  In the calculus of dependent lambda eliminations (CDLE), it is possible to
define inductive datatypes via lambda encodings that feature constant-time
destructors and a course-of-values induction scheme. This paper begins to
address the missing derivations for the dual, coinductive types. Our derivation
utilizes new methods within CDLE, as there are seemingly fundamental
difficulties in adapting previous known approaches for deriving inductive
types. The lambda encodings we present implementing coinductive types feature
constant-time constructors and a course-of-values corecursion scheme.
Coinductive type families are also supported, enabling proofs for many standard
coinductive properties such as stream bisimulation. All work is mechanically
verified by the Cedille tool, an implementation of CDLE.
