Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals

Jasmin Christian Blanchette, Mathias Fleury and Dmitriy Traytel

12 November 2016

Abstract

This Isabelle/HOL formalization introduces a nested multiset datatype and defines Dershowitz and Manna's nested multiset order. The order is proved well founded and linear. By removing one constructor, we transform the nested multisets into hereditary multisets. These are isomorphic to the syntactic ordinals—the ordinals can be recursively expressed in Cantor normal form. Addition, subtraction, multiplication, and linear orders are provided on this type.
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@article{Nested_Multisets_Ordinals-AFP,
  author  = {Jasmin Christian Blanchette, Mathias Fleury and Dmitriy Traytel},
  title   = {Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals},
  journal = {Archive of Formal Proofs},
  month   = November,
  year    = 2016,
  note    = {\url{http://isa-afp.org/entries/Nested_Multisets_Ordinals.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
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