Categories, Allegories, and Circuit Design

Languages based upon binary relations offer an appealing setting for constructing programs from specifications. For example, working with relations rather than functions allows specifications to be more abstract (for example, many programs have a natural specification using the converse operator on relations), and affords a natural treatment of non-determinism in specifications. In this paper we present a novel pictorial interpretation of relational terms as simple pictures of circuits, and a soundness/completeness result that allows relational equations to be proved by pictorial reasoning.

Calculating an Exceptional Machine

In previous work we showed how to verify a compiler for a small language with exceptions. In this article we show how to calculate, as opposed to verify, an abstract machine for this language. The key step is the use of Reynold's defunctionalization, an old program transformation technique that has recently been rejuvenated by the work of Danvy et al.

Proof methods for structured corecursive programs

Corecursive programs produce values of greatest fixpoint types, in contrast to recursive programs, which consume values of least fixpoint types. There are a number of widely used methods for proving properties of corecursive programs, including fixpoint induction, the take lemma, and coinduction. However, these methods are all rather low level, in that they do not exploit the common structure that is often present in corecursive definitions. We argue for a more structured approach to proving properties of corecursive programs. In particular, we show that by writing corecursive programs using a simple operator that encapsulates a common pattern of corecursive definition, we can then use high-level algebraic properties of this operator to conduct proofs in a purely calculational style that avoids the use of inductive or coinductive methods.

Functional Programming With Relations

While programming in a relational framework has much to offer over the functional style in terms of expressiveness, computing with relations is less efficient, and more semantically troublesome. In this paper we propose a novel blend of the functional and relational styles. We identify a class of "causal relations", which inherit some of the bi-directionality properties of relations, but retain the efficiency and semantic foundations of the functional style.

Making Functionality More General

The definition for the notion of a "function" is not cast in stone, but depends upon what we adopt as types in our language. With partial equivalence relations (pers) as types in a relational language, we show that the functional relations are precisely those satisfying the simple equation f = f o fu o f, where "o" and "u" are respectively the composition and converse operators for relations. This article forms part of "A calculational theory of pers as types".

A Relational Derivation of a Functional Program

This article is an introduction to the use of relational calculi in deriving programs. Using the relational caluclus Ruby, we derive a functional program that adds one bit to a binary number to give a new binary number. The resulting program is unsurprising, being the standard $quot;column of half-adders$quot;, but the derivation illustrates a number of points about working with relations rather than with functions.

Report on BCTCS 2005

This report contains edited abstracts from BCTCS 2005, which was held on 22nd to 24th March 2005 in Nottingham, England.

Accurate Step Counting

Starting with an evaluator for a language, an abstract machine for the same language can be mechanically derived using successive program transformations. This has relevance to studying both the space and time properties of programs because these can be estimated by counting transitions of the abstract machine and measuring the size of the additional data structures needed, such as environments and stacks. In this article we use this process to derive a function that accurately counts the number of steps required to evaluate expressions in a simple language.

Journal publishing with Acrobat: the CAJUN project

The publication of material in electronic form should ideally preserve, in a unified document representation, all of the richness of the printed document while maintaining enough of its underlying structure to enable searching and other forms of semantic processing. Until recently it has been hard to find a document representation which combined these attributes and which also stood some chance of becoming a de facto multi-platform standard. This paper sets out experience gained within the Electronic Publishing Research Group at the University of Nottingham in using Adobe Acrobat software and its underlying PDF (Portable Document Format) notation. The CAJUN project1 (CD-ROM Acrobat Journals Using Networks) began in 1993 and has used Acrobat software to produce electronic versions of journal papers for network and CD-ROM dissemination. The paper describes the project's progress so far and also gives a brief assessment of PDF's suitability as a universal document interchange standard.

Separate compilation of structured documents

This paper draws a parallel between document preparation and the traditional processes of compilation and link editing for computer programs. A block-based document model is described which allows for separate compilation of various portions of a document. These portions are brought together and merged by a linker program, called dlink, whose pilot implementation is based on ditroff and on its underlying intermediate code. In the light of experiences with dlink the requirements for a universal object-module language for documents are discussed. These requirements often resemble the characteristics of the intermediate codes used by programming-language compilers but with interesting extra constraints which arise from the way documents are executed .

Adobe's Acrobat -- the Electronic Journal Catalyst?

Adobe's Acrobat software, released in June 1993, is based around a new Portable Document Format (PDF) which offers the possibility of being able to view and exchange electronic documents, independent of the originating software, across a wide variety of supported hardware platforms (PC, Macintosh, Sun UNIX etc.). The principal features of Acrobat are reviewed and its importance for libraries discussed in the context of experience already gained from the CAJUN project (CD-ROM Acrobat Journals Using Networks). This two-year project, funded by two well-known journal publishers, is investigating the use of Acrobat software for the electronic dissemination of journals, on CD-ROM and over networks.

Designing the Spectator Experience

Interaction is increasingly a public affair, taking place in our theatres, galleries, museums, exhibitions and on the city streets. This raises a new design challenge for HCI, questioning how a performer s interaction with a computer experienced is by spectators. We examine examples from art, performance and exhibition design, comparing them according to the extent to which they hide, partially reveal, transform, reveal or even amplify a performerts manipulations. We also examine the effects of these manipulations including movements, gestures and utterances that take place around direct input and output. This comparison reveals four broad design strategies: `secretive,' where manipulations and effects are largely hidden; `expressive,' where they are revealed, enabling the spectator to fully appreciate the performer's interaction; `magical,' where effects are revealed but the manipulations that caused them are hidden; and finally `suspenseful,' where manipulations are apparent, but effects only get revealed when the spectator takes their turn.

A Pyramidal Genetic Algorithm for Multiple-Choice Problems

This paper combines the idea of a hierarchical distributed genetic algorithm with different inter-agent partnering strategies. Cascading clusters of sub-populations are built from bottom up, with higher-level sub-populations optimising larger parts of the problem. Hence, higher-level sub-populations search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. The effects of different partner selection schemes amongst the agents on solution quality are examined for two multiple-choice optimisation problems. It is shown that partnering strategies that exploit problem-specific knowledge are superior and can counter inappropriate (sub-) fitness measurements.

Partnering Strategies for Fitness Evaluation in a Pyramidal Evolutionary Algorithm

This paper combines the idea of a hierarchical distributed genetic algorithm with different inter-agent partnering strategies. Cascading clusters of sub-populations are built from bottom up, with higher-level sub-populations optimising larger parts of the problem. Hence higher-level sub-populations search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. The effects of different partner selection schemes for (sub-)fitness evaluation purposes are examined for two multiple-choice optimisation problems. It is shown that random partnering strategies perform best by providing better sampling and more diversity.