Program Extraction From Proofs of Weak Head Normalization

@article{Biernacka2006ProgramEF,
  title={Program Extraction From Proofs of Weak Head Normalization},
  author={Malgorzata Biernacka and Olivier Danvy and Kristian St{\o}vring},
  journal={Electr. Notes Theor. Comput. Sci.},
  year={2006},
  volume={155},
  pages={169-189}
}
We formalize two proofs of weak head normalization for the simply typed lambdacalculus in first-order minimal logic: one for normal-order reduction, and one for applicative-order reduction in the object language. Subsequently we use Kreisel’s modified realizability to extract evaluation algorithms from the proofs, following Berger; the proofs are based on Tait-style reducibility predicates, and hence the extracted algorithms are instances of (weak head) normalization by evaluation, as already… CONTINUE READING
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