Correctness of Java Card Method Lookup via Logical Relations

We formalise the Java Card bytecode optimisation from class file to CAP file format as a set of constraints between the two formats, and define and prove its correctness. Java Card bytecode is formalised as an abstract operational semantics, which can then be instantiated into the two formats. The optimisation is given as a logical relation such that the instantiated semantics are observably equal. The proof has been automated using the Coq theorem prover.