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Proof Pearl: Looping Around the Orbit

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Theorem Proving in Higher Order Logics (TPHOLs 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4732))

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Abstract

We reexamine the While combinator of higher-order logic (HOL) and introduce the For combinator. We argue that both combinators should be part of the toolbox of any HOL practitioner, not only because they make efficient computations within HOL possible, but also because they facilitate elegant inductive reasoning about loops. We present two examples that support this argument.

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References

  1. Krauss, A.: Partial Recursive Functions in Higher-Order Logic. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, Springer, Heidelberg (2006)

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  2. Owens, S., Slind, K.: Adapting Functional Programs to Higher-Order Logic (submitted)

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  3. Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL: A Proof Assistant for Higher-Order Logic. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  4. Berghofer, S., Nipkow, T.: Executing Higher-Order Logic. In: Callaghan, P., Luo, Z., McKinna, J., Pollack, R. (eds.) TYPES 2000. LNCS, vol. 2277, Springer, Heidelberg (2002)

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  5. Gonthier, G.: A computer-checked proof of the Four Color Theorem, http://research.microsoft.com/~gonthier/4colproof.pdf

  6. Nipkow, T., Bauer, G., Schultz, P.: Flyspeck I: Tame Graphs. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, Springer, Heidelberg (2006)

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  7. Hales, T.: The Flyspeck Project, http://www.math.pitt.edu/~thales/flyspeck/

  8. Hales, T.: A proof of the Kepler conjecture. Annals of Mathematics 162, 1065–1185

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  9. Looping around the Orbit, http://www4.in.tum.de/~obua/looping/

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Author information

Authors and Affiliations

  1. Technische Universität München, D-85748 Garching, Boltzmannstr. 3, Germany

    Steven Obua

Authors
  1. Steven Obua
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Editor information

Klaus Schneider Jens Brandt

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© 2007 Springer-Verlag Berlin Heidelberg

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Obua, S. (2007). Proof Pearl: Looping Around the Orbit. In: Schneider, K., Brandt, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2007. Lecture Notes in Computer Science, vol 4732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74591-4_17

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  • DOI: https://doi.org/10.1007/978-3-540-74591-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74590-7

  • Online ISBN: 978-3-540-74591-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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