A Framework for Order-Sorted Algebra
نویسنده
چکیده
Order-sorted algebra is a generalization of many-sorted algebra obtained by having a partially ordered set of sorts rather than merely a set. It has numerous applications in computer science. There are several variants of order sorted algebra, and some relationships between these are known. However there seems to be no single conceptual framework within which all the connections between the variants can be understood. This paper proposes a new approach to the understanding of order-sorted algebra. Evidence is provided for the viability of the approach, but much further work will be required to complete the research programme which is initiated here. The programme is based on the investigation of two topics. Firstly an analysis of the various categories of order-sorted sets and their relationships, and, secondly, the development of abstract notions of order-sorted theory, as opposed to presentations given by a signature of operation symbols. As a first step, categories of order-sorted sets are described, adjunctions between the categories are obtained, and results on ordersorted theories as categories, in the sense of Lawvere, are obtained.
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