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 and deletion 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. We examine the runtime of all
operations indirectly by reproducing results of the logarithmic
relationship between height and the number of nodes. The results are
discussed in greater detail in the corresponding Bachelor's
Add implementation and proof of correctness of imperative deletion operations.
Further add the option to export code to OCaml.