Compaction of Church Numerals
Graduate School/Faculty of Information Science and Technology, Hokkaido University, Kita 14 Nishi 9, Sapporo 060-0814, Japan
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 28 June 2019 / Revised: 5 August 2019 / Accepted: 5 August 2019 / Published: 8 August 2019
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Abstract In this study, we address the problem of compaction of Church numerals. Church numerals are unary representations of natural numbers on the scheme of lambda terms. We propose a novel decomposition scheme from a given natural number into an arithmetic expression using tetration, which enables us to obtain a compact representation of lambda terms that leads to the Church numeral of the natural number. For natural number n, we prove that the size of the lambda term obtained by the proposed method is . Moreover, we experimentally confirmed that the proposed method outperforms binary representation of Church numerals on average, when n is less than approximately 10,000 .
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MDPI and ACS Style
Furuya, I.; Kida, T. Compaction of Church Numerals. Algorithms 2019, 12, 159.
Furuya I, Kida T. Compaction of Church Numerals. Algorithms. 2019; 12(8):159.
Furuya, Isamu; Kida, Takuya. 2019. "Compaction of Church Numerals." Algorithms 12, no. 8: 159.
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