A layered semantics for a parallel object-oriented language

We develop a denotational semantics for POOL, a parallel object-oriented programming language. The main contribution of this semantics is an accurate mathematical model of the most important concept in object-oriented programming: the object. This is achieved by structuring the semantics in layers working at three different levels: for statements, objects and programs. For each of these levels we define a specialized mathematical domain of processes, which we use to assign a meaning to each language construct. This is done in the mathematical framework of complete metric spaces. We also define operators that translate between these domains. At the program level we give a precise definition of the observable input/output behaviour of a particular program, which could be used at a later stage to decide the issue of full abstractness. We illustrate our semantic techniques by first applying them to a toy language similar to CSP.This paper describes work done in ESPRIT Basic Research Action 3020,Integration.     

Safety and progress of recursive procedures

Temporal weakest precondions are introduced for calculational reasoning about the states encountered during execution of not-necessarily terminating recursive procedures. The formalism can distinguish error from useful nontermination. The precondition functions are constructed in a new and more elegant way. Healthiness laws are discussed briefly. Proof rules are introduced that enable calculational proofs of various safety and progress properties. The construction of the precondition functions is justified in an Appendix that provides the operational semantics.Dedicated to the memory of Jan van de Snepscheut     

Boolean-like and frequentistic nonstandard semantics for first-order predicate calculus without functions

 Well-formed formulas of the classical first-order predicate language without functions are evaluated in such a way that truthvalues are subsets of the set of all positive integers. Such an evaluation is projected in two different ways into the unit interval of real numbers so that two real-valued evaluations are obtained. The set of tautologies are proved to be identical, in all the three cases, with the set of classical first-order predicate tautologies, but the induced evaluations meet the properties of probability and possibility measures with respect to nonstandard supremum and infimum operations induced in the unit interval of real numbers.     

Linking operational semantics and algebraic semantics for a probabilistic timed shared-variable language

Complex software systems typically involve features like time, concurrency and probability, with probabilistic computations playing an increasing role. However, it is currently challenging to formalize languages incorporating all those features. Recently, the language PTSC has been proposed to integrate probability and time with shared-variable concurrency (Zhu et al. (2006, 2009) [51] and [53]), where the operational semantics has been explored and a set of algebraic laws has been investigated via bisimulation. This paper investigates the link between the operational and algebraic semantics of PTSC, highlighting both its theoretical and practical aspects.The link is obtained by deriving the operational semantics from the algebraic semantics, an approach that may be understood as establishing soundness of the operational semantics with respect to the algebraic semantics. Algebraic laws are provided that suffice to convert any PTSC program into a form consisting of a guarded choice or an internal choice between programs, which are initially deterministic. That form corresponds to a simple execution of the program, so it is used as a basis for an operational semantics. In that way, the operational semantics is derived from the algebraic semantics, with transition rules resulting from the derivation strategy. In fact the derived transition rules and the derivation strategy are shown to be equivalent, which may be understood as establishing completeness of the operational semantics with respect to the algebraic semantics.That theoretical approach to the link is complemented by a practical one, which animates the link using Prolog. The link between the two semantics proceeds via head normal form. Firstly, the generation of head normal form is explored, in particular animating the expansion laws for probabilistic interleaving. Then the derivation of the operational semantics is animated using a strategy that exploits head normal form. The operational semantics is also animated. These animations, which again supports to claim soundness and completeness of the operational semantics with respect to the algebraic, are interesting because they provide a practical demonstration of the theoretical results.     

Distributed speculative execution for reliability and fault tolerance: an operational semantics

This paper examines the use of speculations, a form of distributed transactions, for improving the reliability and fault tolerance of distributed systems. A speculation is defined as a computation that is based on an assumption that is not validated before the computation is started. If the assumption is later found to be false, the computation is aborted and the state of the program is rolled back; if the assumption is found to be true, the results of the computation are committed. The primary difference between a speculation and a transaction is that a speculation is not isolated—for example, a speculative computation may send and receive messages, and it may modify shared objects. As a result, processes that share those objects may be absorbed into a speculation. We present a syntax, and an operational semantics in two forms. The first one is a speculative model, which takes full advantage of the speculative features. The second one is a nonspeculative, nondeterministic model, where aborts are treated as failures. We prove the equivalence of the two models, demonstrating that speculative execution is equivalent to failure-free computation.