Introduction
In a recent article [1], David Parnas questions the traditional use of formal methods in software development, which he considers an underdeveloped body of knowledge and therefore of little hope for the software industry. He confronts the reader with the following statement, at some stage:
“We must learn to use mathematics in software development, but we need to question, and be prepared to discard, most of the methods that we have been discussing and promoting for all these years.”
At the core of Parnas objections we find the contrast between the current ad-hoc (re)invention of mathematical concepts which are cumbersome and a burden to use and elegant (and therefore useful) concepts which are neglected, often for cultural or (lack of) background reasons.
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References
Parnas, D.L.: Really rethinking ’formal methods’. IEEE Computer 43(1), 28–34 (2010)
Distefano, S., Longo, F., Scarpa, M.: Availability assessment of ha standby redundant clusters. In: 29th IEEE Int. Symp. on Reliable Distributed Systems (2010)
Sernadas, A., Ramos, J., Mateus, P.: Linear algebra techniques for deciding the correctness of probabilistic programs with bounded resources. Technical report, TU Lisbon, Short paper, LPAR, Doha, Qatar (November 22-27, 2008)
Macedo, H., Oliveira, J.: Can we teach computers to generate fast OLAP code? Technical note (May 2010), http://wiki.di.uminho.pt
Trcka, N.: Strong, weak and branching bisimulation for transition systems and Markov reward chains: A unifying matrix approach. In: Andova, S.E. (ed.) Proc. 1st Workshop on Quantitative Formal Methods: Theory and Applications (December 2009)
Conway, J.: Regular Algebra and Finite Machines. Chap.& Hall, London (1971)
Backhouse, R.: Mathematics of Program Construction, 608 pages. Univ. of Nottingham (2004) Draft of book in preparation
Maddux, R.: The origin of relation algebras in the development and axiomatization of the calculus of relations. Studia Logica 50, 421–455 (1991)
Freyd, P., Scedrov, A.: Categories, Allegories. Mathematical Library, vol. 39. North-Holland, Amsterdam (1990)
Bloom, S.L., Sabadini, N., Walters, R.F.C.: Matrices, machines and behaviors. Applied Categorical Structures 4, 343–360 (1996), doi:10.1007/BF00122683
Macedo, H., Oliveira, J.: Matrices As Arrows! A Biproduct Approach to Typed Linear Algebra. In: Bolduc, C., Desharnais, J., Ktari, B. (eds.) MPC 2010. LNCS, vol. 6120, pp. 271–287. Springer, Heidelberg (2010)
MacLane, S.: Categories for the Working Mathematician (Graduate Texts in Mathematics). Springer, Heidelberg (September 1998)
Bonchi, F., Silva, A., Bonsangue, M., Rutten, J.: Quantitative Kleene coalgebras. In: Information and Computation. Academic Press, London (November 2010) ISSN: 0890-5401
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Macedo, H.D., Oliveira, J.N. (2012). Towards Linear Algebras of Components. In: Barbosa, L.S., Lumpe, M. (eds) Formal Aspects of Component Software. FACS 2010. Lecture Notes in Computer Science, vol 6921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27269-1_20
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