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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