## Conditional Term Graph Rewriting (1997)

Venue: | In Proceedings of the 6th International Conference on Algebraic and Logic Programming |

Citations: | 2 - 2 self |

### BibTeX

@INPROCEEDINGS{Ohlebusch97conditionalterm,

author = {Enno Ohlebusch},

title = {Conditional Term Graph Rewriting},

booktitle = {In Proceedings of the 6th International Conference on Algebraic and Logic Programming},

year = {1997},

pages = {144--158}

}

### OpenURL

### Abstract

. For efficiency reasons, term rewriting is usually implemented by graph rewriting. It is known that graph rewriting is a sound and complete implementation of (almost) orthogonal term rewriting systems; see [BEG + 87]. In this paper, we extend the result to properly oriented orthogonal conditional systems with strict equality. In these systems extra variables are allowed in conditions and right-hand sides of rules. 1 Introduction Attempts to combine the functional and logic programming paradigms have recently been receiving increasing attention; see [Han94b] for an overview of the field. It has been argued in [Han95] that strict equality is the only sensible notion of equality for possibly nonterminating programs. In this paper, we adopt this point of view--so every functional logic program is regarded as an orthogonal conditional term rewriting system (CTRS) with strict equality. The standard operational semantics for functional (or equational) logic programming is conditional narr...

### Citations

787 | Rewrite systems
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- 1990
(Show Context)
Citation Context ... space reasons, several proofs are omitted. 2 Preliminaries The reader is assumed to be familiar with the basic concepts of term rewriting (which can be found in the surveys of Dershowitz & Jouannaud =-=[DJ90]-=- and Klop [Klo92], for instance). Here, we merely recall less common definitions and some basic facts concerning conditional term rewriting. Let (F ; R) be a term rewriting system (TRS). A function sy... |

586 | Term Rewriting Systems
- Klop
- 1992
(Show Context)
Citation Context ...several proofs are omitted. 2 Preliminaries The reader is assumed to be familiar with the basic concepts of term rewriting (which can be found in the surveys of Dershowitz & Jouannaud [DJ90] and Klop =-=[Klo92]-=-, for instance). Here, we merely recall less common definitions and some basic facts concerning conditional term rewriting. Let (F ; R) be a term rewriting system (TRS). A function symbol f 2 F is cal... |

349 | The integration of functions into logic programming: From theory to practice
- Hanus
- 1994
(Show Context)
Citation Context ...ables are allowed in conditions and right-hand sides of rules. 1 Introduction Attempts to combine the functional and logic programming paradigms have recently been receiving increasing attention; see =-=[Han94b]-=- for an overview of the field. It has been argued in [Han95] that strict equality is the only sensible notion of equality for possibly nonterminating programs. In this paper, we adopt this point of vi... |

301 | Uniform narrowing strategies
- Echahed
- 1992
(Show Context)
Citation Context ...a CTRS R with strict equality, we tacitly assume that R is extended with R eq . The next proposition shows that the definition above specifies the desired behavior of a CTRS with strict equality; cf. =-=[AEH94]-=-. Proposition5. Let R be a 3-CTRS with strict equality. The following statements are equivalent for all terms s and t in T (F ; V): 1. s==t is reducible to true in R ] R eq . 2. s and t are reducible ... |

89 |
Conditional rewrite rules: Confluence and termination
- Bergstra, Klop
- 1986
(Show Context)
Citation Context ...ormal form with respect to Ru . Orthogonal normal 2-CTRS satisfy the so-called parallel moves lemma. Thus they are (level-) confluent. We next briefly recall this result achieved by Bergstra and Klop =-=[BK86]-=-; see also Suzuki et al. [SMI95]. 1 Note that Ru may contain rules l ! r with Var(r) 6` Var(l). Definition1. Let A : s ! [p;l!r(c] t be a rewrite step in a CTRS R and let q 2 Pos(s). The set qnA of de... |

89 | Computing in Systems Described by Equations - O'Donnell - 1977 |

24 | Level-Confluence of Conditional Rewrite Systems with Extra Variables in Right-Hand Sides
- Suzuki, Middeldorp, et al.
- 1995
(Show Context)
Citation Context ...extra variables are instantiated by ground constructor terms only. We obtain as a consequence that functional CTRSs are level-confluent. This is not a new result--it is a special case of a theorem in =-=[SMI95]-=-. Our proof, however, is simpler than that in [SMI95]. Section 4 is dedicated to graph rewriting. We neither follow the approach of [BEG + 87] nor that of [Plu93]. Instead, we use the term based model... |

22 | On Extra Variables in (Equational) Logic Programming
- Hanus
- 1995
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Citation Context ...sound and complete implementation of CTRSs with strict equality ([Han95], Theorem 3.5 and page 676: "Conditions 1 and 2 are necessary to extend Theorem 3.5 ..."). But the proof of this fact =-=(given in [Han94a]-=-, Theorem 3.8) is incorrect. There is the following counterexample: R = 8 ! : a ! x ( g(x)==e g(b) ! e; g(c) ! e h(x) ! f(x; x); f(b; c) ! d Since a!R b and a!R c (consequently, the system is not conf... |

18 | Completeness results for basic narrowing. Applicable Algebra - Middeldorp, Hamoen - 1994 |

12 |
Evaluation of Functional Expressions by Hypergraph Rewriting
- Plump
- 1993
(Show Context)
Citation Context ...-it is a special case of a theorem in [SMI95]. Our proof, however, is simpler than that in [SMI95]. Section 4 is dedicated to graph rewriting. We neither follow the approach of [BEG + 87] nor that of =-=[Plu93]-=-. Instead, we use the term based model of [KO95] in which directed acyclic graphs correspond to well-marked terms. The first part of Section 4 is a mirror image of Section 3: it is shown that the grap... |

9 | Church-Rosser theorem for replacement systems - Staples - 1975 |

6 |
Modularity in noncopying term rewriting
- Kurihara, Ohuchi
- 1995
(Show Context)
Citation Context ...r proof, however, is simpler than that in [SMI95]. Section 4 is dedicated to graph rewriting. We neither follow the approach of [BEG + 87] nor that of [Plu93]. Instead, we use the term based model of =-=[KO95]-=- in which directed acyclic graphs correspond to well-marked terms. The first part of Section 4 is a mirror image of Section 3: it is shown that the graph rewrite relation of a functional CTRS has almo... |