Development and user testing of new user interfaces for mathematics and programming tools

This dissertation discusses the development and testing, with human participants, of several novel user interfaces for interactive theorem provers. Interactive theorem provers are software tools used to precisely describe and correctly reason about mathematical ideas and, in particular, to create and check what are often very complex mathematical proofs. One important application is the development of proofs about software so as to ensure higher levels of reliability in critical (e.g. aviation, automotive, financial, medical) software than are possible with software testing alone. Improved user interfaces for interactive theorem provers are important for allowing more widespread, efficient, and effective use of these tools. In addition, most of the user interface ideas generated in the context of interactive theorem provers can be generalized for use with other applications, especially programming environments, and present new directions for human-computer interaction more broadly.