Laws of Programming for References

We propose a set of algebraic laws for reasoning with sequential imperative programs that use object references like in Java. The theory is based on previous work by adding laws to cope with object references. The incrementality of the algebraic method is fundamental; with a few exceptions, existing laws for copy semantics are entirely reused, as they are not affected by the proposed laws for reference semantics. As an evidence of relative completeness, we show that any program can be transformed, through the use of our laws, to a normal form which simulates it using an explicit heap with copy semantics.