The Lean theorem prover (system description). 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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References in zbMATH (referenced in 12 articles , 2 standard articles )

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  1. Angiuli, Carlo; Harper, Robert: Meaning explanations at higher dimension (2018)
  2. Blanchette, Jasmin Christian; Bouzy, Aymeric; Lochbihler, Andreas; Popescu, Andrei; Traytel, Dmitriy: Friends with benefits. Implementing corecursion in foundational proof assistants (2017)
  3. Carter, Nathan C.; Monks, Kenneth G.: A web-based toolkit for mathematical word processing applications with semantics (2017)
  4. Ford, Ian: Semantic representation of general topology in the Wolfram language (2017)
  5. Fulton, Nathan; Mitsch, Stefan; Bohrer, Brandon; Platzer, André: Bellerophon: tactical theorem proving for hybrid systems (2017)
  6. Nagashima, Yutaka; Kumar, Ramana: A proof strategy language and proof script generation for Isabelle/HOL (2017)
  7. van Doorn, Floris; von Raumer, Jakob; Buchholtz, Ulrik: Homotopy type theory in Lean (2017)
  8. Bright, Curtis; Ganesh, Vijay; Heinle, Albert; Kotsireas, Ilias; Nejati, Saeed; Czarnecki, Krzysztof: mathcheck2: a SAT+CAS verifier for combinatorial conjectures (2016)
  9. Cockx, Jesper; Devriese, Dominique; Piessens, Frank: Eliminating dependent pattern matching without K (2016)
  10. Selsam, Daniel; de Moura, Leonardo: Congruence closure in intensional type theory (2016)
  11. von Raumer, Jakob: Formalizing double groupoids and cross modules in the Lean theorem prover (2016)
  12. de Moura, Leonardo; Kong, Soonho; Avigad, Jeremy; van Doorn, Floris; von Raumer, Jakob: The Lean theorem prover (system description) (2015)