Efficient lambda encodings for Mendler-style coinductive types in Cedille

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.