Department of Computer Science and Technology

Technical reports

Conversion of notations

Silas S. Brown

June 2004, 159 pages

This technical report is based on a dissertation submitted November 2003 by the author for the degree of Doctor of Philosophy to the University of Cambridge, St John’s College.

DOI: 10.48456/tr-591


Music, engineering, mathematics, and many other disciplines have established notations for writing their documents. The effectiveness of each of these notations can be hampered by the circumstances in which it is being used, or by a user’s disability or cultural background. Adjusting the notation can help, but the requirements of different cases often conflict, meaning that each new document will have to be transformed between many versions. Tools that support the programming of such transformations can also assist by allowing the creation of new notations on demand, which is an under-explored option in the relief of educational difficulties.

This thesis reviews some programming tools that can be used to manipulate the tree-like structure of a notation in order to transform it into another. It then describes a system “4DML” that allows the programmer to create a “model” of the desired result, from which the transformation is derived. This is achieved by representing the structure in a geometric space with many dimensions, where the model acts as an alternative frame of reference.

Example applications of 4DML include the transcription of songs and musical scores into various notations, the production of specially-customised notations to assist a sight-impaired person in learning Chinese, an unusual way of re-organising personal notes, a “website scraping” system for extracting data from on-line services that provide only one presentation, and an aid to making mathematics and diagrams accessible to people with severe print disabilities. The benefits and drawbacks of the 4DML approach are evaluated, and possible directions for future work are explored.

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BibTeX record

  author =	 {Brown, Silas S.},
  title = 	 {{Conversion of notations}},
  year = 	 2004,
  month = 	 jun,
  url = 	 {},
  institution =  {University of Cambridge, Computer Laboratory},
  doi = 	 {10.48456/tr-591},
  number = 	 {UCAM-CL-TR-591}