Janis Voigtländer. Proving correctness via free theorems: The case of the destroy/build-rule. In Robert Glück, Oege de Moor, editors, Proceedings of the 2008 ACM SIGPLAN Symposium on Partial Evaluation and Semantics-based Program Manipulation, PEPM 2008, San Francisco, California, USA, January 7-8, 2008. pages 13-20, ACM, 2008. [doi]
Free theorems feature prominently in the field of program transformation for pure functional languages such as Haskell. However, somewhat disappointingly, the semantic properties of so based transformations are often established only very superficially. This paper is intended as a case study showing how to use the existing theoretical foundations and formal methods for improving the situation. To that end, we investigate the correctness issue for a new transformation rule in the short cut fusion family. This destroy/build-rule provides a certain reconciliation between the competing foldr/build- and destroy/unfoldr-approaches to eliminating intermediate lists. Our emphasis is on systematically and rigorously developing the rule’s correctness proof, even while paying attention to semantic aspects like potential nontermination and mixed strict/nonstrict evaluation.