Abstract
It seems that there are some pragmatic advantages in using Abstract Semantic Algebras (ASAs) instead of λ-notation in denotational semantics. The values of ASAs correspond to “actions” (or “processes”), and the operators correspond to primitive ways of combining actions. There are simple ASAs for the various independent “facets” of actions: a functional ASA for data-flow, an imperative ASA for assignments, a declarative ASA for bindings, etc. The aim is to obtain general ASAs by systematic combination of these simple ASAs.
Here we specify a basic ASA that captures the common features of the functional, imperative and declarative ASAs — and highlights their differences. We discuss the correctness of ASA specifications, and sketch the proof of the consistency and (limiting) completeness of the functional ASA, relative to a simple model.
Some familiarity with denotational semantics and algebraic specifications is assumed.
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References
J. A. Goguen, “Parameterised programming”, in Proc. Workshop on Reusability in Programming (ed. A. Perlis) (1983).
J. V. Guttag, J. J. Horning, “The algebraic specification of abstract data types”, Acta Inf. 10 (1978), 27–52.
M. G. Main, D. B. Benson, “Functional behavior of non-deterministic programs”, in Proc. FCT'83, Borgholm, springer LNCS 158 (1983).
J. Meseguer, “An order-complete universal algebra and functorial semantics”, in Proc. FCT'77, Poznań, Springer LNCS 56 (1977).
R. Milner, “Fully abstract models of typed lambda-calculus”, TCS 4 (1977), 1–22.
P. D. Mosses, “Making denotational semantics less concrete”, in Proc. Int. Workshop on Semantics of Programming Languages, Bad Honnef, Ber.Nr.41, Abteilung Informatik, Univ. Dortmund (1977).
—, “A constructive approach to compiler correctness”, in Proc. ICALP'80, Noordwijkerhout, Springer LNCS 85 (1980).
—, “A semantic algebra for binding constructs”, in Proc. Int. Coll. on Formalization of Programming Concepts, Peniscola, Springer LNCS 107 (1981).
—, “Abstract semantic algebras!”, in Proc. IFIP TC2 Working Conf. on Formal Description of Programming Concepts — II, Garmisch-Partenkirchen, 1982 (North-Holland, 1983).
J. C. Reynolds, "Semantics of the domain of flow diagrams”. J.ACM 24 (1977), 484–503.
C. P. Wadsworth, “The relation between the computational and denotational properties for Scott's D∞-models of the lambda-calculus”, SIAM. J. Comput. 5 (1976), 488–521.
M. Wand, “Final algebra semantics and data type extensions", JCSS 19 (1979), 27–44.
M. Wirsing, P. Pepper, H. Partsch, W. Dosch, M. Broy, “On hierarchies of abstract data types”, Acta Inf. 20 (1983), 1–34.
S. N. Zilles, P. Lucas, J. W. Thatcher, “A look at algebraic specifications”, IBM Res. Rep. RJ-3568 (June, 1982).
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© 1984 Springer-Verlag Berlin Heidelberg
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Mosses, P. (1984). A basic Abstract Semantic Algebra. In: Kahn, G., MacQueen, D.B., Plotkin, G. (eds) Semantics of Data Types. SDT 1984. Lecture Notes in Computer Science, vol 173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13346-1_4
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DOI: https://doi.org/10.1007/3-540-13346-1_4
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