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

  • Brigitte Pientka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4732)

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.

Keywords

Deductive System Logical Framework Polymorphic Type Transitivity Rule Subtyping Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Brigitte Pientka
    • 1
  1. 1.School of Computer Science, McGill University 

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