Abstract
In Section 1.5 we introduced guard functions and finite and infinite sums of partial functions and multifunctions and used these as tools to describe guarded commands and various conditional and repetitive constructs. All this was in Pfn or Mfn. The task of this chapter is to develop axioms on a general semantic category to make similar constructions possible in a wider context and to clarify the algebraic processes of manipulation and simplification as partly demonstrated by Example 1.5.31.
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Notes and References for Chapter 3
C. C. Elgot, “Monadic computation and iterative algebraic theories,” in Proceedings of Logic Colloquium ’73 (H. E. Rose and J. C. Shepherson, Eds.), North-Holland, Amsterdam, 1975.
E. G. Manes and D. B. Benson. “The inverse semigroup of a sum-ordered semiring,” Semigroup Forum, 31, 1985, pp. 129–152.
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© 1986 Springer-Verlag New York Inc.
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Manes, E.G., Arbib, M.A. (1986). Partially Additive Semantics. 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_3
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DOI: https://doi.org/10.1007/978-1-4612-4962-7_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-9377-4
Online ISBN: 978-1-4612-4962-7
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