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The \(p\)-adic integers as final coalgebra. (English) Zbl 06484977
Paiva, Valeria (ed.) et al., Logic, language, information, and computation. 22nd international workshop, WoLLIC 2015, Bloomington, IN, USA, July 20–23, 2015. Proceedings. Berlin: Springer (ISBN 978-3-662-47708-3/pbk; 978-3-662-47709-0/ebook). Lecture Notes in Computer Science 9160, 189-199 (2015).
Summary: We express the classical \(p\)-adic integers \(\hat{\mathbb {Z}}_p\), as a metric space, as the final coalgebra to a certain endofunctor. We realize the addition and the multiplication on \(\hat{\mathbb {Z}}_p\) as the coalgebra maps from \(\hat{\mathbb {Z}}_p\times \hat{\mathbb {Z}}_p\).
For the entire collection see [Zbl 1319.03010].
MSC:
03B70 Logic in computer science
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