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Proof Pearl: The Power of Higher-Order Encodings in the Logical Framework LF

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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

In this proof pearl, we demonstrate the power of higher-order encodings in the logical framework Twelf[PS99] by investigating proofs about an algorithmic specification of bounded subtype polymorphism, a problem from the POPLmark challenge [ABF + 05].. Our encoding and representation of the problem plays to the strengths of the logical framework LF. Higher-order abstract syntax is used to deal with issues of bound variables. More importantly, we exploit the full advantage of parametric and higher-order judgments. As a key benefit we get a tedious narrowing lemma, which must normally be proven separately, for free. Consequently, we obtain an extremely compact and elegant encoding of the admissibility of general transitivity and other meta-theoretic properties.

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Authors and Affiliations

  1. School of Computer Science, McGill University,  

    Brigitte Pientka

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  1. Brigitte Pientka
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Klaus Schneider Jens Brandt

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Pientka, B. (2007). Proof Pearl: The Power of Higher-Order Encodings in the Logical Framework LF. 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_19

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  • DOI: https://doi.org/10.1007/978-3-540-74591-4_19

  • 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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