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.

This paper presents a denotational model of inheritance. The model is based on an intuitive motivation of inheritance as a mechanism for deriving modified versions of recursive definitions. The correctness of the model is demonstrated by proving it equivalent to an operational semantics of inheritance based upon the method lookup algorithm of object-oriented languages.

. 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...

Traditionally, circuits with combinational loops are found only in asynchronous designs. However, combinational loops can also be useful for synchronous circuit design. Combinational loops can arise from high-level language behavioral compiling, and can be used to reduce circuit size. We provide a symbolic algorithm that detects if a sequential circuit with combinational loops exhibits standard synchronous behavior, and if so, produces an equivalent circuit without combinational loops. We present applications to hardware and software synthesis from the Esterel synchronous programming language.

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.

Following our own experience developing a concurrent object-oriented language as well of that of other researchers, we have identb))1 several key problems intT design of a concurrency model compat1}+ wit t he mechanisms ofobject}+4gTT1t programming. We propose an approacht language design in which anexecut1}+ notcut describingte behaviour ofcommunicatTT agent isext+T5+ bysynt4g81 pat4g8 tt encapsulat languageconste1T)+ Weindicat how various language models can beaccommodat5T and how mechanisms such as inherit}+5 can be modeled. Finally, weint6+TT1 a newnotb( oft ypest hat charact(1}T6 concurrent object in t1+6 oft15+ ext5g41}T visible behaviour. 1.

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A tension in language design has been between simple semantics on the one hand, and rich possibilities for side-effects, exception handling and so on on the other. The introduction of monads has made a large step towards reconciling these alternatives. First proposed by Moggi as a way of structuring semantic descriptions, they were adopted by Wadler to structure Haskell programs, and now offer a general technique for delimiting the scope of effects, thus reconciling referential transparency and imperative operations within one programming language. Monads have been used to solve long-standing problems such as adding pointers and assignment, inter-language working, and exception handling to Haskell, without compromising its purely functional semantics. The course will introduce monads, effects and related notions, and exemplify their applications in programming (Haskell) and in compilation (MLj). The course will present typed metalanguages for monads and related categorica...

The knowledge as to whether a software component is testable or not is important to the software engineering process: a program that is not easily testable may have to go through several iterations of program and test redesign. In this paper, we formally investigate the meaning of software testability. We define a new concept, domain testability, by applying the concepts of observability and controllability to software. Observability refers to the ease of determining if specified inputs affect the outputs; controllability refers to the ease of producing a specified output from a specified input. Observability and controllability properties are already used for assessing the testability of hardware components. A domain testable program is observable and controllable: it does not exhibit any test input-output inconsistencies. We discuss the domain testability properties of several programs that have been presented in the literature, and investigate the observability and controllability...