## Abstract

We propose a (limited) solution to the problem of constructing stream values defined by recursive equations that do not respect the guardedness condition. The guardedness condition is imposed on definitions of corecursive functions in Coq, AGDA, and other higher-order proof assistants. In this paper, we concentrate in particular on those non-guarded equations where recursive calls appear under functions. We use a correspondence between streams and functions over natural numbers to show that some classes of non-guarded definitions can be modelled through the encoding as structural recursive functions. In practice, this work extends the class of stream values that can be defined in a constructive type theory-based theorem prover with inductive and coinductive types, structural recursion and guarded corecursion.

Original language | English |
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Title of host publication | Types for proofs and programs |

Editors | S Berardi, F Damiani, U DeLiguoro |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 220-236 |

Number of pages | 17 |

ISBN (Print) | 978-3-642-02443-6 |

DOIs | |

Publication status | Published - 2009 |

Event | Types for Proofs and Programs: International Conference - Villa Gualino, Turin, Italy Duration: 26 Mar 2008 → 29 Mar 2008 http://types2008.di.unito.it/ |

### Conference

Conference | Types for Proofs and Programs: International Conference |
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Abbreviated title | TYPES 2008 |

Country/Territory | Italy |

City | Turin |

Period | 26/03/08 → 29/03/08 |

Internet address |

## Keywords

- Constructive Type Theory
- Structural Recursion
- Coinductive types
- Guarded Corecursion
- Coq
- DEFINITIONS
- PRODUCTIVITY