# Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL

@inproceedings{Blanchette2017NestedMH, title={Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL}, author={Jasmin Christian Blanchette and Mathias Fleury and Dmitriy Traytel}, booktitle={FSCD}, year={2017} }

We present a collection of formalized results about finite nested multisets, developed using the Isabelle/HOL proof assistant. The nested multiset order is a generalization of the multiset order that can be used to prove termination of processes. Hereditary multisets, a variant of nested multisets, offer a convenient representation of ordinals below 0. In Isabelle/HOL, both nested and hereditary multisets can be comfortably defined as inductive datatypes. Our formal library also provides…

## 12 Citations

### Type-Theoretic Approaches to Ordinals

- MathematicsArXiv
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. In a constructive setting, no concrete formulation of ordinal numbers can simultaneously have all the properties one might be interested in; for example, being able to calculate limits of sequences…

### Connecting Constructive Notions of Ordinals in Homotopy Type Theory

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This work considers three different notions of ordinals in homotopy type theory, and shows how they relate to each other: a notation system based on Cantor normal forms, a refined notion of Brouwer trees, and wellfounded extensional orders.

### Formalization of logical calculi in Isabelle/HOL

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A formal framework for propositional satifisfiability with the conflict-driven clause learning (CDCL) procedure using the Isabelle/HOL proof assistant is developed and the inclusion of rules for forget and restart and the refinement approach are included.

### Formalization of Logic in the Isabelle Proof Assistant

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This thesis describes formalizations in Isabelle of several logics as well as tools built upon these, including the Natural Deduction Assistant (NaDeA), which is a tool for teaching first-order logic that allows users to build proofs in natural deduction.

### Formalizing the metatheory of logical calculi and automatic provers in Isabelle/HOL (invited talk)

- Computer ScienceCPP
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This paper describes and reflects on three verification subprojects to which I contributed: a first-order resolution prover, an imperative SAT solver, and generalized term orders for λ-free higher-order logic.

### Foundational (Co)datatypes and (Co)recursion for Higher-Order Logic

- Computer ScienceFroCoS
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We describe a line of work that started in 2011 towards enriching Isabelle/HOL’s language with coinductive datatypes, which allow infinite values, and with a more expressive notion of inductive…

### Three equivalent ordinal notation systems in cubical Agda

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### Formalizing Bachmair and Ganzinger’s Ordered Resolution Prover

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We present an Isabelle/HOL formalization of the first half of Bachmair and Ganzinger’s chapter on resolution theorem proving, culminating with a refutationally complete first-order prover based on…

### A Mechanizable First-Order Theory of Ordinals

- Computer ScienceTABLEAUX
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A first-order theory of ordinals without resorting to set theory is presented, which is implemented in the KeY program verification system and used to prove termination of a Java program computing the Goodstein sequences.

### Verified Progress Tracking for Timely Dataflow

- Computer Science
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This work modeled the progress tracking protocol as a combination of two independent transition systems in the Isabelle/HOL proof assistant and identified abstract assumptions on dataflow programs that are sufficient for safety and were not previously formalized.

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