A Verified Imperative Implementation of B-Trees

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