Journal of Automated Reasoning

, Volume 47, Issue 4, pp 369–398 | Cite as

Monotonicity Inference for Higher-Order Formulas

Article

Abstract

Formulas are often monotonic in the sense that satisfiability for a given domain of discourse entails satisfiability for all larger domains. Monotonicity is undecidable in general, but we devised three calculi that infer it in many cases for higher-order logic. The third calculus has been implemented in Isabelle’s model finder Nitpick, where it is used both to prune the search space and to soundly interpret infinite types with finite sets, leading to dramatic speed and precision improvements.

Keywords

Higher-order logic Model finding Isabelle/HOL 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Jasmin Christian Blanchette
    • 1
  • Alexander Krauss
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMunichGermany

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