Adaptation of Notations in Living Mathematical Documents
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Notations are central for understanding mathematical discourse. Readers would like to read notations that transport the meaning well and prefer notations that are familiar to them. Therefore, authors optimize the choice of notations with respect to these two criteria, while at the same time trying to remain consistent over the document and their own prior publications. In print media where notations are ﬁxed at publication time, this is an over-constrained problem. In living documents notations can be adapted at reading time, taking reader preferences into account. We present a representational infrastructure for notations in living mathematical documents. Mathematical notations can be deﬁned declaratively. Author and reader can extensionally deﬁne the set of available notation deﬁnitions at arbitrary document levels, and they can guide the notation selection function via intensional annotations. We give an abstract speciﬁcation of notation deﬁnitions and the ﬂexible rendering algorithms and show their coverage on paradigmatic examples. We show how to use this framework to render OpenMath and Content-MathML to Presentation-MathML, but the approach extends to arbitrary content and presentation formats. We discuss prototypical implementations of all aspects of the rendering pipeline
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