. one which serves the needs of the implementor, another one that is suitable for specification and yet another one that will be used to explain the language to the user. In this case one has to guarantee that the various semantics are 'consistent'. The attempt of this paper is to clarify the notion 'consistency' and to present a general framework and theorems for consistency results

Labelled transition systems as a Stone space

A fully abstract and universal domain model for modal transition systems and refinement is shown to be a maximal-points space model for the bisimulation quotient of labelled transition systems over a finite set of events. In this domain model we prove that this quotient is a Stone space whose compact, zero-dimensional, and ultra-metrizable Hausdorff topology measures the degree of bisimilarity such that image-finite labelled transition systems are dense. Using this compactness we show that the set of labelled transition systems that refine a modal transition system, its ''set of implementations'', is compact and derive a compactness theorem for Hennessy-Milner logic on such implementation sets. These results extend to systems that also have partially specified state propositions, unify existing denotational, operational, and metric semantics on partial processes, render robust consistency measures for modal transition systems, and yield an abstract interpretation of compact sets of labelled transition systems as Scott-closed sets of modal transition systems.Comment: Changes since v2: Metadata updat