A functional approach presents a fresh perspective on the problem of animation. We present an implementation of a functional animation system written in Haskell, and illustrate how it may be used to create simple and colourful animations.

The Flagship Project1 was a research collaboration between the University of Manchester, Imperial College London and International Computers Ltd. The project was unusual in that it aimed to produce a complete computing system based on a declarative programming style. Three areas of a declarative system were addressed: (1) programming languages and programming environments; (2) the machine architecture and computational models; and (3) the software environment. This overview paper discusses each of these areas, the intention being to present the project as a coherent whole.

In this paper we present an equivalence between TIM, a machine developed to implement non-strict functional programming languages, and the set of Categorical Multi-Combinators, a rewriting system developed with similar aims. These two models of computation at first appear to be quite different, but we show a direct equivalence between them, thereby adding some new structure to the ‘design-space’ of abstract machines for non-strict languages.

Many of the details that a programmer must manage when programming in a procedural language are handled by the implementation in a functional language. In a parallel functional language, we would expect the assignment of processes to processors and the scheduling of processes to be handled by the implementation. The partitioning of a program into processes may be handled by the implementation as well.

We will assume that a parallel functional program may create processes dynamically, and that processes may synchronize in an arbitrary manner. It does not matter whether processes are defined in the source program or generated by the implementation.

On parallel systems where each processor has some local memory, it is common practice not to move processes once they have started to execute. We will show that if each process must be executed on a single processor, then no fully automatic scheduling strategy can ensure good performance.

We also will show that if all processes are sequential processes (i.e. do not contain internal parallelism), and if a process may be moved whenever it resumes execution following synchronization with another process, then good performance can be assured, at least in theory.

We present here a generalization of A-translation to a class of pure type systems. We apply this translation to give a direct proof of the existence of a looping combinator in a large class of inconsistent type systems, a class which includes type systems with a type of all types. This is the first non-automated solution to this problem.

This paper discusses the transformation power of Burstall and Darlington's folding/unfolding system, i.e. what kind of programs can be derived from a given one. A necessary condition of derivability is proved. The notion of inherent complexity of recursive functions in introduced. A bound on efficiency gain by folding/unfolding transformations is obtained for all reasonable computation models. The well-known partial correctness and incompleteness of the system are corollaries of the result. Examples of underivability are given, e.g. binary searching cannot be derived from linear searching, merge sorting cannot be derived from insert sorting.

In 1979, Klop (1980), answering a question raised by Mann in 1972, showed that the extension of λ-calculus with subjective pairing is not confluent. We refer to Klop (1980) and Barendregt (1981, revised 1984) for a perspective. The term presented by Klop to provide a counterexample is fairly simple, but the proof of non-confluence, although intuitively quite simple, involves some technical properties. Among others, a suitable standardization result on derivations in the extended system is needed in the proof. Klop's proof was revisited by Bunder (1985), who seemingly used less technical apparatus than Klop, starting with the same term as Klop. Although Bunder's proof does not explicitly use a standardization result, his proof proceeds internally with some rearrangements of derivations, so that it is fair to say that some standardization technique is present in Bunder (1985).

And Joktan begat Almodad, and Sheleph, and Hazarmaveth, and Jerah, and Handoram, and Uzal, and Diklah, and Obal, and Abimael, and Sheba, and Ophir, and Havilah, and Jobab: all these were the sons of Joktan.

— Genesis 10:26–29