A Verified Imperative Implementation of B-Trees

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Abstract

In this work, we use the interactive theorem prover Isabelle/HOL to verify an imperative implementation of the classical B-tree data structure invented by Bayer and McCreight [ACM 1970]. The implementation supports set membership, insertion, deletion, iteration and range queries with efficient binary search for intra-node navigation. This is accomplished by first specifying the structure abstractly in the functional modeling language HOL and proving functional correctness. Using manual refinement, we derive an imperative implementation in Imperative/HOL. We show the validity of this refinement using the separation logic utilities from the Isabelle Refinement Framework . The code can be exported to the programming languages SML, OCaml and Scala. This entry contains two developments:

B-Trees: This formalisation is discussed in greater detail in the corresponding Bachelor's Thesis.
B+-Trees:: This formalisation also supports range queries and is discussed in a paper published at ICTAC 2022.

Change history: [2022-08-16]: Added formalisations of B+-Trees

License

BSD License

History

May 2, 2021: Add implementation and proof of correctness of imperative deletion operations. Further add the option to export code to OCaml.

Topics

Session BTree

Depends on

The Imperative Refinement Framework