Abstract
The purpose of this chapter is to present the basic definitions and results on which the following chapters rely. Most of this material is quite standard and for that reason the presentation will be concise. More detailed presentations with greater emphasis on motivation, exercises, and examples may be found in [EM85, Wir90, LEW96, ST]. The most basic assumption of work on algebraic specification is that a program is modeled as analgebra,that is, a set of data together with a number of functions over this set. The branch of mathematics which deals with algebras in a general sense (as opposed to the study of specific classes of algebras, such as groups and rings) is calleduniversal algebraor sometimesgeneral algebra. This chapter presents the basics of universal algebra, generalized to themany-sortedcase as required to model programs which manipulate several kinds orsortsof data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 IFIP International Federation for Information Processing
About this chapter
Cite this chapter
Sannella, D., Tarlecki, A. (1999). Algebraic Preliminaries. In: Astesiano, E., Kreowski, HJ., Krieg-Brückner, B. (eds) Algebraic Foundations of Systems Specification. IFIP State-of-the-Art Reports. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59851-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-59851-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64151-0
Online ISBN: 978-3-642-59851-7
eBook Packages: Springer Book Archive