Advertisement

Foundations of Differential Dataflow

  • Martín Abadi
  • Frank McSherry
  • Gordon D. Plotkin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9034)

Abstract

Differential dataflow is a recent approach to incremental computation that relies on a partially ordered set of differences. In the present paper, we aim to develop its foundations. We define a small programming language whose types are abelian groups equipped with linear inverses, and provide both a standard and a differential denotational semantics. The two semantics coincide in that the differential semantics is the differential of the standard one. Möbius inversion, a well-known idea from combinatorics, permits a systematic treatment of various operators and constructs.

Keywords

Abelian Group Partial Order Operational Semantic Nest Iteration Denotational Semantic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bhatotia, P., Wieder, A., Rodrigues, R., Acar, U.A., Pasquin, R.: Incoop: MapReduce for incremental computations. In: Proc. 2nd ACM Symposium on Cloud Computing, 7p. (2011)Google Scholar
  2. 2.
    McSherry, F., Murray, D.G., Isaacs, R., Isard, M.: Differential dataflow. In: Proc. Sixth Biennial Conference on Innovative Data Systems Research (2013), http://www.cidrdb.org
  3. 3.
    Mihaylov, S.R., Ives, Z.G., Guha, S.: REX: recursive, delta-based data-centric computation. Proc. VLDB Endowment 5(11), 1280–1291 (2012)Google Scholar
  4. 4.
    Murray, D.G., McSherry, F., Isaacs, R., Isard, M., Barham, P., Abadi, M.: Naiad: a timely dataflow system. In: Proc. ACM SIGOPS 24th. Symposium on Operating Systems Principles, pp. 439–455 (2013)Google Scholar
  5. 5.
    Rota, G.-C.: On the foundations of combinatorial theory I, Theory of Möbius functions. Probability Theory and Related Fields 2(4), 340–368 (1964)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Stanley, R.P.: Enumerative Combinatorics, vol. 1. CUP (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Martín Abadi
    • 1
  • Frank McSherry
    • 1
  • Gordon D. Plotkin
    • 1
    • 2
  1. 1.Microsoft ResearchMountain ViewUSA
  2. 2.LFCS, School of InformaticsUniversity of EdinburghEdinburghUK

Personalised recommendations