Abstract
Psi-calculi are extensions of the pi-calculus, accommodating arbitrary nominal datatypes to represent not only data but also communication channels, assertions and conditions, giving it an expressive power beyond the applied pi-calculus and the concurrent constraint pi-calculus.
We have formalised psi-calculi in the interactive theorem prover Isabelle using its nominal datatype package. One distinctive feature is that the framework needs to treat binding sequences, as opposed to single binders, in an efficient way. While different methods for formalising single binder calculi have been proposed over the last decades, representations for such binding sequences are not very well explored.
The main effort in the formalisation is to keep the machine checked proofs as close to their pen-and-paper counterparts as possible. We discuss two approaches to reasoning about binding sequences along with their strengths and weaknesses. We also cover custom induction rules to remove the bulk of manual alpha-conversions.
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References
Abadi, M., Fournet, C.: Mobile values, new names, and secure communication. In: Proceedings of POPL 2001, pp. 104–115. ACM, New York (2001)
Aydemir, B., Charguéraud, A., Pierce, B.C., Pollack, R., Weirich, S.: Engineering formal metatheory. In: POPL 2008: Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp. 3–15. ACM, New York (2008)
Ballarin, C.: Locales and locale expressions in isabelle/isar. In: Berardi, S., Coppo, M., Damiani, F. (eds.) TYPES 2003. LNCS, vol. 3085, pp. 34–50. Springer, Heidelberg (2004)
Barendregt, H.P.: The Lambda Calculus – Its Syntax and Semantics. Studies in Logic and the Foundations of Mathematics, vol. 103. North-Holland, Amsterdam (1984)
Bengtson, J., Johansson, M., Parrow, J., Victor, B.: Psi-calculi: Mobile processes, nominal data, and logic. Technical report, Uppsala University (2009); (submitted), http://user.it.uu.se/~joachim/psi.pdf
Bengtson, J., Parrow, J.: Formalising the pi-calculus using nominal logic. In: Seidl, H. (ed.) FOSSACS 2007. LNCS, vol. 4423, pp. 63–77. Springer, Heidelberg (2007)
Berghofer, S., Urban, C.: Nominal Inversion Principles. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 71–85. Springer, Heidelberg (2008)
Buscemi, M.G., Montanari, U.: Open bisimulation for the concurrent constraint π-calculus. In: Drossopoulou, S. (ed.) ESOP 2008. LNCS, vol. 4960, pp. 254–268. Springer, Heidelberg (2008)
de Bruijn, N.G.: Lambda calculus notation with nameless dummies. a tool for automatic formula manipulation with application to the church-rosser theorem. Indagationes Mathematicae 34, 381–392 (1972)
Hirschkoff, D.: A full formalisation of π-calculus theory in the calculus of constructions. In: Gunter, E.L., Felty, A.P. (eds.) TPHOLs 1997. LNCS, vol. 1275, pp. 153–169. Springer, Heidelberg (1997)
Honsell, F., Miculan, M., Scagnetto, I.: π-calculus in (co)inductive type theory. Theoretical Comput. Sci. 253(2), 239–285 (2001)
Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
Pitts, A.M.: Nominal logic, a first order theory of names and binding. Information and Computation 186, 165–193 (2003)
Röckl, C., Hirschkoff, D.: A fully adequate shallow embedding of the π-calculus in Isabelle/HOL with mechanized syntax analysis. J. Funct. Program. 13(2), 415–451 (2003)
Urban, C.: Nominal techniques in Isabelle/HOL. Journal of Automated Reasoning 40(4), 327–356 (2008)
Urban, C., Berghofer, S., Norrish, M.: Barendregt’s variable convention in rule inductions. In: Pfenning, F. (ed.) CADE 2007. LNCS, vol. 4603, pp. 35–50. Springer, Heidelberg (2007)
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Bengtson, J., Parrow, J. (2009). Psi-calculi in Isabelle. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2009. Lecture Notes in Computer Science, vol 5674. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03359-9_9
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DOI: https://doi.org/10.1007/978-3-642-03359-9_9
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