Realizability at Work: Separating Two Constructive Notions of Finiteness

Marc Bezem, Thierry Coquand, Keiko Nakata, Erik Parmann, Michael Wagner
2018 Types for Proofs and Programs  
We elaborate in detail a realizability model for Martin-Löf dependent type theory with the purpose to analyze a subtle distinction between two constructive notions of finiteness of a set A. The two notions are: (1) A is Noetherian: the empty list can be constructed from lists over A containing duplicates by a certain inductive shortening process; (2) A is streamless: every enumeration of A contains a duplicate.
doi:10.4230/lipics.types.2016.6 dblp:conf/types/BezemC0P16 fatcat:t22m6u4wpfhjndcfqunsynckwy