From a Speci cation to an Equivalence Proof in Object-Oriented Parallelism

We investigate the use of a TLA speciication for modeling and proving parallelization within an object-oriented language. Our model is based on Eiiel== a parallel extension of Eiiel, where sequential programs can be reused for parallel or concurrent programming with very minor changes. We want to prove that both versions of a given program (sequential and parallel) are equivalent with respect to some properties. This article presents a description in TLA+ that captures the general Eiiel== execution model, and, as a case-study, speciies a program (a binary search tree) in both its sequential and parallel form. We then prove a property that demonstrates a behavioral equivalence for the two versions.