Compaction of Church Numerals for Higher-Order Compression

We addressed the problem of compacting the Church numerals, which is useful for higher-order compression. We proposed a novel decomposition scheme for a natural number using tetration, which leads to the compact representation of λ-terms equivalent to the Church numerals. For natural number n, we proved that the size of the lambda term obtained by our method is O(slog2n log n/ log log ). We also quantitatively confirmed via experiments that in many cases, our method can produce shorter λ-terms more than existing methods.