### Abstract

We consider the problem of how to compactly encode simply-Typed λ-Terms into bit strings. The work has been motivated by Kobayashi et al.'s recent work on higher-order data compression, where data are encoded as functional programs (or, λ-Terms) that generate them. To exploit its good compression power, the compression scheme has to come with a method for compactly encoding the λ-Terms into bit strings. To this end, we propose two type-based bit-encoding schemes; the first one encodes a λ-Term into a sequence of symbols by using type information, and then applies arithmetic coding to convert the sequence to a bit string. The second one is more sophisticated; we prepare a context-free grammar (CFG) that describes only well-Typed terms, and then use a variation of arithmetic coding specialized for the CFG. We have implemented both schemes and confirmed that they often output more compact codes than previous bit encoding schemes for λ-Terms.

Original language | English |
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Pages (from-to) | 146-157 |

Number of pages | 12 |

Journal | ACM SIGPLAN Notices |

Volume | 51 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2016 Sep 4 |

### Keywords

- Bit encoding
- Data compression
- Simply-Typed lambda-calculus

### ASJC Scopus subject areas

- Computer Science(all)

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## Cite this

*ACM SIGPLAN Notices*,

*51*(9), 146-157. https://doi.org/10.1145/2951913.2951918