  We describe a way to represent computable functions between coinductive types
as particular transducers in type theory. This generalizes earlier work on
functions between streams by P. Hancock to a much richer class of coinductive
types. Those transducers can be defined in dependent type theory without any
notion of equality but require inductive-recursive definitions. Most of the
properties of these constructions only rely on a mild notion of equality
(intensional equality) and can thus be formalized in the dependently typed
language Agda.
