Why Judgmental Equality Fails Under Defunctionalization

This article examines the tension between judgmental equality and defunctionalization in dependently typed languages. While α-β and η-equality are standard in many systems, they fail to hold once functions are transformed into data constructors. The paper proposes a middle-ground solution: assigning globally unique names to comatches to preserve equality under transformation, while rejecting general η-equality to avoid logical inconsistencies. The result is a type system closed under defunctionalization and refunctionalization without sacrificing soundness.