A Formalization of Opaque Definitions for a Dependent Type Theory

Paper in proceeding, 2025

Definitions allow for reuse of code. Typical type-checkers for dependently typed programming languages automatically unfold definitions, but excessive unfolding can lead to types that are hard to read, or performance issues. Such problems can be mitigated through the use of opaque definitions, which give the programmer control over when unfolding is allowed. However, subject reduction fails to hold for certain designs. We study the metatheory of a type theory with opaque definitions, inspired by Agda. We give typing and reduction rules and show that the type theory enjoys properties like subject reduction, normalization, consistency, and decidability of conversion. The development is fully mechanized in Agda.