Verifying a copying garbage collector in GP 2

Abstract

Cheney’s copying garbage collector is regarded as a challenging test case for formal approaches to the verification of imperative programs with pointers. The algorithm works for possibly cyclic data structures with unrestricted sharing which cannot be handled by standard separation logics. In addition, the algorithm relocates data and requires establishing an isomorphism between the initial and the final data structure of a program run. We present an implementation of Cheney’s garbage collector in the graph programming language GP 2 and a proof that it is totally correct. Our proof is shorter and less complicated than comparable proofs in the literature. This is partly due to the fact that the GP 2 program abstracts from details of memory management such as address arithmetic. We use sound proof rules previously employed in the verification of GP 2 programs but treat assertions semantically because current assertion languages for graph transformation cannot express the existence of an isomorphism between initial and final graphs.