Towards semantic mathematical editing

Abstract

Currently, there exists a big gap between formal computer-understandable mathematics and informal mathematics, as written by humans. When looking more closely, there are two important subproblems: making documents written by humans at least syntactically understandable for computers, and the formal verification of the actual mathematics in the documents. In this paper, we will focus on the first problem.For the time being, most authors use ▪, ▪, or one of its graphical front-ends in order to write documents with many mathematical formulas. In the past decade, we have developed an alternative wysiwyg system GNU ▪, which is not based on ▪. All these systems are only adequate for visual typesetting and do not carry much semantics. Stated in the MathML jargon, they concentrate on presentation markup, not content markup.In recent versions of ▪, we have started to integrate facilities for the semantic editing of formulas. In this paper, we will describe these facilities and expand on the underlying motivation and design choices.To go short, we continue to allow the user to enter formulas in a visually oriented way. In the background, we continuously run a packrat parser, which attempts to convert (potentially incomplete) formulas into content markup. As long as all formulas remain sufficiently correct, the editor can then operate both on a visual or semantic level, independently of the low-level representation being used.An important related topic, which will also be discussed at length, is the automatic correction of syntax errors in existing mathematical documents. In particular, the syntax corrector that we have implemented enables us to upgrade existing documents and test our parsing grammar on various books and papers from different sources. We will provide a detailed analysis of these experiments.