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Abstract. Lean is a new open source theorem prover being developed at Microsoft Research and Carnegie Mellon University, with a small trusted kernel based on dependent type theory. It aims to bridge the gap between interactive and automated theorem proving, by situating automated tools and methods in a framework that supports user interaction and the construction of fully specified axiomatic proofs. Lean is an ongoing and long-term effort, but it already provides many useful components, integrated development environments, and a rich API which can be used to embed it into other systems. It is currently being used to formalize category theory, homotopy type theory, and abstract algebra. We describe the project goals, system architecture, and main features, and we discuss applications and continuing work.

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Recent clinical studies suggest that the efficacy of hormone therapy for prostate cancer depends on the characteristics of individual patients. In this paper, we develop a computational framework for identifying patient-specific androgen ablation therapy schedules for postponing the potential cancer relapse. We model the population dynamics of heterogeneous prostate cancer cells in response to androgen suppression as a nonlinear hybrid automaton. We estimate personalized kinetic parameters to characterize patients and employ δ-reachability analysis to predict patient-specific therapeutic strategies. The results show that our methods are promising and may lead to a prognostic tool for prostate cancer therapy.