This paper explores some methodological and pragmatic aspects of the design of the human-computer interface. In particular, it argues that many interactive dialogues can be formulated conveniently and clearly using notations based upon sequences of definitions ("definitive notations"). Such a notation is an implicit ingredient in the "spread-sheet" packages which have recently become so popular in business applications. To apply similar principles to more complex tasks, such as CAD applications, requires abstraction and generalisation, and poses challenging technical problems.
The three sections of the paper respectively consider: background and motivation, elementary definitive notations (illustrated by an unconventional desk calculator), and complex definitive notations (with particular reference to the design of ARCA, a definitive notation for the interactive description and manipulation of combinatorial diagrams).