Abstract
Refinement algebras are axiomatic algebras for reasoning about programs in a total-correctness framework. We extend demonic and angelic refinement algebra with operators for encoding and decoding. Encoding gives one the least data refinement of a program with respect to a given data-refinement abstraction. Decoding gives one the greatest program that can be data refined into the decoded program with respect to a given abstraction statement. The resulting algebra is applied to reasoning about action systems.
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References
Armstrong, A., Gomes, V.B.F., Struth, G.: Algebraic principles for rely-guarantee style concurrency verification tools. In: Jones, C., Pihlajasaari, P., Sun, J. (eds.) FM 2014. LNCS, vol. 8442, pp. 78–93. Springer, Heidelberg (2014)
Armstrong, A., Gomes, V.B.F., Struth, G.: Kleene algebra with tests and demonic refinement algebras. Archive of Formal Proofs (2014)
Back, R.-J., Kurki-Suonio, R.: Distributed cooperation with action systems. ACM Trans. Program. Lang. Syst. 10(4), 513–554 (1988)
Back, R.-J., von Wright, J.: Encoding, decoding and data refinement. Formal Asp. Comput. 12(5), 313–349 (2000)
Cohen, E.: Separation and reduction. In: Backhouse, R., Oliveira, J.N. (eds.) MPC 2000. LNCS, vol. 1837, pp. 45–59. Springer, Heidelberg (2000)
Desharnais, J., Möller, B., Struth, G.: Kleene algebra with domain. ACM Trans. Comput. Log. 7(4), 798–833 (2006)
Guttmann, W.: Algebras for correctness of sequential computations. Sci. Comput. Program. 85, 224–240 (2014)
Hayes, I.J.: Generalised rely-guarantee concurrency: An algebraic foundation. Unpublished manuscript, The University of Queensland (February 2015)
Hoare, T., Möller, B., Struth, G., Wehrman, I.: Concurrent Kleene algebra and its foundations. J. Log. Algebr. Program. 80(6), 266–296 (2011)
Höfner, P., Khédri, R., Möller, B.: An algebra of product families. Software and System Modeling 10(2), 161–182 (2011)
Höfner, P., Struth, G.: Automated reasoning in Kleene algebra. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 279–294. Springer, Heidelberg (2007)
Kozen, D.: Kleene algebra with tests. ACM Trans. Program. Lang. Syst. 19(3), 427–443 (1997)
McIver, A., Gonzalia, C., Cohen, E., Morgan, C.C.: Using probabilistic Kleene algebra pKA for protocol verification. J. Log. Algebr. Program. 76(1), 90–111 (2008)
McIver, A., Meinicke, L., Morgan, C.: Hidden-Markov program algebra with iteration. Mathematical Structures in Computer Science 25(2), 320–360 (2015)
Meinicke, L., Hayes, I.: Probabilistic choice in refinement algebra. In: Audebaud, P., Paulin-Mohring, C. (eds.) MPC 2008. LNCS, vol. 5133, pp. 243–267. Springer, Heidelberg (2008)
Meinicke, L., Solin, K.: Refinement algebra for probabilistic programs. Formal Asp. Comput. 22(1), 3–31 (2010)
Nelson, G.: A generalization of Dijkstra’s calculus. ACM Trans. Program. Lang. Syst. 11(4), 517–561 (1989)
Preoteasa, V.: Refinement algebra with dual operator. Sci. Comput. Program. 92, 179–210 (2014)
Solin, K.: Normal forms in total correctness for while programs and action systems. J. Log. Algebr. Program. 80(6), 362–375 (2011)
Solin, K.: Dual choice and iteration in an abstract algebra of action. Studia Logica 100(3), 607–630 (2012)
Solin, K., von Wright, J.: Enabledness and termination in refinement algebra. Sci. Comput. Program. 74(8), 654–668 (2009)
von Wright, J.: Towards a refinement algebra. Sci. Comput. Program. 51(1-2), 23–45 (2004)
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Solin, K. (2015). Encoding and Decoding in Refinement Algebra. In: Kahl, W., Winter, M., Oliveira, J. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2015. Lecture Notes in Computer Science(), vol 9348. Springer, Cham. https://doi.org/10.1007/978-3-319-24704-5_13
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DOI: https://doi.org/10.1007/978-3-319-24704-5_13
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