We present SL♢, a Separation Logic that allows controlling the heap space consumption of a program in the presence of dynamic memory allocation and garbage collection. A user of the logic works with space credits, a resource that is consumed when an object is allocated and produced when a group of objects is logically deallocated, that is, when the user is able to prove that it has become unreachable and therefore can be collected. To prove such a fact, the user maintains pointed-by assertions that record the immediate predecessors of every object. Our calculus, SpaceLang, has mutable state, shared-memory concurrency, and code pointers. We prove that SL♢ is sound and present several simple examples of its use.

@article{paperbot1576,
  title = {A separation logic for heap space under garbage collection},
  author = {Jean-Marie Madiot and François Pottier},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {6},
  number = {POPL},
  year = {2022},
  doi = {10.1145/3498672}
}