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In the calculus of dependent lambda eliminations (CDLE), it is possible todefine inductive datatypes via lambda encodings that feature constant-timedestructors and a course-of-values induction scheme. This paper begins toaddress the missing derivations for the dual, coinductive types. Our derivationutilizes new methods within CDLE, as there are seemingly fundamentaldifficulties in adapting previous known approaches for deriving inductivetypes. The lambda encodings we present implementing coinductive types featureconstant-time constructors and a course-of-values corecursion scheme.Coinductive type families are also supported, enabling proofs for many standardcoinductive properties such as stream bisimulation. All work is mechanicallyverified by the Cedille tool, an implementation of CDLE.

Efficient lambda encodings for Mendler-style coinductive types in Cedille