In section two of chapter three we proved a representation theorem stating that a domain D is, up to isomorphism, the ideal completion of its compact elements, Dc. An ordered set having the properties derivable for Dc was christened a cusl or conditional upper semilattice with least element. It turns out that a somewhat weaker version of cusl's, namely precusVs, serves just as well as a representation of domains and is better suited for the purposes of the last section of this chapter, which deals with solutions of domain equations to identity. In this chapter we sketch, without detailed proof, the basic results known on the representation of domains in this sense.

We begin with two additional representations of domains, information systems and formal spaces. Both have their origins in the works of D. S. Scott, Scott [1982] and [1982a], where the latter were presented in a less general form as neighbourhood systems. The versions presented here differ at some points from those of Scott for reasons to be explained later. Each of these three representations has its own particular point of departure. Cusl's and precusl's, by virtue of their emphasis on an ordering, give an algebraic representation. Information systems, based upon a relation of entailment, give a logical representation in analogy with the corresponding notion in formal logical systems. Finally, formal spaces, through their emphasis upon a relation of (formal) inclusion between neighbourhoods, provide a topological representation.

A domain is a structure modelling the notion of approximation and of computation. A computation performed using an algorithm proceeds in discrete steps. After each step there is more information available about the result of the computation. In this way the result obtained after each step can be seen as an approximation of the final result. This final result may be reached after finitely many steps as, for example, when computing the greatest common divisor of two positive integers using the Euclidean algorithm. However, it may also be the case that a computation never stops, in which case the final result is the sequence of approximations obtained from each step in the computation. The latter situation occurs by necessity when computing on infinite objects such as real numbers. Thus an appropriate model of approximation can provide a good model of computation.

To be somewhat more technically precise, a domain is a structure having one binary relation ⊑, a partial order, with the intended meaning that x ⊑y just in case x is an approximation of y or y contains at least as much information as x. We also require that a domain should include a least element modelling no information. This is not necessary, but is useful for establishing the existence of fixed points. To model infinite computations we require a domain to be complete in the sense that each increasing sequence of approximations should be represented by an element in the domain, that is, should have a supremum.

The class of partial recursive functions is the mathematical abstraction of the class of partial functions computable by an algorithm. In this chapter we present them in the form of the μ-recursive functions. We then state some basic results, the main motivation being to set the stage for the theory of effective domains. Finally we show that the partial μ-recursive functions can be obtained from some simple initial functions using substitution and the fixed point theorem for computable functional. This illuminates the central role of taking fixed points and supports the claim of Chapter 1 that the function computed by an algorithm or a program is the least fixed point of a computable functional.

Section 9.1 Partial Recursive Functions

An algorithm for a class K of problems is a method or procedure which can be described in a finite way (a finite set of instructions) and which can be followed by someone or something to yield a computation solving each problem in K. The computation should proceed in discrete steps. For a given problem in K the procedure should say exactly how to perform each step in the computation. After performing a step, the procedure should prescribe how to do the next step. This next step must only depend on the problem and on the then existing situation, that is what has been done during previous steps.

The development of graphical user interfaces for interactive applications is subject to a series of well-known problems which could be relevant of the domain of visual design. This typically includes the problem of placing aesthetically interaction objects (IO) according to principles applied in placement strategies. This paper first reviews the problem of IO placement and shows the rationale for the most significant placement strategies found today. It then tries to compare six such strategies along several dimensions and mathematical relationships with respect to three points of view: the designer's point of view, the human factors expert's point of view, and the user's point of view.

Keywords: arrangement, dimensioning, interaction object, localization, interaction object placement, placement strategy, visual design.

Introduction

The problem of placement concerns the spatial position of interaction objects (IO) such as edit box, radio button, list box, … with respect to visual elements in a screen layout. Effective placement can be achieved through a particular placement strategy involving a certain amount of visual techniques such as proximity, alignment, separate reference, centering, and conformity. For instance, Galitz suggests a placement strategy where IOs should be placed according to their nature:

In this paper, the placement is defined as the description of a composite IO (e.g. a form container widget) for displaying IOs to be placed relatively to one another. Composite IOs generally allow IOs to resize themselves as the composite resizes.

Personal computer users typically manage hundreds of directories and thousands of files with hierarchically structured file managers, plus archaic cluttered-desktop window managers, and iconic representations of applications. These users must deal with the annoying overhead of window housekeeping and the greater burden of mapping their organizational roles onto the unnecessarily rigid hierarchy. An alternate approach is presented, Personal Role Manager (PRM), to structure the screen layout and the interface tools to better match the multiple roles that individuals have in an organization. Each role has a vision statement, schedule, hierarchy of tasks, set of people, and collection of documents.

Keywords: personal role manager, desktop metaphor, graphic user interface, coordination, computer-supported cooperative work (CSCW).

Introduction

The transition from the first generation command line interfaces (such as DOS 3 or UNIX) to second generation point-and-click graphical user interfaces (GUIs) was accompanied by an important metaphorical shift. The older systems required users to understand computerdomain concepts such as executable binary software (the .EXE or .COM files), file naming rules, and hierarchical directories. The designers of second generation GUIs presented users with more meaningful metaphors and supported direct manipulation interactions (Shneiderman, 1982). The graphical user interface offered a desktop with applications represented as icons, documents organized into folders, and even a trashcan as an affordance for the delete action. This visual representation of the world of action made objects and actions visible, permitted rapid, incremental and reversible actions, and emphasized pointing and clicking instead of keyboarding.

The current third generation approach emphasizes a “docu-centric” design (Microsoft's Object Linking and Embedding or Apple's OpenDoc Architecture), unified suites of software, and “information at your fingertips” through hypertext linking.

This volume contains the full papers and invited papers from the 1994 conference of the British HCI Group (a specialist group of the British Computer Society). It is a partial record of a more extensive conference that includes tutorials, panels, short papers, posters and demonstrations.

Human-Computer Interaction has been consolidating over the last few years. As a result, many recent conferences have tended to be bland, without really high points or really low points. The invited papers are forward looking and avoid blandness in that way. There are, however, many forward looking full papers. Moreover, the 1994 conference will be remembered as one that moved HCI forward in some areas, rather than just documented its current state within the established areas.

Proceedings Structure

The proceedings begin with the invited papers. This apart, the usual compromises of programme structure have not been carried forward into these proceedings. The full papers in this volume have been reorganised into broad topics. As ever in HCI, these topics are not disjoint and some papers could have easily have gone in one section as another. Readers interested in specific topics are thus advised to read through the full contents to avoid missing papers that may be of interest to them.

The second group of papers covers all stages of interactive systems development (properly iterated of course) from requirements capture and specification, through to evaluation. There are also papers on specific design issues, including application areas such as computer-assisted learning.

The third group of papers is the largest, and covers design knowledge at all levels of abstraction in interactive systems, from low level presentation to high level metaphors.

The embodiment of computers in desktop workstations has had a tremendous impact on the field of HCI. Now that mice and graphics displays are everywhere, the workstation defines the frontier between the computer world and the real world. We spend a lot of time and energy transferring information between those two worlds. This could be reduced by better integrating the real world with the computer world. This article describes two approaches to this integration: Mediaspaces, which allow people to communicate through an audio, video and computer environment, and Augmented Reality, which adds computational power to real world objects. The argument is made that the success of these approaches lies in their ability to build on fundamental human skills, namely the ability to communicate with other people and the ability to interact with objects in the real world.

Keywords: mediaspace, augmented reality, multimedia, video, virtual reality, paper interface, gesture input, metaphor, paradigm.

Introduction

Over the last decade, computers have evolved from mainframes to networks of personal computers and workstations. The range of users and uses of computers has expanded dramatically. Today, a computer is perceived more as an appliance than as a ‘machine’. A key aspect of this evolution has been, and still is, the development of the field of Human-Computer Interaction. HCI has complemented, and sometimes driven, the evolution of the technology to make computer systems easier to use by a wider variety of users in a larger number of contexts.

As most researchers in HCI know, this picture is a bit idyllic and much still needs to be done to improve the scope and usability of computers.