We present a novel strongest-postcondition-style calculus for quantitative reasoning about non-deterministic programs with loops. Whereas existing quantitative weakest pre allows reasoning about the value of a quantity after a program terminates on a given initial state, quantitative strongest post allows reasoning about the value that a quantity had before the program was executed and reached a given final state. We show how strongest post enables reasoning about the flow of quantitative information through programs. Similarly to weakest liberal preconditions, we also develop a quantitative strongest liberal post. As a byproduct, we obtain the entirely unexplored notion of strongest liberal postconditions and show how these foreshadow a potential new program logic - partial incorrectness logic - which would be a more liberal version of O'Hearn's recent incorrectness logic.

@article{paperbot1528,
  title = {Quantitative strongest post: a calculus for reasoning about the flow of quantitative information},
  author = {Linpeng Zhang and Benjamin Lucien Kaminski},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {6},
  number = {OOPSLA1},
  year = {2022},
  doi = {10.1145/3527331}
}