## Exact bounds for lengths of reductions in typed $$\lambda$$-calculus.(English)Zbl 1159.03305

Summary: We determine the exact bounds for the length of an arbitrary reduction sequence of a term in the typed $$\lambda$$-calculus with $$\beta$$-, $$\xi$$- and $$\eta$$-conversion. There will be two essentially different classifications, one depending on the height and the degree of the term and the other depending on the length and the degree of the term.

### MSC:

 03B40 Combinatory logic and lambda calculus
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### References:

 [1] Computer Science Report CS-R9545 (1995) [2] DOI: 10.1007/BF01621476 · Zbl 0719.03007 [3] The lambda calculus 103 (1984) [4] Technical Report ECS-LFCS-98-381 [5] The L. E. J. Brouwer centenary symposium pp 453– (1982)
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