Flexible Encoding of Mathematics on the Computer

Abstract

Abstract. This paper reports on refinements and extensions to the MathLang framework that add substantial support for natural language text. We show how the extended framework supports multiple views of mathematical texts, including natural language views using the exact text that the mathematician wants to use. Thus, MathLang now supports the ability to capture the essential mathematical structure of mathematics written using natural language text. We show examples of how arbitrary mathematical text can be encoded in MathLang without needing to change any of the words or symbols of the texts or their order. In particular, we show the encoding of a theorem and its proof that has been used by Wiedijk for comparing many theorem prover representations of mathematics, namely the irrationality of √ 2 (originally due to Pythagoras). We encode a 1960 version by Hardy and Wright, and a more recent version by Barendregt.

Computerising Mathematical Text

“…The Text and Symbol aspect (TSa) [Kamareddine et al, 2004b;Kamareddine et al, 2007a;Lamar, 2011] allows integrating normal typesetting and authoring software with the mathematical structure represented with CGa. TSa allows weaving together usual mathematical authoring representations such as L A T E X, XML, or T E X MACS with CGa data.…”

Assisted Proof Document Authoring

“…Théry's approach [22] bridges the gap by defining an XML format for manually annotating statements in mathematical papers to link them to formal counterparts, wherein proofs must be supplied; consistency is checked in a prover. Similar approaches include Weak Type Theory [15], MathLang [14]), or the Dialog project [5]. In a sense in the opposite direction, Kohlhase [17] works on the existing mathematical corpus of L A T E X papers and tries to capture their semantic content automatically with additional markup.…”

Liability in software engineering

“…The final objective is to allow contract drafters to manipulate statements either in natural language or in formal language while maintaining the links between the two parts and the consistency of the whole document. This extension is based on our previous work on the links between mathematical texts and natural language explanations ( [15]).…”

“…Note that we do not consider the ordering of Send and Receive trace items for the sake of conciseness. This ordering is not necessary to express the liabilities presented in Section 2 15. Space considerations prevent us from presenting this systematic derivation here.…”