Author(s): Holt CM
Abstract: Visual language design is driven by interaction between syntax and semantics: changing the way a concept is represented affects the ease with which it can be understood and related to other concepts. The use of lines, boxes, and icons to augment text affects intuitions about operations and properties. This paper is concerned with characterising syntax by developing a ""natural"" algebra that tries to reflect it. The nature of boxes gives rise to two kinds of operations, enclosure and adjointness, that can be related to form a ring, which can be embedded in a vector space. Lines connecting boxes can represent an operation that is related to adjointness, but which is more general in arity and the orientation of the edges that can be linked. The decoration of lines and boxes with emblems provides a facility for representing higher-order operations.
Keywords: data, flow, program specification, visual languages