Abstract
We consider higher-order equational logic as a formalism for the specification, simulation and testing of systems. We survey recent theoretical results on the expressiveness and proof theory of higher-order equations. These results are then interpreted within the context of specification language design to show that higher-order equational logic, used as a specification language, provides a useful compromise between the conflicting requirements of logical expressiveness and computational tractability.
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Bergstra, J.A., Heering, J., Klint, P.: Algebraic specification, Addison Wesley, New York, 1989
Bergstra, J.A., Tucker, J.V.: The completeness of the algebraic specification methods for computable data types, Inform. and Control 54, 186–200 (1982)
Bergstra, J.A., Tucker, J.V.: Initial and final algebra semantics for data type specifications; two characterisation theorems, SIAM J. Comput. 12, 366–387 (1983)
Bergstra, J.A., Tucker, J.V.: Algebraic specifications of computable and semi-computable data types. Theoret. Comput. Sci. 50, 137–181 (1987)
Dijkstra, E.W.: A Discipline of Programming, Prentice Hall, Englewood Cliffs, 1976
Dugundji, J.: Topology, William C. Brown, Dubuque, 1989.
Ehrig, H., Mahr, B.: Fundamentals of algebraic specification I: equations and initial semantics, Berlin, Heidelberg, New York: Springer Verlag 1985
Goguen, J.A., Meseguer, J.: Completeness of many-sorted equational logic. Assoc. for Computing Machinery SIGPLAN notices 17, 9–17 (1982)
Goguen, J.A., Meseguer, J.: Initiality, induction and computability. In: Nivat, M., Reynolds, J.C. (eds.) Algebraic methods in semantics, pp. 459–541. Cambridge: Cambridge University Press 1985
Goguen, J.A., Meseguer, J., Plaisted, D.: Programming with parameterized abstract objects in OBJ, 163–193 in: D. Ferrari, M. Bolognani and J.A. Goguen (eds), Theory and practice of software technology, North Holland, 1983.
Gordon, V.S., Bieman, J.: Rapid prototyping: lessons learned, IEEE Software 12, 85–95, (1995)
Heering, J., Meinke, K., Möller, B., Nipkow, T., (eds.) HOA '93: an international workshop on higher-order algebra, logic and term rewriting, (Lect. Notes Comput. Sci., vol. 816) Berlin, Heidelberg, New York: Springer Verlag 1994
Hinman, P.G.: Recursion-theoretic hierarchies, Berlin, Heidelberg, New York: Springer Verlag 1978
Jones, C.B.: Systematic software development using VDM, Prentice Hall, Englewood Cliffs, 1986
Kelley, J.L.: General Topology, Springer Verlag, Berlin, 1955
Klop, J.W.: Term rewriting, in: Abramsky, S., Gabbay, D., Maibaum, T.S.E., (eds.) Handbook of logic in computer science, Vol II, pp. 1–111. Oxford: Oxford University Press 1993
Kosiuczenko, P., Meinke, K.: On the power of higher-order algebraic specification methods, Information and Computation, 124, 85–101, (1996).
Meinke, K.: Universal algebra in higher types, Theoretical Computer Science, 100, 385–417, (1992)
Meinke, K.: A recursive second-order initial algebra specification of primitive recursion, Acta Informatica, 31, 329–340, (1994)
Meinke, K.: A completeness theorem for the expressive power of higher-order algebraic specifications, Journal of Computer and System Sciences, to appear, 1996.a
Meinke, K.: Proof theory of higher-order equational logic: normal forms, continuity and term rewriting, technical report, Department of Computer Science, University College of Swansea, 1996.b to appear
Meinke, K., Tucker, J.V.: Universal algebra, in: Abramsky, S., Gabbay, D., Maibaum, T.S.E., (eds.) Handbook of logic in computer science, pp. 189–411 Oxford: Oxford University Press 1993
Möller, B.: Higher-order algebraic specifications. Facultät für Mathematik und Informatik, Technische Universität München, Habilitationsschrift, 1987
Spivey, J.M.: The Z notation, Prentice Hall, Englewood Cliffs, 1992
Steggles, L.J.: Extensions of Higher-Order Algebra, Case Studies and Fundamental Theory, Ph.D. Thesis, Dept. of Computer Science, University of Wales, Swansea, 1995
Normann, D.: Recursion on the countable functionals, Lecture Notes in Mathematics 811, Springer Verlag, Berlin, 1980
Wirsing, M.: Algebraic specification. In: van Leeuwen, J. (ed.) Handbook of theoretical computer science, pp. 675–788. Amsterdam: North Holland 1990
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Meinke, K. (1996). Higher-order equational logic for specification, simulation and testing. In: Dowek, G., Heering, J., Meinke, K., Möller, B. (eds) Higher-Order Algebra, Logic, and Term Rewriting. HOA 1995. Lecture Notes in Computer Science, vol 1074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61254-8_23
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DOI: https://doi.org/10.1007/3-540-61254-8_23
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