Haslbeck, Maximilian P.L.

Lammich, Peter

Separation Logic with Time Credits is a well established method to formally verify the correctness and run-time of algorithms, which has been applied to various medium-sized use-cases. Reﬁnement is a technique in program veriﬁcation that makes software projects of larger scale manageable. Combining these two techniques for the ﬁrst time, we present a methodology for verifying the functional correctness and the run-time analysis of algorithms in a modular way. We use it to verify Kruskal’s minimum spanning tree algorithm and the Edmonds–Karp algorithm for network ﬂow. An adaptation of the Isabelle Reﬁnement Framework [15] enables us to specify the functional result and the run-time behaviour of abstract algorithms which can be reﬁned to more concrete algorithms. From these, executable imperative code can be synthesized by an extension of the Sepref tool [11], preserving correctness and the run-time bounds of the abstract algorithm

Refinement with Time – Refining the Run-time of Algorithms in Isabelle/HOL

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