2016/04/05 by Denis Firsov, Tarmo Uustalu, Niccolò Veltri
Computer Science · #cs.LO #cs.PL
paper · pdf · doi:10.4204/eptcs.207.4
published as EPTCS 207, 2016, pp. 76-88 · In Proceedings MSFP 2016, arXiv:1604.00384
arxiv created 2016/04/05 · arxiv updated 2016/04/06
In constructive mathematics, several nonequivalent notions of finiteness exist. In this paper, we continue the study of Noetherian sets in the dependently typed setting of the Agda programming language. We want to say that a set is Noetherian, if, when we are shown elements from it one after another, we will sooner or later have seen some element twice. This idea can be made precise in a number of ways. We explore the properties and connections of some of the possible encodings. In particular, we show that certain implementations imply decidable equality while others do not, and we construct counterexamples in the latter case. Additionally, we explore the relation between Noetherianness and other notions of finiteness.