David Basin Burkhart Wolff
نویسندگان
چکیده
Our goal is to develop a general formalization of abstract algebra suitable for a general reasoning. One of the most common ways to formalize abstract algebra is to make use of a module system to specify an algebra as a theory. However, this approach suffers from the fact that modules are usually not first-class objects in the formal system. In this paper, we develop a new approach based on the use of dependent record types. In our account, all algebraic structures are first-class objects, with the natural subtyping properties due to record extension (for example, a group is a subtype of a monoid). Our formalization cleanly separates the axiomatization of the algebra from its typing properties, corresponding more closely to a textbook presentation.
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تاریخ انتشار 2003