On Garbage and Program Logic

Abstract

Garbage collection relieves the programmer of the burden of managing dynamically allocated memory, by providing an automatic way to reclaim unneeded storage. This eliminates or lessens program errors that arise from attempts to access disposed memory, and generally leads to simpler programs. One might therefore expect that reasoning about programs in garbage collected languages would be much easier than in languages where the programmer has more explicit control over memory. But existing program logics are based on a low level view of storage that is sensitive to the presence or absence of unreachable cells, and Reynolds has pointed out that the Hoare triples derivable in these logics are even incompatible with garbage collection. We present a semantics of program logic assertions based on a view of the heap as finite, but extensible; this is for a logical language with primitives for dereferencing pointer expressions. The essential property of the semantics is that all propositions are invariant under operations of adding or removing garbage cells; in short, they are garbage insensitive. We use the assertion language to formulate notions of partial and total correctness for a small programming language, and provide logical characterizations of two natural notions of observational equivalence between programs.KeywordsProgram LogicPartial StateTotal StateOperational SemanticGarbage CollectionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.