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Abstract: We define a notion of cut and a proof reduction process for a class of theories, including all equational theories and a first-order formulation of higher-order logic. Proofs normalize for all equational theories. We show that the proof of the normalization theorem for the usual formulation of higher-order logic can be adapted to prove normalization for its first-order formulation. The "hard part" of the proof, that cannot be carried out in higher-order logic itself (the normalization of the... (Update)
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BibTeX entry: (Update)
@inproceedings{ dowek97proof,
author = "Gilles Dowek",
title = "Proof Normalization for a First-Order Formulation of Higher-Order Logic",
booktitle = "Theorem Proving in Higher Order Logics",
pages = "105--119",
year = "1997",
url = "citeseer.ist.psu.edu/article/dowek98proof.html" }
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