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. 1 On the way to a mathematical vernacular for computers Mathematicians now use computer software for a variety of tasks: typing mathematical texts, performing calculation, analyzing theories, verifying proofs. Software tools like

FoC is a computer algebra library with a strong emphasis on formal certification of its algorithms. We present in this article our work on the link between the FoC language and OMDoc, an emerging XML standard to represent and share mathematical contents. On the one hand, we focus on the elaboration of the documentation system FoCDoc. After an analysis of an OMDoc approach of the documentation we present our own XML implementation (FoCDoc) and how we generate, from a FoC program, documentation files in HTML (MathML), LaTEX and OMDoc. On the other

syntax. The MathLang abstract syntax (that is to say the way we represent MathLang data) is de ned in the following sections. The abstract syntax will only be used in the WTC The Backus-Naur form (BNF) is a metasyntax to formally describe languages.