Erwin Engeler was born in Schaffhausen on 13 February 1930 a citizen of Wagenhausen (Thurgovia). He attended school in Diessenhofen (TG) and Schaffhausen and looks back on his various schools warmly as having provided a conducive environment. His schoolwork also left him time for other activities. For one, he pursued a career as a boy scout which he crowned by attaining the position of Rover Commissary of all Thurgovia. For another, he was an avid client of the municipal library of Schaffhausen. One book which he found there was Hilbert-Bernays' ‘Grundlagen der Mathematik’. One wonders what Erwin would have said if a soothsayer had told him that the author's own copy would one day be passed on to him by the late Bernays' family.

This paper exhibits accurate encodings of the λ-calculus in the π-calculus. The former is canonical for calculation with functions, while the latter is a recent step (Milner et al. 1989) towards a canonical treatment of concurrent processes. With quite simple encodings, two λ-calculus reduction strategies are simulated very closely; each reduction in λ-calculus is mimicked by a short sequence of reductions in π-calculus. Abramsky's precongruence of applicative bisimulation (Abramsky 1989) over λ-calculus is compared with that induced by the encoding of the lazy λ-calculus into π-calculus; a similar comparison is made for call-by-value λ-calculus.

Unfold/fold transformations have been used in logic programming for some years to transform programs into more efficient ones. We describe recent work on the extent to which these transformations produce programs which are equivalent to the original one. Various notions of equivalence are considered: same success set; finite failure set; least Herbrand model; completion. This is used to illustrate the rather unsatisfactory relationship between logic programming and logic shown by the wide variety of different declarative semantics proposed for logic programs.

This paper uses concepts from sheaf theory to explain phenomena in concurrent systems, including object, inheritance, deadlock, and non-interference, as used in computer security. The approach is very; general, and applies not only to concurrent object oriented systems, but also to systems of differential equations, electrical circuits, hardware description languages, and much more. Time can be discrete or continuous, linear or branching, and distribution is allowed over space as well as time. Concepts from categpru theory help to achieve this generality: objects are modelled by sheaves; inheritance by sheaf morphisms; systems by diagrams; and interconnection by diagrams of diagrams. In addition, behaviour is given by limit, and the result of interconnection by colimit. The approach is illustrated with many examples, including a semantics for a simple concurrent object-based programming language.

The concept of abstract data types (ADTs) has emerged in the last fifteen years or so as one of the major programming design tools, with the emphasis on modular construction of large-scale programe. ADTs provide the means for seperating how data objects may be used from the different ways in which they actually are, or might be, implemented. A foundation for the theory of compputation with ADTs must provide answers to such questions as: What are ADTs and how may they be specified? What does it mean to implement an ADT? How may we construct new ADTs from old ones? What does it mean to compute with ADTs? This paper is devoted to a new and rather general, constructively based approach to these questions.

A constructive characterization is given of the isomorphisms which must hold in all models of the typed lambda calculus with surjective pairing. Using the close relation between closed Cartesian categories and models of these calculi, we also produce a characterization of those isomorphisms which hold in all CCC's. Using the correspondence between these calculi and proofs in intuitionistic positive propositional logic, we thus provide a characterization of equivalent formulae of this logic, where the definition of equivalence of terms depends on having “invertible” proofs between the two terms. Work of Rittri (1989), on types as search keys in program libraries, provides an interesting example of use of these characterizations.