Year: 2024
Type: preprint
Abstract: We propose an enhancement to inductive types and records in a dependent type theory, namely (co)conditions. With a primitive interval type, conditions generalize the cubical syntax of higher inductive types in homotopy type theory, while coconditions generalize the cubical path type. (Co)conditions are also useful without an interval type. The duality between conditions and coconditions is presented in an interesting way: The elimination principles of inductive types with conditions can be internalized with records with coconditions and vice versa. However, we do not develop the metatheory of conditions and coconditions in this paper. Instead, we only present the type checking.
Source: arXiv (Cornell University)
Authors: Zhang, Tesla, Isaev, Valery
Institution: Carnegie Mellon University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4398794884