The Taming of the Rew: a Type Theory with Computational Assumptions Jesper Cockx, Nicolas Tabareau, Théo Winterhalter
The Taming of the Rew: A Type Theory with Computational Assumptions Jesper Cockx, Nicolas Tabareau, Théo Winterhalter To cite this version: Jesper Cockx, Nicolas Tabareau, Théo Winterhalter. The Taming of the Rew: A Type Theory with Computational Assumptions. Proceedings of the ACM on Programming Languages, ACM, 2020, POPL 2021, 10.1145/3434341. hal-02901011v2 HAL Id: hal-02901011 https://hal.archives-ouvertes.fr/hal-02901011v2 Submitted on 8 Oct 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The Taming of the Rew A Type Theory with Computational Assumptions JESPER COCKX, TU Delft, Netherlands NICOLAS TABAREAU, Inria, France THÉO WINTERHALTER, Inria, France Dependently typed programming languages and proof assistants such as Agda and Coq rely on computation to automatically simplify expressions during type checking. To overcome the lack of certain programming primitives or logical principles in those systems, it is common to appeal to axioms to postulate their existence. However, one can only postulate the bare existence of an axiom, not its computational behaviour. Instead, users are forced to postulate equality proofs and appeal to them explicitly to simplify expressions, making axioms dramatically more complicated to work with than built-in primitives.
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