Proof Pearl: Abella Formalization of λ-Calculus Cube Property

  • Beniamino Accattoli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7679)


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.


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Beniamino Accattoli
    • 1
    • 2
  1. 1.INRIA and LIX (École Polytechnique)PalaiseauFrance
  2. 2.Carnegie Mellon UniversityPittsburghUSA

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