Adaptation of living mathematical documents

Abstract. Notations are central for understanding mathematical dis-course. 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 pub-lication 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 math-ematical documents. Mathematical notations can be defined declara-tively. 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 exam-ples. 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.