Correctness Proof on an Algorithm to Insert Memory Reuse Commands into ML-like

We present a static analysis that estimates reusable memory cells and a sourcelevel transformation that adds explicit memory-reuse commands into the program text. For benchmark ML programs, our analysis and transformation achieves the memory reuse ratio from 5.2% to 91.3% and reduces the memory peak from 0.0% to 71.9%. The small-ratio cases are for programs that have too prevalent sharings among memory cells. For other cases, our experimental results are encouraging in terms of accuracy and cost. Major features of our analysis are: (1) poly-variant analysis of functions by parameterization for the argument heap cells; (2) use of multiset formulas in expressing the sharings and partitionings of heap cells; (3) deallocations conditioned by dynamic flags that are passed as extra arguments to functions; (4) individual heap cell as the granularity of explicit memory-free. Our analysis and transformation is fully automatic.