Abstract. We extended Isabelle/HOL with a pair of definitional commands for datatypes and codatatypes. They support mutual and nested (co)recursion through well-behaved type constructors, including mixed recursion-corecursion, and are complemented by syntaxes for introducing primitive (co)recursive functions and by a general proof method for reasoning coinductively. As a case study, we ported Isabelle's Coinductive library to use the new commands, eliminating the need for tedious ad hoc constructions.

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We describe a proof of the Central Limit Theorem that has been formally verified in the Isabelle proof assistant. Our formalization builds upon and extends Isabelle's libraries for analysis and measure-theoretic probability. The proof of the theorem uses characteristic functions, which are a kind of Fourier transform, to demonstrate that, under suitable hypotheses, sums of random variables converge weakly to the standard normal distribution. We also discuss the libraries and infrastructure that supported the formalization, and reflect on some of the lessons we have learned from the effort.