Dependent Type Theory • Before we started Lean, we have studied different theorem provers: ACL2, Agda, Automath, Coq, HOL, HOL Light, Isabelle, Mizar, PVS. • Dependent Type Theory is really beautiful

Isabelle/ZF, Metamath, Mizar; simple type theory: HOL4, HOL Light, Isabelle/HOL; dependent type theory: Agda, Coq, Lean, Matita, PVS; Lisp-like first-order logic: ACL2. For a history of proof assistants and you will find it easy to move to an- other proof assistant based on dependent type theory, such as Agda or Coq, or to a system based on simple type theory, such as HOL4 or Isabelle/HOL. We assume that you

previous page) #eval val Current research programs, including work on observational type theory and cubical type theory, aim to extend type theory in ways that permit reductions for casts involving function