Abstract
In this paper, an approach to synthesize correct programs from specifications is presented. The idea is to extract code from definitions appearing in statements which have been mechanically proved with the help of a proof assistant. This approach has been found when proving the correctness of certain Computer Algebra programs (for Algebraic Topology) by using the Isabelle proof assistant. To ease the understanding of our techniques, they are illustrated by means of examples in elementary arithmetic.
Partially supported by SEUI-MEC, project TIC2002-01626.
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References
Aransay, J., Ballarin, C., Rubio, J.: Deduction and Computation in Algebraic Topology. In: Proceedings IDEIA 2002, pp. 47–54. Universidad de Sevilla (2002)
Aransay, J., Ballarin, C., Rubio, J.: Towards a higher reasoning level in formalized Homological Algebra. In: Proceedings Calculemus, Aracné Éditrice, pp. 84–88 (2003)
Aransay, J., Ballarin, C., Rubio, J.: Four approaches to automated reasoning with differential algebraic structures. In: Buchberger, B., Campbell, J. (eds.) AISC 2004. LNCS (LNAI), vol. 3249, pp. 222–235. Springer, Heidelberg (2004)
Berghofer, S.: Program Extraction in Simply-Typed Higher Order Logic. In: Geuvers, H., Wiedijk, F. (eds.) TYPES 2002. LNCS, vol. 2646, pp. 21–38. Springer, Heidelberg (2003)
Berghofer, S.: Answer to Tom Ridge (February 18, 2005), http://isabelle-users.cl.cam.ac.uk
Brown, R.: The twisted Eilenberg-Zilber theorem. Celebrazioni Arch. Secolo XX, Simp. Top., 34–37 (1967)
The Coq Proof Assistant Reference Manual, http://coq.inria.fr/doc/main.html
Davenport, J.M.: Effective Mathematics: the Computer Algebra viewpoint. Lecture Notes in Mathematics, vol. 873, pp. 31–43 (1981)
Davenport, J.M.: Algebraic computations and structures. Lecture Notes in Pure and Applied Mathematics, vol. 113, pp. 129–144. Marcel Dekker, New York (1989)
Dousson, X., Sergeraert, F., Siret, Y.: The Kenzo program, http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo/
Kaufmann, M., Manolios, P., Strother Moore, J.: Computer-Aided Reasoning: An Approach. Kluwer Academic Publishers, Dordrecht (2000)
Kopylov, A., Nogin, A.: Markov’s principle for propositional type theory. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 570–584. Springer, Heidelberg (2001)
Lambán, L., Pascual, V., Rubio, J.: An object-oriented interpretation of the EAT system. Applicable Algebra in Engineering, Communication and Computing 14, 187–215 (2003)
Markov, A.A.: On constructive mathematics. AMS Translations 98, 1–9 (1971)
Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL: A proof assistant for higher order logic. LNCS, vol. 2283. Springer, Heidelberg (2002)
Rubio, J.: Constructive proofs or constructive statements? Dagstuhl Proceedings 05021 (2005), http://www.dagstuhl.de/05021/
Rubio, J., Sergeraert, F.: Constructive Algebraic Topology. Bulletin des Sciences Mathématiques 126, 389–412 (2002)
Rudnicki, P.: An Overview of the MIZAR Project. In: Proceedings Workshop on Types for Proofs and Programs, pp. 311–330 (1992), http://web.cs.ualberta.ca/piotr/Mizar/MizarOverview.ps
Schirmer, N.: A verification environment for sequential imperative programs in Isabelle/HOL. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 398–414. Springer, Heidelberg (2005)
Takeyama, M., Haiyan, Q., Dybjer, P.: Verifying Haskell programs by combining testing, model checking and interactive theorem proving. Information and software technology 15, 1011–1025 (2004)
Wenzel, M., Wiedijk, F.: A Comparison of Mizar and Isar. Journal of Automated Reasoning 29, 389–411 (2002)
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Aransay, J., Ballarin, C., Rubio, J. (2005). Extracting Computer Algebra Programs from Statements. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2005. EUROCAST 2005. Lecture Notes in Computer Science, vol 3643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556985_21
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DOI: https://doi.org/10.1007/11556985_21
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