Distilling Programs to Prove Termination

G.W. Hamilton
(Dublin City University)

The problem of determining whether or not any program terminates was shown to be undecidable by Turing, but recent advances in the area have allowed this information to be determined for a large class of programs. The classic method for deciding whether a program terminates dates back to Turing himself and involves finding a ranking function that maps a program state to a well-order, and then proving that the result of this function decreases for every possible program transition. More recent approaches to proving termination have involved moving away from the search for a single ranking function and toward a search for a set of ranking functions; this set is a choice of ranking functions and a disjunctive termination argument is used. In this paper, we describe a new technique for determining whether programs terminate. Our technique is applied to the output of the distillation program transformation that converts programs into a simplified form called distilled form. Programs in distilled form are converted into a corresponding labelled transition system and termination can be demonstrated by showing that all possible infinite traces through this labelled transition system would result in an infinite descent of well-founded data values. We demonstrate our technique on a number of examples, and compare it to previous work.

In Laurent Fribourg and Matthias Heizmann: Proceedings 8th International Workshop on Verification and Program Transformation and 7th Workshop on Horn Clauses for Verification and Synthesis (VPT/HCVS 2020), Dublin, Ireland, 25-26th April 2020, Electronic Proceedings in Theoretical Computer Science 320, pp. 140–154.
This work owes a lot to the input of Neil Jones, who provided many useful insights and ideas on the subject matter presented here.
Published: 7th August 2020.

ArXived at: http://dx.doi.org/10.4204/EPTCS.320.10 bibtex PDF
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