Title: Formalising and Proving Incremental Mutation Testing Abstract: Proponents of Agile development processes claim that adhering to Agile principles leads to the delivery of high quality code in evolutionary increments. Con fidence in resulting systems is mostly gained through the use of unit test suites, entrusted to catch regressions as soon as they occur. Consequently, the system can only be as trustworthy as its tests, meaning that measurements of the tests' quality is crucial. Whilst mutation testing has been proposed as a means of uncovering test suite defects, it has not been widely adopted in the industry; mainly due to its computational expense and manual e ffort required by developers investigating unkilled mutants. To make mutation testing a ffordable, we propose incremental mutation testing - a variation of mutation testing which leverages the iterative nature of agile development by limiting the scope of mutant generation to sections of code which have changed since the last mutation run. This talk describes how incremental mutation testing has been formalised proven to be sound.