Report
Functorial Semantics for Partial Theories
| العنوان: | Functorial Semantics for Partial Theories |
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| المؤلفون: | Di Liberti, Ivan, Loregian, Fosco, Nester, Chad, Sobociński, Paweł |
| المصدر: | Proc. ACM Program. Lang., Vol. 5, No. POPL, Article 57 (2020) |
| سنة النشر: | 2020 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Logic in Computer Science, Mathematics - Category Theory, 18C35, 18C10, 18B10, 03C05 |
| الوصف: | We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case, our definition is syntactic: we use an appropriate class of string diagrams as terms. This allows for equational reasoning about the class of models defined by a partial theory. We demonstrate the expressivity of such equational theories by considering a number of examples, including partial combinatory algebras and cartesian closed categories. Moreover, despite the increase in expressivity of the syntax we retain a well-behaved notion of semantics: we show that our categories of models are precisely locally finitely presentable categories, and that free models exist. Comment: 27 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1145/3434338 |
| URL الوصول: | http://arxiv.org/abs/2011.06644 |
| رقم الانضمام: | edsarx.2011.06644 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1145/3434338 |
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