The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and systems behaviour developed by Milner, Hennessy et al. based on operational semantics. • Logics of programs. Stone duality provides a junction between semantics (spaces of points = denotations of computational processes) and logics (lattices of properties of processes). Moreover, the underlying logic is geometric, which can be computationally interpreted as the logic of observable properties—i.e. properties which can be determined to hold of a process on the basis of a finite amount of information about its execution. These ideas lead to the following programme:

This thesis develops a semantic model of inheritance and investigates its applications for the analysis and design of programming languages. Inheritance is a mechanism for incremental programming in the presence of self-reference. This interpretation of inheritance is formalized using traditional techniques of fixed-point theory, resulting in a compositional model of inheritance that is directly applicable to object-oriented languages. Novel applications of inheritance revealed by the model are illustrated to show that inheritance has wider significance beyond object-oriented class inheritance. Constraints induced by self-reference and inheritance are investigated using type theory and yield a formal characterization of abstract classes and a demonstration that the subtype relation is a direct consequence of the basic mechanism of inheritance. The model is proven equivalent to the operational semantics of inheritance embodied by the interpreters of object-oriented languages like Smalltalk. Concise descriptions of inheritance behavior in several object-oriented languages, including Smalltalk, Beta, Simula, and Flavors, are presented in a common framework that facilitates direct comparison of their features.

We have improved the performance of the Mach 3.0 operating system by redesigning its internal thread and interprocess communication facilities to use continuations as the basis for control transfer. Compared to previous versions of Mach 3.0, our new system consumes 85% less space per thread. Cross-address space remote procedure calls execute 14% faster. Exception handling runs over 60% faster. In addition to improving system performance, we have used continuations to generalize many control transfer optimizations that are common to operating systems, and have recast those optimizations in terms of a single implementation methodology. This paper describes our experiences with using continuations in the Mach operating system. 1 Introduction We have achieved significant improvements in the performance of the Mach 3.0 operating system kernel [Accetta et al. 86] by redesigning it to use continuations as the basis for control transfers between execution contexts. In our system, a thread b...

We give a brief account of the discoveries of continuations and related concepts by, A. Van Wijngaarden , A. W. Mazurkiewicz , F. L. Morris , C. P. Wadsworth , J. H. Morris , M. J. Fischer , and S. K. Abdali.

The last few years have seen a renewed interest in continuations for expressing advanced control structures in programming languages, and new models such as Abstract Continuations have been proposed to capture these dimensions. This article investigates an alternative formulation, exploiting the latent expressive power of the standard continuation-passing style (CPS) instead of introducing yet other new concepts. We build on a single foundation: abstracting control as a hierarchy of continuations, each one modeling a specific language feature as acting on nested evaluation contexts. We show how iterating the continuation-passing conversion allows us to specify a wide range of control behavior. For example, two conversions yield an abstraction of Prologstyle backtracking. A number of other constructs can likewise be expressed i...

. Any multiprocessing facility must include three features: elementary exclusion, data protection, and process saving. While elementary exclusion must rest on some hardware facility (e.g., a test-and-set instruction), the other two requirements are fulfilled by features already present in applicative languages. Data protection may be obtained through the use of procedures (closures or funargs), and process saving may be obtained through the use of the catch operator. The use of catch, in particular, allows an elegant treatment of process saving. We demonstrate these techniques by writing the kernel and some modules for a multiprocessing system. The kernel is very small. Many functions which one would normally expect to find inside the kernel are completely decentralized. We consider the implementation of other schedulers, interrupts, and the implications of these ideas for language design. 1. Introduction In the past few years, researchers have made progress in understanding the mecha...

We review the origins of structural operational semantics. The main publication ‘A Structural Approach to Operational Semantics, ’ also known as the ‘Aarhus Notes, ’ appeared in 1981 [G.D. Plotkin, A structural approach to operational semantics, DAIMI FN-19, Computer Science Department, Aarhus University, 1981]. The development of the ideas dates back to the early 1970s, involving many people and building on previous work on programming languages and logic. The former included abstract syntax, the SECD machine, and the abstract interpreting machines of the Vienna school; the latter included the λ-calculus and formal systems. The initial development of structural operational semantics was for simple functional languages, more or less variations of the λ-calculus; after that the ideas were gradually extended to include languages with parallel features, such as Milner’s CCS. This experience set the ground for a more systematic exposition, the subject of an invited course of lectures at Aarhus University; some of these appeared in print as the 1981 Notes. We discuss the content of these lectures and some related considerations such as ‘small state’ versus ‘grand state, ’ structural versus compositional semantics, the influence of the Scott–Strachey approach to denotational semantics, the treatment of recursion and jumps, and static semantics. We next discuss relations with other work and some immediate further development. We conclude with an account of an old, previously unpublished, idea: an alternative, perhaps more readable, graphical presentation of systems of rules for operational semantics.

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We present a process algebra or programming language, based on CCS, which may be used to describe discrete event simulations with parallelism. It has extensions to describe the passing of time and probabilistic choice, either discrete, between a countable number of processes, or continuous to choose a random amount of time to wait. It has a clear operational semantics and we give approaches to denotational semantics given in terms of an algebra of equivalences over processes. It raises questions about when two simulations are equivalent and what we mean by non-determinism in the context of the specification of a simulation. It also exemplifies some current approaches to adding time and probability to process algebras. 1 Introduction Imagine we wish to simulate the behaviour of a complex system with computerised components, such as a telephone network. First, let us look at the implementation of such a complex system. When it is implemented, typically work will start with some type of ...

The foundations of functional programming languages are examined from both historical and technical perspectives. Their evolution is traced through several critical periods: early work on lambda calculus and combinatory calculus, Lisp, Iswim, FP, ML, and modern functional languages such as Miranda ’ and Haskell. The fundamental premises on which