Coalgebras in functional programming and type theory

This is a survey article on the use of coalgebras in functional programming and type theory. It presents the basic theory underlying the implementation of coinductive types, families and predicates. It gives an overview of the application of corecursive methods to the study of general recursion, formal power series, tabulations of functions on inductive data. It also sketches some advanced topics in the study of the solutions to non-guarded corecursive equations and the design of non-standard type theory.