Abstract
In previous work we presented a foundational calculus for spatially distributed computing based on intuitionistic modal logic. With the modalities □ and \(\Diamond\) we were able to capture two key invariants: the mobility of portable code and the locality of fixed resources. This work investigates issues in distributed control flow through a similar propositions-as-types interpretation of classical modal logic. The resulting programming language is enhanced with the notion of a network-wide continuation, through which we can give computational interpretation of classical theorems (such as \(\Box A \equiv \lnot \Diamond \lnot A\)). Such continuations are also useful primitives for building higher-level constructs of distributed computing. The resulting system is elegant, logically faithful, and computationally reasonable.
The ConCert Project is supported by the National Science Foundation under grant ITR/SY+SI 0121633: “Language Technology for Trustless Software Dissemination”.
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References
Abel, A.: A third-order representation of the λμ-Calculus. In: Ambler, S.J., Crole, R.L., Momigliano, A. (eds.) Electronic Notes in Theoretical Computer Science, vol. 58, Elsevier, Amsterdam (2001)
Girard, J.-Y.: Towards a geometry of interaction. Contemporary Mathematics 92, 69–108
Girard, J.-Y.: Linear logic. Theoretical Computer Science 50(1), 1–102 (1987)
Griffin, T.G.: The formulae-as-types notion of control. In: Conf. Record 17th Annual ACM Symp. on Principles of Programming Languages, POPL 1990, San Francisco, CA, USA, January 17-19, pp. 47–57. ACM Press, New York (1990)
Jia, L., Walker, D.: Modal proofs as distributed programs. In: 13th European Symposium on Programming, March 2004, pp. 219–223 (2004)
Moody, J.: Modal logic as a basis for distributed computation. Technical Report CMU-CS-03-194, Carnegie Mellon University (October 2003)
Murphy VII, T., Crary, K., Harper, R.: Distribed control flow with classical modal logic (technical report). Technical Report CMU-CS-04-177, Carnegie Mellon University (December 2004)
Murphy VII, T., Crary, K., Harper, R., Pfenning, F.: A symmetric modal lambda calculus for distributed computing. In: Proceedings of the 19th IEEE Symposium on Logic in Computer Science (LICS 2004), July 2004, IEEE Press, Los Alamitos (2004)
Murthy, C.: Classical proofs as programs: How, what and why. Technical Report TR91-1215, Cornell University (1991)
Parigot, M.: λμ-Calculus: An algorithmic interpretation of classical natural deduction. In: Voronkov, A. (ed.) LPAR 1992. LNCS, vol. 624, Springer, Heidelberg (1992)
Pfenning, F., Schürmann, C.: System description: Twelf – a metalogical framework for deductive systems. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 202–206. Springer, Heidelberg (1999)
Reppy, J.H.: Concurrent Programming in ML. Cambridge University Press, Cambridge (1999)
Schürmann, C., Pfenning, F.: A coverage checking algorithm for LF. In: Basin, D., Wolff, B. (eds.) TPHOLs 2003. LNCS, vol. 2758, pp. 120–135. Springer, Heidelberg (2003)
Simpson, A.: The Proof Theory and Semantics of Intuitionistic Modal Logic. PhD thesis, University of Edinburgh (1994)
Wadler, P.: Call-by-value is dual to call-by-name. In: Proceedings of the 8th International Conference on Functional Programming (ICFP), August 2003, ACM Press, New York (2003)
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Murphy VII, T., Crary, K., Harper, R. (2005). Distributed Control Flow with Classical Modal Logic. In: Ong, L. (eds) Computer Science Logic. CSL 2005. Lecture Notes in Computer Science, vol 3634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538363_6
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DOI: https://doi.org/10.1007/11538363_6
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