On Deterministic Conditional Rewriting

The class of Deterministic Conditional Term Rewriting Systems (DCTRSs) is of utmost importance for the tight relationships exhibited with functional programming, logic programming and inductive reasoning. However, its analysis is extremely diicult, and to date there are only very few works on the subject, each analyzing a particular aspect of DCTRSs. In this paper, we perform a thorough analysis of DCTRSs, ranging from the study of termination criteria, to new veriication methods for the major properties of DCTRSs like termination and connuence, to the identiication of subclasses of DTCRSs that exhibit a particularly nice behaviour. Moreover, we also address the study of modularity of DCTRSs, providing a number of new powerful results. This is particularly important, since to the best of our knowledge there is so far not a single result on the modularity of DC-TRSs, and of 3-CTRSs in general. Finally, most of the analysis of the paper is performed relying on the recent tool of unravelings, that allows to automatically lift results from the much simpler unconditional rewriting systems to DCTRSs. This way, we clarify what are the links between TRSs and DCTRSs, providing better intuitions on how the gained experience on TRSs can be prootably reused to understand the much more complicated world of DCTRSs.