## Rewrite Proofs and Computations (1995)

Venue: | Proof and Computation |

Citations: | 11 - 0 self |

### BibTeX

@INPROCEEDINGS{Jouannaud95rewriteproofs,

author = {Jean-pierre Jouannaud},

title = {Rewrite Proofs and Computations},

booktitle = {Proof and Computation},

year = {1995},

pages = {173--218},

publisher = {Springer Verlag}

}

### OpenURL

### Abstract

. Rewriting is a general paradigm for expressing computations in various logics, and we focus here on rewriting techniques in equational logic. When used at the proof level, rewriting provides with a very powerful methodology for proving completeness results, a technique that is illustrated here. We also consider whether important properties of rewrite systems such as confluence and termination can be proved in a modular way. Finally, we stress the links between rewriting and tree automata. Previous surveys include [21; 18; 37; 12; 45; 46]. The present one owes much to [21]. Keywords. completion, confluence, critical pair, ground reducibility, inductive completion, local confluence, modularity, narrowing, order-sorted algebras, rewrite rule, rewriting, term algebra, termination, tree automata. 1 Introduction The use of equations is traditional in mathematics. Its use in computer science has culminated with the success of algebraic specifications, a method of specifying software by enc...

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Citation Context ...r important properties of rewrite systems such as confluence and termination can be proved in a modular way. Finally, we stress the links between rewriting and tree automata. Previous surveys include =-=[21; 18; 37; 12; 45; 46]-=-. The present one owes much to [21]. Keywords. completion, confluence, critical pair, ground reducibility, inductive completion, local confluence, modularity, narrowing, order-sorted algebras, rewrite... |

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Citation Context ...r important properties of rewrite systems such as confluence and termination can be proved in a modular way. Finally, we stress the links between rewriting and tree automata. Previous surveys include =-=[21; 18; 37; 12; 45; 46]-=-. The present one owes much to [21]. Keywords. completion, confluence, critical pair, ground reducibility, inductive completion, local confluence, modularity, narrowing, order-sorted algebras, rewrite... |

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Citation Context ...mma \Delta y ! y 13 R9 1 \Delta y ' y collapse (12,7) 14 y ' y simplify (2) 15 delete 16 (x \Gamma ) \Gamma ' x deduce (1,9) 17 R9 orient (x \Gamma ) \Gamma ! x 18 R7 x \Delta y ' x \Delta y collapse =-=(9,17)-=- 19 1 \Gamma \Delta y ! y delete 20 (x \Gamma ) \Gamma ! x x \Delta (x \Gamma \Delta y) ' y deduce (3,17) 21 R18 orient 22 x \Delta (x \Gamma \Delta y) ! y x \Delta x \Gamma ' 1 deduce (1,21) 23 R21 o... |

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Citation Context ...r important properties of rewrite systems such as confluence and termination can be proved in a modular way. Finally, we stress the links between rewriting and tree automata. Previous surveys include =-=[21; 18; 37; 12; 45; 46]-=-. The present one owes much to [21]. Keywords. completion, confluence, critical pair, ground reducibility, inductive completion, local confluence, modularity, narrowing, order-sorted algebras, rewrite... |

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Citation Context ... \Gamma ' 1 deduce (1,5) 7 R5 orient 8 1 \Gamma ! 1 (x \Gamma ) \Gamma \Delta y ' x \Delta y deduce (3,3) 9 R7 orient 10 (x \Gamma ) \Gamma \Delta y ! x \Delta y 1 \Gamma \Delta y ' 1 \Delta y deduce =-=(7,9)-=- 11 R9 orient 1 \Gamma \Delta y ! 1 \Delta y 12 R9 compose (11,2) 1 \Gamma \Delta y ! y 13 R9 1 \Delta y ' y collapse (12,7) 14 y ' y simplify (2) 15 delete 16 (x \Gamma ) \Gamma ' x deduce (1,9) 17 R... |

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