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020 - Programming Paradigms and the Semantics of Geometric Symbols


The development of interactive computing has inspired interest in

  • the use of geometric symbols rather than textual messages
  • the presentation of active environments rather than passive documents.


Two fundamental technical problems respectively associated with these concerns are:

  • developing computer representations that reflect the semantics of geometric data
  • constructing comprehensible state-based models for environments.


Our main thesis is that there is a strong connection between these apparently separate problems. We shall argue that

  • the semantics of a geometric object has to be understood with reference to its potential transformations,
  • the effective representation of such transformations requires more powerful and expressive state-based computer models than have yet been developed.



There is no record of the talk associated with the above abstract, but the model developed to illustrate the principal theme appears as cabinetdigitBeynon1990 in the EM projects archive.

For a more extended discussion and development of the semantic issues raised by this illustrative example, see cabinetdigitpresBeynon2007