Two tricks to trivialize higher-indexed families

Tesla Zhang

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arXiv · 2309.14187

Two tricks to trivialize higher-indexed families

Tesla Zhang

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Abstract

The conventional general syntax of indexed families in dependent type theories follow the style of "constructors returning a special case", as in Agda, Lean, Idris, Coq, and probably many other systems. Fording is a method to encode indexed families of this style with index-free inductive types and an identity type. There is another trick that merges interleaved higher inductive-inductive types into a single big family of types. It makes use of a small universe as the index to distinguish the original types. In this paper, we show that these two methods can trivialize some very fancy-looking indexed families with higher inductive indices (which we refer to as higher indexed families).

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Tesla Zhang. 2023-09-25. Two tricks to trivialize higher-indexed families. https://arxiv.org/abs/2309.14187

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