Journal of Symbolic Computation
Parametrization for order-sorted algebraic specification
Journal of Computer and System Sciences
Computational aspects of an order-sorted logic with term declarations
Computational aspects of an order-sorted logic with term declarations
Semantics of order-sorted specifications
Theoretical Computer Science
Many-sorted logic and its applications
Many-sorted logic and its applications
Specification in OOZE with examples
Object-oriented specification case studies
Regular Article: Another look at parameterization for order-sorted algebraic specifications
Proceedings of the 30th IEEE symposium on Foundations of computer science
A computer algebra system based on order-sorted algebra
Journal of Symbolic Computation - Special issue on design and implementation of symbolic computation systems
Specification and proof in membership equational logic
Theoretical Computer Science - Trees in algebra and programming
Explicit Graphs in a Functional Model for Spatial Databases
IEEE Transactions on Knowledge and Data Engineering
Order-sorted Algebraic Specifications with Higher-order Functions
AMAST '95 Proceedings of the 4th International Conference on Algebraic Methodology and Software Technology
Category Theory and Computer Science
Unique-Sort Order-Sorted Theories: A Description as Monad Morphisms
Proceedings of the 2nd International CTRS Workshop on Conditional and Typed Rewriting Systems
Proceedings of the 12th ACM symposium on Access control models and technologies
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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 order-sorted theories as categories, in the sense of Lawvere, are obtained.