Restoring Natural Language as a Computerised Mathematics Input Method

  • Authors:

  • Fairouz Kamareddine;Robert Lamar;Manuel Maarek;J. B. Wells

  • Affiliations:

  • ULTRA group, Heriot-Watt University,;ULTRA group, Heriot-Watt University,;ULTRA group, Heriot-Watt University,;ULTRA group, Heriot-Watt University,

  • Venue:
  • Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
  • Year:
  • 2007

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Abstract

Methods for computerised mathematics have found little appeal among mathematicians because they call for additional skills which are not available to the typical mathematician. We herein propose to reconcile computerised mathematics to mathematicians by restoring natural language as the primary medium for mathematical authoring. Our method associates portions of text with grammatical argumentation roles and computerises the informal mathematical style of the mathematician. Typical abbreviations like the aggregation of equations a = b c, are not usually accepted as input to computerised languages. We propose specific annotations to explicate the morphology of such natural language style, to accept input in this style, and to expand this input in the computer to obtain the intended representation (i.e., a = b and b c). We have named this method syntax souringin contrast to the usual syntax sugaring. All results have been implemented in a prototype editor developed on top of ${\rm\kern-.15em T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}$ $_{{\rm {\sc MACS}}}$ as a GUI for the core grammatical aspect of MathLang, a framework developed by the ULTRA group to computerise and formalise mathematics.