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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Reductions of residuals are finite
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by R. Hindley PDF
Trans. Amer. Math. Soc. 240 (1978), 345-361 Request permission

Abstract:

An important theorem of the $\lambda \beta K$-calculus which has not been fully appreciated up to now is D. E. Schroer’s finiteness theorem (1963), which states that all reductions of residuals are finite. The present paper gives a new proof of this theorem and extends it from $\lambda \beta$-reduction to $\lambda \beta \eta$-reduction and reductions with certain extra operators added, for example the pairing, iteration and recursion operators. Combinatory weak reduction, with or without extra operators, is also included.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 240 (1978), 345-361
  • MSC: Primary 03B40
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0489603-9
  • MathSciNet review: 489603