Natural numbers from integers

In homotopy type theory, a natural number type is freely generated by an element and an endomorphism. Similarly, an integer type is freely generated by an element and an automorphism. Using only dependent sums, identity types, extensional dependent products, and a type of two elements with large eli...

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Bibliographic Details
Published in:Proceedings - Symposium on Logic in Computer Science
Main Authors: Sattler, Christian, Wärn, David
Format: Conference Proceeding
Language:English
Published: 2024
Subjects:
descent
homotopy type theory
inductive types
integers
Matematik
Mathematical sciences
natural numbers
ISBN:9798400706608
ISSN:1043-6871
Online Access:Get full text
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Summary:In homotopy type theory, a natural number type is freely generated by an element and an endomorphism. Similarly, an integer type is freely generated by an element and an automorphism. Using only dependent sums, identity types, extensional dependent products, and a type of two elements with large elimination, we construct a natural number type from an integer type. As a corollary, homotopy type theory with only ς, Id, Π, and finite colimits with descent (and no universes) admits a natural number type. This improves and simplifies a result by Rose.
ISBN:9798400706608
ISSN:1043-6871
DOI:10.1145/3661814.3662129