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Proving and Disproving Termination of Higher-Order Functions

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Frontiers of Combining Systems (FroCoS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3717))

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Abstract

The dependency pair technique is a powerful modular method for automated termination proofs of term rewrite systems (TRSs). We present two important extensions of this technique: First, we show how to prove termination of higher-order functions using dependency pairs. To this end, the dependency pair technique is extended to handle (untyped) applicative TRSs. Second, we introduce a method to prove non-termination with dependency pairs, while up to now dependency pairs were only used to verify termination. Our results lead to a framework for combining termination and non-termination techniques for first- and higher-order functions in a very flexible way. We implemented and evaluated our results in the automated termination prover AProVE.

Supported by the Deutsche Forschungsgemeinschaft DFG under grant GI 274/5-1.

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Authors and Affiliations

  1. LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074, Aachen, Germany

    Jürgen Giesl, René Thiemann & Peter Schneider-Kamp

Authors
  1. Jürgen Giesl
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  2. René Thiemann
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  3. Peter Schneider-Kamp
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Editors and Affiliations

  1. Fakultät für Informatik, Technische Universität Wien, Favoritenstr. 9 – E185/2, A-1040, Wien, Austria

    Bernhard Gramlich

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Giesl, J., Thiemann, R., Schneider-Kamp, P. (2005). Proving and Disproving Termination of Higher-Order Functions. In: Gramlich, B. (eds) Frontiers of Combining Systems. FroCoS 2005. Lecture Notes in Computer Science(), vol 3717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11559306_12

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  • DOI: https://doi.org/10.1007/11559306_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29051-3

  • Online ISBN: 978-3-540-31730-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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