How to count linear and affine closed lambda terms?

## Author: Pierre Lescanne

## Paper Information

Title: | How to count linear and affine closed lambda terms? |

Authors: | Pierre Lescanne |

Proceedings: | Linearity/TLLA Pre-proceedings |

Editors: | Maribel Fernandez, Valeria de Paiva, Thomas Ehrhard and Lorenzo Tortora De Falco |

Keywords: | linear term, affine term, combinatoric, lambda calculus |

Abstract: | ABSTRACT. Affine lambda-terms are lambda-terms in which each bound variable occurs at most once and linear lambda-terms are lambda-terms in which each bound variable occurs once and only once. In this paper we count the number of affine closed lambda-terms of size n, linear closed lambda-terms of size n, affine closed beta-normal forms of size n and linear closed beta-normal forms of size n, for several measures of the size of lambda-terms. From these formulas, we show how we can derive programs for generating all the terms of size n for each class. The foundation of all of this is a specific data structure, made of contexts in which one counts all the holes at each level of abstractions by lambda's. |

Pages: | 6 |

Talk: | Jul 08 09:20 (Session 34J) |

Paper: |