Natural numbers from integers
Paper i 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

Författare

Christian Sattler

Chalmers, Data- och informationsteknik, Computing Science

David Wärn

Chalmers, Data- och informationsteknik, 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,

Ämneskategorier

Algebra och logik

Energiteknik

DOI

10.1145/3661814.3662129

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Senast uppdaterat

2024-07-30