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.

Floating-point arithmetic is defined by the IEEE-754 standard and has often been formalized. We propose a new Coq formalization based on the bit-level representation of the standard and we prove strong links between this new formalization and a previous high-level one. In this process, we have defined functions for any rounding mode described by the standard. Our library can now be applied to certify both software and hardware. Developing results in those two dramatically different directions, like no other formal development so far, guarantees that nothing was forgotten or poorly specified in our formalization. It also lets us compare our work with the existing bit-level formalizations developed with other proof assistants.

We describe the design and prototype implementation of a combination of theorem prover interface technologies. On one side, we take from Proof General the idea of a prover-independent interaction language and its proposed implementation within the PG Kit middleware architecture. On the other side, we take from IsaWin a sophisticated graphical metaphor using direct manipulation for developing proofs. We believe that the resulting system will provide a powerful, robust and generic environment for developing proofs within interactive proof assistants that also opens the way for studying and implementing new mechanisms for managing interactive proof development. 1

This position paper discusses various issues concerning requirements and design of proof assistant user interfaces (UIs). After a review of some of the difficulties faced by UI projects in academia, it presents a high-level description of proof assistant interaction. This is followed by an exposition of use cases and object identification. Several examples demonstrate the usefulness of these requirement elicitation techniques in the theorem proving domain. The second half of the paper begins with a consideration of the “principle of least effort ” for the design of theorem prover user interfaces. This is followed by a brief review of the “GUI versus text mode ” debate, proposals for better use of GUI facilities and a plea for better support of customisation. The paper ends with a discussion of architecture and system design issues. In particular, it argues for a platform architecture with an extensible set of components and the use of XML protocols for communication between UIs and proof assistant backends.

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