Natural numbers from integers
Paper in proceeding, 2024

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.

homotopy type theory

inductive types

descent

integers

natural numbers

Author

Christian Sattler

Chalmers, Computer Science and Engineering (Chalmers), Computing Science

David Wärn

Chalmers, Computer Science and Engineering (Chalmers), Computing Science

Proceedings - Symposium on Logic in Computer Science

10436871 (ISSN)

67
9798400706608 (ISBN)

39th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2024
Tallinn, Estonia,

Subject Categories

Algebra and Logic

Energy Engineering

DOI

10.1145/3661814.3662129

More information

Latest update

7/30/2024