We present a generic mediator, called PlatΩ, between text-editors and proof assistants. PlatΩ aims at integrated support for the development, publication, formalization, and verification of mathematical documents in a natural way as possible: The user authors his mathematical documents with a scientific WYSIWYG text-editor in the informal language he is used to, that is a mixture of natural language and formulas. These documents are then semantically annotated preserving the textual structure by using the flexible, parameterized proof language which we present. From this informal semantic representation PlatΩ automatically generates the corresponding formal representation for a proof assistant, in our case Ωmega. The primary task of PlatΩ is the maintenance of consistent formal and informal representations during the interactive development of the document.

Abstract. This paper introduces Proof General Kit, a framework for software components tailored to interactive proof development. The goal of the framework is to enable flexible environments for managing formal proofs across their life-cycle: creation, maintenance and exploitation. The framework connects together different kinds of component, exchanging messages using a common communication infrastructure and protocol called PGIP. The main channel connects provers to displays. Provers are the back-end interactive proof engines and displays are components for interacting with the user, allowing browsing or editing of proofs. At the core of the framework is a broker middleware component which manages proof-in-progress and mediates between components. 1 Introducing Proof General Kit The use of interactive machine proof is becoming more widespread, and larger and more complex formalisations are being undertaken in application areas such as hardware or software verification, and formalisation of mathematics, even up

This article discusses the integration of the authoring of a mathematical document with the formalisation of the mathematics contained in that document. To achieve this we have started the development of a Coq plugin for the TEXmacs scientific editor, called tmEgg. TEXmacs allows the wysiwyg editing of mathematical documents, much in the style of LATEX. Our plugin allows to integrate into a TEXmacs document mathematics formalised in the Coq proof assistant: formal definitions, lemmas and proofs. The plugin is still under development. Its main current hallmark is a document-consistent interaction model, instead of the calculator-like approach usual for TEXmacs plugins. This means that the Coq code in the TEXmacs document is interpreted as one (consistent) Coq file: executing a Coq command in the document means to execute it in the context (state) of all the Coq commands before it. 1

Abstract. In only few decades, computers have changed the way we approach documents. Throughout history, mathematicians and philosophers had clarified the relationship between mathematical thoughts and their textual and symbolic representations. We discuss here the consequences of computer-based formalisation for mathematical authoring habits and we present an overview of our approach for computerising mathematical texts. 1.

• UI keeps proof script for batch replay • Linear processing, commands become “locked” • Focus on mechanics of proving – user-friendly? H. Gast Asynchronous Proof Document Management (UITP ’08, 22.8.2008) 2Document-Centered View • Metaphor “proof document” • User edits human-readble a proof document • Prover checks the consistency • Assisted authoring [2] • Isar as human-readable proof language [8] • Backflow: Assistance by prover for editing • Processing linear • PlatΩ approach [6] • Near-natural, text-book style input language • Front-end parses structure & computes structural diff • Triggers necessary (re-)checking by Ωmega prover H. Gast Asynchronous Proof Document Management (UITP ’08, 22.8.2008) 3Asynchronous Proof Processing [7]