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Proof Pearl: Abella Formalization of λ-Calculus Cube Property

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7679)

Abstract

In 1994 Gerard Huet formalized in Coq the cube property of ł-calculus residuals. His development is based on a clever idea, a beautiful inductive definition of residuals. However, in his formalization there is a lot of noise concerning the representation of terms with binders. We re-interpret his work in Abella, a recent proof assistant based on higher-order abstract syntax and provided with a nominal quantifier. By revisiting Huet’s approach and exploiting the features of Abella, we get a strikingly compact and natural development, which makes Huet’s idea really shine.

Keywords

  • Deductive System
  • Proof Theory
  • Development Property
  • Proof Assistant
  • Parallel Reduction

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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Accattoli, B. (2012). Proof Pearl: Abella Formalization of λ-Calculus Cube Property. In: Hawblitzel, C., Miller, D. (eds) Certified Programs and Proofs. CPP 2012. Lecture Notes in Computer Science, vol 7679. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35308-6_15

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  • DOI: https://doi.org/10.1007/978-3-642-35308-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35307-9

  • Online ISBN: 978-3-642-35308-6

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