Internal and Observational Parametricity for Cubical Agda
summary
An implementation called Agda --bridges adds internal parametricity to cubical Agda, successfully type checks the cubical library and mechanizes key results including the relativity theorem. The paper identifies a sufficient condition, the structure relatedness principle (SRP), proves a general parametricity theorem for SRP-satisfying types, and ships a modular library (ROT) to build those equivalences. The system trades internal expressive power for manual proof work versus parametricity translations, and currently lacks automation and support for iterated parametricity.
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