Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals. 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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References in zbMATH (referenced in 3 articles )
Showing results 1 to 3 of 3.
- Schlichtkrull, Anders; Blanchette, Jasmin; Traytel, Dmitriy; Waldmann, Uwe: Formalizing Bachmair and Ganzinger’s ordered resolution prover (2020)
- Biendarra, Julian; Blanchette, Jasmin Christian; Bouzy, Aymeric; Desharnais, Martin; Fleury, Mathias; Hölzl, Johannes; Kunčar, Ondřej; Lochbihler, Andreas; Meier, Fabian; Panny, Lorenz; Popescu, Andrei; Sternagel, Christian; Thiemann, René; Traytel, Dmitriy: Foundational (co)datatypes and (co)recursion for higher-order logic (2017)
- Blanchette, Jasmin Christian; Fleury, Mathias; Traytel, Dmitriy: Nested multisets, hereditary multisets, and syntactic ordinals in Isabelle/HOL (2017)