An algebra of pictures is described that is sufficiently powerful to denote the structure of a well-known Escher woodcut, Square Limit. A decomposition of the picture that is reasonably faithful to Escher’s original design is given. This illustrates how a suitably chosen algebraic specification can be both a clear description and a practical implementation method. It also allows us to address some of the criteria that make a good algebraic description.

Animation is a temporally continuous phenomenon, but is typically programmed in terms of a discrete sequence of changes. The use of discreteness serves to accommodate the machine that is presenting an animation, rather than the person modeling an animation with the help of a computer. Using a continuous model of time for animation allows for natural specification, avoiding some artificial details, but is difficult to implement with generality, robustness and efficiency. This paper presents and motivates continuous modeled animation, and sketches out a naive functional implementation for it. An examination of some of the practical problems with this implementation leads to several alternate representations, all of which have difficulties in themselves, some quite subtle. We hope that the insights and techniques discussed in this paper lead to still better representations, so that animation may be specified in natural terms without significant loss of performance.

While interactive multimedia animation is a very compelling medium, few people are able to express themselves in it. There are too many low-level details that have to do not with the desired content—e.g., shapes, appearance and behavior—but rather how to get a computer to present the content. For instance, behaviors like motion and growth are generally gradual, continuous phenomena. Moreover, many such behaviors go on simultaneously. Computers, on the other hand, cannot directly accommodate either of these basic properties, because they do their work in discrete steps rather than continuously, and they only do one thing at a time. Graphics programmers have to spend much of their effort bridging the gap between what an animation is and how to present it on a computer. We propose that this situation can be improved by a change of language, and present Fran, synthesized by complementing an existing declarative host language, Haskell, with an embedded domain-specific vocabulary for modeled animation. As demonstrated in a collection of examples, the resulting animation descriptions are not only relatively easy to write, but also highly composable.

This paper explores the idea of reactivity in multimedia, and proposes systems which can react to continuously-evolving behaviours as well as to more traditional discrete events. The idea is presented in a scenario as well as in a number of small programming examples.

The development of complex, multi-user, interactive systems is a difficult process that requires both a rapid iterative approach, and the ability to reason carefully about system designs. This thesis argues that a combination of declarative prototyping and formal specification provides a suitable way of satisfying these requirements. The focus of this thesis is on the development of software tools for prototyping interactive systems. In particular, it uses a declarative approach, based on the functional programming paradigm. This thesis makes two contributions. The most significant contribution is the presentation of FranTk, a new Graphical User Interface language, embedded in the functional language Haskell. It is suitable for prototyping complex, concurrent, multi-user systems. It allows systems to be built in a high level, structured manner. In particular, it provides good support for specifying real-time properties of such systems. The second contribution is a mechanism that allows a formal specification to be derived from a high level FranTk prototype. The approach allows this to be done automatically. This specification can then be checked, with tool support, to verify some safety properties about a system. To avoid the state space explosion problem that would be faced when verifying an entire system, we focus on partial verification. This concentrates on key areas of a design: in particular this means that we only derive a specification from parts of a prototype. To demonstrate the scalability of both the prototyping and verification approaches, this thesis uses a series of case studies including a multi-user design rationale editor and a prototype data-link