A Verified Implementation of B+-Trees in Isabelle/HOL

08/18/2022

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by   Niels Mündler, et al.

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In this paper we present the verification of an imperative implementation of the ubiquitous B+-tree data structure in the interactive theorem prover Isabelle/HOL. The implementation supports membership test, insertion and range queries with efficient binary search for intra-node navigation. The imperative implementation is verified in two steps: an abstract set interface is refined to an executable but inefficient purely functional implementation which is further refined to the efficient imperative implementation.