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.
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© 1999 IFIP International Federation for Information Processing
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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
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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
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