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EnglishThe article surveys a recent series of papers by the authors investigating the categorical foundations of various rule-based formalisms. The starting point is the well-known representation of term rewriting systems as cartesian 2-categories, based on the characterization of finite terms as arrows of a Lawvere theory. We first show that many term-like structures (including cyclic term graphs, mu-terms and rational terms) can be characterized as arrows of suitable theories. Next we represent rules as cells over a theory, and we show that the free 2-category generated by these cells faithfully represents the rewrite sequences of the original rewriting system.
| Titolo: | Categorical rewriting of term-like structures |
| Autori: | Corradini A.; Gadducci F. |
| Autori interni: | |
| Anno del prodotto: | 2001 |
| Abstract: | The article surveys a recent series of papers by the authors investigating the categorical foundations of various rule-based formalisms. The starting point is the well-known representation of term rewriting systems as cartesian 2-categories, based on the characterization of finite terms as arrows of a Lawvere theory. We first show that many term-like structures (including cyclic term graphs, mu-terms and rational terms) can be characterized as arrows of suitable theories. Next we represent rules as cells over a theory, and we show that the free 2-category generated by these cells faithfully represents the rewrite sequences of the original rewriting system. |
| Digital Object Identifier (DOI): | 10.1016/S1571-0661(04)80195-6 |
| Appare nelle tipologie: | 2.1 Contributo in volume (Capitolo o Saggio) |
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