Abstract
The paper studies the transformational refinement of data structures in the framework of higher-order algebraic specifications. We present novel procedures that mechanize the refinement of entire data structures within a single complex transformation step. The transformations validate a general refinement relation that captures different types of simulations. General transformation rules describe algebraic implementations based on abstraction and representation functions. Specialized transformations cover particular changes between data structures. All transformation procedures have been implemented in the Lübeck Transformation System. The system uses analysis algorithms to establish the soundness conditions of the transformations by syntactic criteria. We report practical experiences about manipulating data structures with the system. The paper summarizes results from the second author’s PhD thesis [20].
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References
Back, R.-J., von Wright, J.: Refinement Calculus, A Systematic Introduction. Graduate Texts in Computer Science. Springer, Heidelberg (1998)
Bauer, F.L., Möller, B., Partsch, H., Pepper, P.: Formal program construction by transformation computer-aided, intuition-guided programming. IEEE Transactions on Software Engineering 15, 165–180 (1989)
Bidoit, M., Hennicker, R., Wirsing, M.: Behavioural and abstractor specifications. Science of Computer Programming 25(2-3), 149–186 (1995)
Bidoit, M., Hennicker, R., Wirsing, M.: Behavioural and abstractor specifications. Science of Computer Programming 25(2-3), 149–186 (1995)
Broy, M., Möller, B., Wirsing, M.: Algebraic implementations preserve program correctness. Science of Computer Programming 7, 35–53 (1986)
Burstall, R.M., Goguen, J.A.: Putting theories together to make specifications. In: Proc. 5th Intl. Joint Conference on Artificial Intelligence, pp. 1045–1058 (1977)
de Roever, W.-P., Engelhardt, K.: Data Refinement: Model-Oriented Proof Methods and their Comparison. Cambridge Tracts in Theoretical Computer Science, vol. 47. Cambridge University Press, Cambridge (1998)
Dijkstra, E.W.: Notes on structured programming. In: Dahl, O., Dijkstra, E.W., Hoare, C.A.R. (eds.) Structured Programming, Academic Press, London (1971)
Dosch, W., Magnussen, S.: Algebraic data structure refinement with the Lübeck Transformation System. In: Indermark, K., Noll, T. (eds.) Kolloquium Programmiersprachen und Grundlagen der Programmierung, number AIB2001-11 in Aachener Informatik Berichte, Rurberg, Oktober 2001, RWTH Aachen, pp. 7–12 (2001)
Dosch, W., Magnussen, S.: Computer aided fusion for algebraic program derivation. Nordic Journal of Computing 8(3), 279–297 (2001)
Dosch, W., Magnussen, S.: Lübeck Transformation System: A transformation system for equational higher-order algebraic specifications. In: Cerioli, M., Reggio, G. (eds.) WADT 2001 and CoFI WG Meeting 2001. LNCS, vol. 2267, pp. 85–108. Springer, Heidelberg (2002)
Ebbinghaus, H.-D., Flum, J., Thomas, W.: Einführung in die mathematische Logik. Spektrum Verlag (1996)
Ehrich, H.-D., Gogolla, M., Lippek, U.W.: Algebraische Spezifikation abstrakter Datentypen. Teubner, Stuttgart (1989)
Ehrig, H., Mahr, B.: Fundamentals of Algebraic Specifications 1, Equations and Initial Semantics. EATCS Monographs on Theoretial Computer Science, vol. 6. Springer, Heidelberg (1985)
Feather, M.: A survey and classification of some program transformation approaches and techniques. In: Meertens, L.G.L.T. (ed.) Proceedings TC2 Working Conference on Program Specification and Transformation, pp. 165–195. North Holland, Amsterdam (1987)
Hearn, B.M., Meinke, K.: ATLAS: A typed language for algebraic specifications. In: Heering, J., Meinke, K., Möller, B., Nipkow, T. (eds.) HOA 1993. LNCS, vol. 816, pp. 146–168. Springer, Heidelberg (1994)
Hoare, C.A.R.: Proof of correctness of data representations. Acta Informatica 1, 271–281 (1972)
Loeckx, J., Ehrich, H.-D., Wolf, M.: Specification of Abstract Data Types. Wiley&Teubner (1996)
Loeckx, J., Ehrich, H.-D., Wolf, M.: Algebraic specification of abstract data types. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, vol. 5, pp. 217–316. Oxford Science Publications (2000)
Magnussen, S.J.: Mechanizing the Transformation of Higher-Order Algebraic Specifications for the Development of Software Systems. Logos Verlag, Berlin (2003)
Meinke, K.: Universal algebra in higher types. Theoretical Computer Science 100, 385–417 (1992)
Meinke, K., Tucker, J.V.: Universal algebra. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, vol. 1, pp. 189–411. Oxford Science Publications (1992)
Wirsing, M.: Algebraic specification. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 675–788. Elsevier Science Publishers, Amsterdam (1990)
Wirsing, M., Partsch, H., Pepper, P., Dosch, W., Broy, M.: On hierarchies of abstract data types. Acta Informatica 20, 1–33 (1983)
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Dosch, W., Magnussen, S. (2004). Computer-Aided Refinement of Data Structures on Higher-Order Algebraic Specifications. In: Ramamoorthy, C.V., Lee, R., Lee, K.W. (eds) Software Engineering Research and Applications. SERA 2003. Lecture Notes in Computer Science, vol 3026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24675-6_6
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DOI: https://doi.org/10.1007/978-3-540-24675-6_6
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