Theories of higher-order must-alias analysis, often under the guise of environment analysis, provide deep behavioral insight. But these theories---in particular those that are most insightful otherwise---can reason about recursion only in limited cases. This weakness is not inherent to the theories but to the frameworks in which they're defined: machine models which thread the heap through evaluation. Since these frameworks allocate each abstract resource in the heap, the constituent theories of environment analysis conflate co-live resources identified in the abstract, such as recursively-created bindings. We present heap fragments as a general technique to allow these theories to reason about recursion in a general and robust way. We instantiate abstract counting in a heap-fragment framework and compare its performance to a precursor entire-heap framework. We also sketch an approach to realizing binding invariants, a more powerful environment analysis, in the heap-fragment framework.

@article{paperbot1127,
  title = {Newly-single and loving it: improving higher-order must-alias analysis with heap fragments},
  author = {Kimball Germane and Jay McCarthy},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {5},
  number = {ICFP},
  year = {2021},
  doi = {10.1145/3473601}
}