Object-Z is an extension of the formal specification language Z, augmenting the class concept as a structuring facility. The paper introduces and discusses a structural mapping system from Object-Z to the programming language C++, and reports on its implementation on Unix. The structural mapping translates an Object-Z specification consisting of classes into class interfaces of C++ such as data members and prototypes of member functions. Thus it is not intended as a code generation system, but rather as a tool for analyzing specification (including syntax and type checking) and for aiding a software developer in obtaining code. Through the implementation of the mapping system several language features of Object-Z and C++ concerning object-orientation are clarified.>

Categorical combinators have been derived from the study of categorical semantics of lambda calculus, and it has been found that they may be used in implementation of functional languages. In this paper categorical combinators are extended so that functions with multiple arguments can be directly handled, thus making them more suitable for practical computation. A rewriting system named ${\operatorname{CCLM}}\beta $ is formulated for these combinators. This system naturally corresponds to the type-free $\lambda \beta $-calculus. The relationship between these two systems is established, and as a result of this, the Church–Rosser property of ${\operatorname{CCLM}}\beta $ is proved. A similar relationship is also established between the original ${\operatorname{CCL}}\beta $ by Curien and the type-free $\lambda \beta $-calculus with product. Finally the embedding theorem of ${\operatorname{CCLM}}\beta $ into ${\operatorname{CCL}}\beta $ is shown.

Abstract There have been proposed and used many programming concepts for realizing interprocess communication and synchronization, and two fundamental categories among them are variable sharing (e.g. semaphores) and message passing (signals, input/output in CSP and redezvous in Ada). The aim of this paper is to investigate the relationship between these two mechanisms, and in particular, program transformation between them. We here propose a transformation method between parallel programs written in each of these two, which uses transformation schemes named monitor transformations. We exhibit the method by showing through a chain of program transformations the equivalence of two versions of a parallel algorithm called dynamic sorting array.

Butler [6] gave recurrence relations for computing the number Nr(n) of r-valued (r ≥ 2) switching functions of n variables realizable by a cascaded network of n - 1 r-valued cells. The cascades are assumed to have a fixed-input variable assignment. In this correspondence similar recurrence relations are presented for the number Mr(n) of such cascade realizable functions that depend on all n input variables. In particular, for the ternary valued case, explicit formulas for N3(n) and M3(n) are given. Some asymptotic properties of Nr(n) and Mr(n) are also derived, which show that their growth is asymptotically exponential as n increases.

A spectrum is an algebraic representation of a set of “switching elements” each of which carries out an operation in a definite time lag. The notion of functional completeness ($\sim $-completeness) in the family of spectra was introduced by V. B. Kudryavcev and A. Nozaki. In this paper we investigate the maximal incomplete spectra and thus give a new effective criterion for a spectrum to be functionally complete.