## Abstract

Automated analysis of recursive derivations in logic programming is known to be a hard problem. Both termination and nontermination are undecidable problems in Turing-complete languages. However, some declarative languages offer a practical work-around for this problem, by making a clear distinction between whether a program is meant to be understood inductively or coinductively. For programs meant to be understood inductively, termination must be guaranteed, whereas for programs meant to be understood coinductively, productive non-termination (or “productivity”) must be ensured. In practice, such classification helps to better understand and implement some nonterminating computations. Logic programming was one of the first declarative languages to make this distinction: in the 1980’s, Lloyd and van Emden’s “computations at infinity” captured the big-step operational semantics of derivations that produce infinite terms as answers. In modern terms, computations at infinity describe “global productivity” of computations in logic programming. Most programming languages featuring coinduction also provide an observational, or small-step, notion of productivity as a computational counterpart to global productivity. This kind of productivity is ensured by checking that finite initial fragments of infinite computations can always be observed to produce finite portions of their infinite answer terms. In this paper we introduce a notion of observational productivity for logic programming as an algorithmic approximation of global productivity, give an effective procedure for semi-deciding observational productivity, and offer an implemented automated observational productivity checker for logic programs.

Original language | English |
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Title of host publication | Logic-Based Program Synthesis and Transformation. LOPSTR 2016 |

Publisher | Springer |

Pages | 168-186 |

Number of pages | 19 |

ISBN (Electronic) | 9783319631394 |

ISBN (Print) | 9783319631387 |

DOIs | |

Publication status | Published - 25 Jul 2017 |

Event | 26th International Symposium on Logic-Based Program Synthesis and Transformation 2016 - Edinburgh, United Kingdom Duration: 6 Sept 2016 → 8 Sept 2016 |

### Publication series

Name | Lecture Notes in Computer Science |
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Volume | 10184 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 26th International Symposium on Logic-Based Program Synthesis and Transformation 2016 |
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Abbreviated title | LOPSTR 2016 |

Country/Territory | United Kingdom |

City | Edinburgh |

Period | 6/09/16 → 8/09/16 |

## Keywords

- Coinduction
- Corecursion
- Logic programming
- Productivity
- Termination

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science