Formal Specification and Verification of JDK’s Identity Hash Map Implementation

Hash maps are a common and important data structure in efficient algorithm implementations. Despite their wide-spread use, real-world implementations are not regularly verified. In this paper, we present the first case study of the \IHM class in the Java JDK. We specified its behavior using the Java Modeling Language (JML) and proved correctness for the main insertion and lookup methods with \key, a semi-interactive theorem prover for JML-annotated Java programs. Furthermore, we report how unit testing and bounded model checking can be leveraged to find a suitable specification more quickly. We also investigated where the bottlenecks in the verification of hash maps lie for \key by comparing required automatic proof effort for different hash map implementations and draw conclusions for the choice of hash map implementations regarding their verifiability