Researchers Revisit Codata, Dependent Types, and the Limits of the Expression Problem

This article surveys foundational and modern work on codata types, dependent type theory, and the expression problem, situating a new approach that leverages defunctionalization and refunctionalization to establish a syntactic duality between data and codata. It explores modular proofs, dependent pattern and copattern matching, definable Π- and Σ-types, and the trade-offs of working within an inconsistent dependent type theory—prioritizing type soundness while challenging conventional semantic assumptions.