MathLang Translation to Isabelle Syntax

Abstract. Converting mathematical documents from a human-friendly natural language to a form that can be readily processed by computers is often a tedious, manual task. Translating between varied computerised forms is also a difficult problem. MathLang, a system of methods and representations for computerising mathematics, tries to make these tasks more tractable by breaking the translation down into manageable portions. This paper presents a method for creating rules to translate documents from MathLang’s internal representation of mathematics to documents in the language of the Isabelle proof assistant. It includes a set of example rules applicable for a particular document. The resulting documents are not completely verifiable by Isabelle, but they represent a point to which a mathematician may take a document without the involvement of an Isabelle expert.

A change-oriented architecture for mathematical authoring assistance

The computer-assisted authoring of mathematical documents using a scientific text-editor requires new mathematical knowledge management and transformation techniques to organize the overall workflow of anassistance system like the ΩMEGAsystem.The challenge is that, throughout the system, various kinds of given and derived knowledge units occur in different formats and with different dependencies. If changes occur in these pieces of knowledge, they need to be effectively propagated. We present a Change-Oriented Architecture for mathematical authoring assistance. Thereby, documents are used as interfaces and the components of the architecture interact by actively changing the interface documents and by reacting on changes. In order to optimize this style of interaction, we present two essential methods in this thesis. First, we develop an efficient method for the computation of weighted semantic changes between two versions of a document. Second, we present an invertible grammar formalism for the automated bidirectional transformation between interface documents. The presented architecture provides an adequate basis for the computer-assisted authoring of mathematical documents with semantic annotations and a controlled mathematical language