The Taming of the Rew: A Type Theory with Computational Assumptions
summary
Adds Rewriting Type Theory to dependently typed systems so user-supplied rewrite rules run automatically during typechecking instead of requiring explicit equality proofs, and proves conditions that keep the system sound. It gives a concrete triangle property (parallel-reduction based) check that is modular and automatable to ensure global confluence and thus preserve subject reduction, formalizes proofs in MetaCoq, and ships an Agda implementation with the confluence checker that users can enable and use.
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