Normalization by Evaluation for λ→2

  • Thorsten Altenkirch
  • Tarmo Uustalu
Conference paper

DOI: 10.1007/978-3-540-24754-8_19

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2998)
Cite this paper as:
Altenkirch T., Uustalu T. (2004) Normalization by Evaluation for λ→2. In: Kameyama Y., Stuckey P.J. (eds) Functional and Logic Programming. FLOPS 2004. Lecture Notes in Computer Science, vol 2998. Springer, Berlin, Heidelberg


We show that the set-theoretic semantics of λ→2—simply typed lambda calculus with a boolean type but no type variables—is complete by inverting evaluation using decision trees. This leads to an implementation of normalization by evaluation which is witnessed by the source of part of this paper being a literate Haskell script. We show the correctness of our implementation using logical relations.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Thorsten Altenkirch
    • 1
  • Tarmo Uustalu
    • 2
  1. 1.School of Computer Science and ITUniversity of NottinghamNottinghamUnited Kingdom
  2. 2.Institute of CyberneticsTallinn Technical UniversityTallinnEstonia

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