CERTIFICATE OF APPROVAL

Interactive theorem provers are software tools that help users create machine-checked proofs. Although difficult to use, they have been playing an important role in the effort to create highly reliable software. I present several novel user interface ideas for interactive theorem provers, generalizable to other mathematics and programming tools. Prototypes tailored to the Coq interactive theorem prover were developed and tested in an experiment with human participants. The results show promising directions for making interactive theorem provers easier to use. ii This dissertation discusses the development and testing, with human partic-ipants, 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 o