Special Issue on User Interfaces in Theorem Proving: Preface

David Aspinall, Christoph Lüth
2007 Journal of automated reasoning  
Theorem proving is coming of age. While its foundations predate the first computers, and systems have been built since the 1950s, dramatic improvements of proving power and expressivity have been made over the last fifteen years. And like other parts of computing, the complex symbolic manipulations of theorem provers have greatly benefited from the rapid increase in computing power. This means that applications of theorem proving and related methods have now become large, diverse and mature,
more » ... ging from real-world hardware and software verification to the formalisation of complex and deep mathematical proofs. One area that is still very much in need of improvement is interfaces for theorem provers. There is no broad agreement about what makes a good user interface in this area, and little is known about how to bridge the gap between imprecise human interaction and the highly stringent demands of fully formal mathematics. Yet there is universal recognition that interfaces must improve if theorem proving is to become more accessible and productive. Many present systems are unbearably complicated to use and can take months to learn because their interfaces are inadequate for beginning users. Experts are held back too: many interface operations which could significantly enhance productivity are not supported, although they are commonplace in other modern applications. An example operation is searching: instead of carefully structuring data in order to later efficiently retrieve them, nowadays the emphasis has shifted towards flexible and speedy searching in a large shared body of knowledge. Theorem provers ought to provide such search facilities, for theorems, definitions, and proofs. Second, we have the critical question of how proofs are shown to the user: presentations of proof should be readily comprehensible to both author and subsequent readers. Finally, there is the issue of the interaction itself, taking place between the user and prover to help direct proof construction. Here, there is much scope for graphically oriented interfaces with intuitive gestures to supplement or even replace textual interaction. This seems especially possible in restricted problem domains.
doi:10.1007/s10817-007-9075-0 fatcat:ikxjp56qozhmbhqthymb7ntr7a