Symbolic backwards execution (SBE) is a useful variation on standard forward symbolic evaluation; it allows a symbolic evaluation to start anywhere in the program and proceed by executing in reverse to the program start. SBE brings goal-directed reasoning to symbolic evaluation and has proven effective in e.g. automated test generation for imperative languages. In this paper we define DDSE, a novel SBE which operates on a functional as opposed to imperative language; furthermore, it is defined as a natural extension of a backwards-executing interpreter. We establish the soundness of DDSE and define a test generation algorithm for this toy language. We report on an initial reference implementation to confirm the correctness of the principles.

@article{PalmerPSW20,
  title = {Higher-order demand-driven symbolic evaluation},
  author = {Zachary Palmer and Theodore Park and Scott Smith and Shiwei Weng},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {4},
  number = {ICFP},
  year = {2020},
  doi = {10.1145/3408984}
}