A trace model for pointers and objects

Object-oriented programs [Dahl, Goldberg, Meyer] are notoriously prone to the following kinds of error, which could lead to increasingly severe problems in the presence of tasking 1. Following a null pointer 2. Deletion of an accessible object 3. Failure to delete an inaccessible object 4. Interference due to equality of pointers 5. Inhibition of optimisation due to fear of (4) Type disciplines and object classes are a great help in avoiding these errors. Stronger protection may be obtainable with the help of assertions, particularly invariants, which are intended to be true before and after each call of a method that updates the structure of the heap. This note introduces a mathematical model and language for the formulation of assertions about objects and pointers, and suggests that a graphical calculus [Curtis, Lowe] may help in reasoning about program correctness. It deals with both garbage-collected heaps and the other kind. The theory is based on a trace model of graphs, using ideas from process algebra; and our development seeks to exploit this analogy as a unifying principle.