Program Extraction From Proofs of Weak Head Normalization

Authors:
Małgorzata Biernacka;Olivier Danvy;Kristian Støvring
Affiliations:
BRICS11Basic Research in Computer Science (www.brics.dk), funded by the Danish National Research Foundation., Department of Computer Science, University of Aarhus, IT-parken, Aabogade 34, 8200 Aar ...;BRICS11Basic Research in Computer Science (www.brics.dk), funded by the Danish National Research Foundation., Department of Computer Science, University of Aarhus, IT-parken, Aabogade 34, 8200 Aar ...;BRICS11Basic Research in Computer Science (www.brics.dk), funded by the Danish National Research Foundation., Department of Computer Science, University of Aarhus, IT-parken, Aabogade 34, 8200 Aar ...
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2006

Citing 4
Cited 1

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Abstract

We formalize two proofs of weak head normalization for the simply typed lambda-calculus 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 identified by Coquand and Dybjer.