Modularity is a well-known programming paradigm in computer science. Programmers should design their programs in a modular way, that is, as a combination of small programs. These so-called modules are implemented separately and are then integrated to form the program as a whole. Because TRSs have many important applications in computer science, it is important (not only from a theoretical viewpoint but also from a practical point of view) to know under which conditions a combined system inherits desirable properties from its constituent systems. For this reason modular aspects of term rewriting have been extensively studied in the past decade. To render a detailed account of all known modularity results goes beyond the scope of this book. Instead, we will give an overview of the most important results for TRSs (Section 8.2) and CTRSs (Section 8.7). We will also present selected results in detail.
KeywordsDisjoint Union Function Symbol Reduction Sequence Modular Property Dependency Pair
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