Abstract
We first present a new proof for the standardization theorem, a fundamental theorem in λ-calculus. Since our proof is largely built upon structural induction on lambda terms, we can extract some bounds for the number of β-reduction steps in the standard β-reduction sequences obtained from transforming a given β-reduction sequences. This result sharpens the standardization theorem. As an application, we establish a super-exponential bound for the lengths of β-reduction sequences from any given simply typed λ-terms.
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Xi, H. (1997). Upper bounds for standardizations and an application. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1997. Lecture Notes in Computer Science, vol 1289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63385-5_54
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DOI: https://doi.org/10.1007/3-540-63385-5_54
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