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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Vydáno v:Proceedings - Symposium on Logic in Computer Science
Hlavní autoři: Sattler, Christian, Wärn, David
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: 2024
Témata:
descent
homotopy type theory
inductive types
integers
Matematik
Mathematical sciences
natural numbers
ISBN:9798400706608
ISSN:1043-6871
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Shrnutí: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