Compact bit encoding schemes for simply-typed lambda-terms

Takeda, Kotaro; Kobayashi, Naoki; Yaguchi, Kazuya; Shinohara, Ayumi

doi:10.1145/2951913.2951918

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…About bit encoding of λ-terms, Tromp [5] proposed a method for untyped λ-terms. In addition, very recently, Takeda et al [6] proposed an efficient method to encode simply-typed λ-terms. Combining our method with these encodings is one of our future works.…”

Section: Resultsmentioning

confidence: 99%

Compaction of Church Numerals for Higher-Order Compression

Furuya

Kida

2018

2018 Data Compression Conference

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In this study, we address the problem of compacting Church numerals. Church numerals appear as a representation of the repetitive part of data in higher-order compression. We propose a novel decomposition scheme for a natural number using tetration, which leads to a compact representation of λ-terms equivalent to the original Church numerals. For natural number n, we prove that the size of the lambda term obtained by the proposed method is O((slog 2 n) log n/ log log n ). Moreover, we quantitatively confirmed experimentally that the proposed method outperforms a binary expression of Church numerals when n is less than approximately 10000.

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Section: Resultsmentioning

confidence: 99%

Compaction of Church Numerals for Higher-Order Compression

Furuya

Kida

2018

2018 Data Compression Conference

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“…For bit encoding of λ-terms, Tromp [16] proposed a method for untyped λ-terms. Very recently, Takeda et al [17] proposed an efficient encoding scheme for simply-typed λ-terms. Finding an efficient bit encoding for our method is also our future work.…”

Section: Discussionmentioning

confidence: 99%

Compaction of Church Numerals

Furuya

Kida

2019

Algorithms

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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 O((slog 2 n) (log n/ log log n) ). 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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10 Years of the Higher-Order Model Checking Project (Extended Abstract)

Kobayashi

2019

Proceedings of the 21st International Symposium on Principles and Practice of Declarative Programming

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Compact bit encoding schemes for simply-typed lambda-terms

Cited by 3 publications

References 8 publications

Compaction of Church Numerals for Higher-Order Compression

Compaction of Church Numerals for Higher-Order Compression

Compaction of Church Numerals

10 Years of the Higher-Order Model Checking Project (Extended Abstract)

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