Abstract
A collection of sets X1, …, Xn together with various functions of the form X i 1 x ⋯ x X i k→X i k+1 constitutes a “many-sorted algebra.” Section 1 gives examples of data types which arise as many-sorted algebras. An “equational specification” for a data type posits a many-sorted algebraic structure subject to a finite set of equations. What is attractive about this idea is that equational specifications are easily formalized within programming languages and have been partially implemented in experimental languages such as CLEAR, ACT ONE, CLU, and others. This provides a tool to define data types useful in programming and additionally promises to make available a useful research aid for pure mathematicians who study equationally defined algebraic structures.
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Notes and References for Chapter 14
J. A. Goguen, J. W. Thatcher, E. G. Wagner, and J. B. Wright, “Initial algebra semantics and continuous algebras,” Journal of the Association of Computing Machinery, 24, 1977, pp. 68–95.
H. Ehrig and B. mahr, Fundamentals of Equational Specification 1, Springer-Verlag, 1985.
G. Birkhoff and J. D. Lipson, “Heterogeneous algebras,” Journal of Combinational Theory, 8, 1970, pp. 115–133.
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© 1986 Springer-Verlag New York Inc.
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Manes, E.G., Arbib, M.A. (1986). Equational Specification. In: Algebraic Approaches to Program Semantics. Texts and Monographs in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4962-7_14
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DOI: https://doi.org/10.1007/978-1-4612-4962-7_14
Publisher Name: Springer, New York, NY
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