Formal specification of a small example based on GKS

Abstract

Implicit regeneration is a fundamental concept of the Graphical Kernel System (GKS), an IS0 International Standard, hut it is difficult to understand as presented in the English language specification of GKS. Consequently, it is a good example to use in determining whether formal specification techniques can be used effectively to describe and clarify graphics concepts of this kind. The problem is first motivated informally with a description of GKS concepts and terminology. A formal specification of implicit regeneration using a simplified model is then presented, and the notation that is used for its formalization (VDM) is described. Finally, properties of implicit regeneration are formulated and the specification is proved to conform to these properties. This demonstrates the applicability of formal specification to graphics software, because a sufficiently precise description of a complicated concept is provided that enables its consistency to be checked against an intuitive understanding of the concept as derived from the GKS document.

An OBJ3 functional specification for boundary representation

“…Some important topics seem to remain outside their framework. This is the case for man-mat hine communication, a major problem in interactive computer graphics, where formal methods must be develop following [25,8]. Similarly, transition from specifications to safe and efficient implementations does not have today any complete solution [2], even using high-level programming languages, such as object oriented ones.…”

“…Formal specification methods [14,19,4,33] are widely recognized as a helpful tool to define sound data objects and operations, and their use is growing in computer graphics [25,8,21,29]. In solid modeling, where models become more and more sophisticated and abstract, there is surprisingly few attempts of this kind (see however [1,9]).…”

Formal Methods and Standards - An Idiosyncratic View

“…The need to accommodate storage tubes and vector refresh displays (which have quite different updating characteristics) led to some complex mechanisms in the standard for controlling when picture changes would take place and when the picture would be redrawn. The earliest work constructed a simple model of the GKS system and investigated the circumstances under which equivalent pictures would be produced [11]. The model was expressed in VDM.…”

Semi-automatic transformation from formal specifications to programs

“…Some work on the translation of the executable part of VDM specications into programs has been reported in [12] and [6]. The issue of transforming implicit VDM operation specications, the major feature of VDM, has 3 The work is supported in part by Hiroshima City University not been addressed. The same problem also exists for other model-based formal methods such as Z [14] and B-Method [1].…”

“…The same problem also exists for other model-based formal methods such as Z [14] and B-Method [1]. As such formal methods become well known in academia and industry due to their welldeveloped mathematical notational and proof rules for specications based on formal predicate logic and set theory [3,13,2], research on the automatic transformation of formal specications to programs will help promote the application of formal methods in both academia and industry.…”