Algebraic Reasoning for Object-Oriented Programming

We present algebraic laws for a language similar to a subset of sequential Java that includes inheritance, recursive classes, dynamic binding, access control, type tests and casts, assignment, but no sharing. These laws are proved sound with respect to a weakest precondition semantics. We also show that they are complete in the sense that they are sufficient to reduce an arbitrary program to a normal form substantially close to an imperative program; the remaining object-oriented constructs could be further eliminated if our language had recursive records. This suggests that our laws are expressive enough to formally derive behaviour preserving program transformations; we illustrate that through the derivation of provably-correct refactorings.