### Abstract

We introduce the notion of well-founded recursive order-sorted equational logic (OS) theories modulo axioms. Such theories define functions by well-founded recursion and are inherently terminating. Moreover, for well-founded recursive theories important properties such as conuence and sufficient completeness are modular for so-called fair extensions. This enables us to incrementally check these properties for hierarchies of such theories that occur naturally in modular rule-based functional programs. Well-founded recursive OS theories modulo axioms contain only commutativity and associativity-commutativity axioms. In order to support arbitrary combinations of associativity, commutativity and identity axioms, we show how to eliminate identity and (under certain conditions) associativity (without commutativity) axioms by theory transformations in the last part of the paper.

Original language | English (US) |
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Title of host publication | PPDP'11 - Proceedings of the 2011 Symposium on Principles and Practices of Declarative Programming |

Pages | 5-16 |

Number of pages | 12 |

DOIs | |

State | Published - Sep 2 2011 |

Event | 13th International ACM SIGPLAN Symposium on Principles and Practice of Declarative Programming, PPDP 2011 - Odense, Denmark Duration: Jul 20 2011 → Jul 22 2011 |

### Publication series

Name | PPDP'11 - Proceedings of the 2011 Symposium on Principles and Practices of Declarative Programming |
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### Other

Other | 13th International ACM SIGPLAN Symposium on Principles and Practice of Declarative Programming, PPDP 2011 |
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Country | Denmark |

City | Odense |

Period | 7/20/11 → 7/22/11 |

### Keywords

- Conuence
- Modularity
- Order-sorted rewriting modulo axioms
- Sufficient completeness
- Termination
- Well-founded recursive theory

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

*PPDP'11 - Proceedings of the 2011 Symposium on Principles and Practices of Declarative Programming*(pp. 5-16). (PPDP'11 - Proceedings of the 2011 Symposium on Principles and Practices of Declarative Programming). https://doi.org/10.1145/2003476.2003481