Certified Reasoning with Infinity

  • Asankhaya Sharma
  • Shengyi Wang
  • Andreea Costea
  • Aquinas Hobor
  • Wei-Ngan Chin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9109)


We demonstrate how infinities improve the expressivity, power, readability, conciseness, and compositionality of a program logic. We prove that adding infinities to Presburger arithmetic enables these improvements without sacrificing decidability. We develop Omega++, a Coq-certified decision procedure for Presburger arithmetic with infinity and benchmark its performance. Both the program and proof of Omega++ are parameterized over user-selected semantics for the indeterminate terms (such as 0 * ∞).


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Asankhaya Sharma
    • 1
  • Shengyi Wang
    • 1
  • Andreea Costea
    • 1
  • Aquinas Hobor
    • 1
  • Wei-Ngan Chin
    • 1
  1. 1.School of Computing, Yale-NUS CollegeNational University of SingaporeSingaporeSingapore

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