## Termination of on-demand rewriting and termination of OBJ programs (2001)

Venue: | In Proc. of 3rd International Conference on Principles and Practice of Declarative Programming, PPDP'01 |

Citations: | 30 - 20 self |

### BibTeX

@INPROCEEDINGS{Lucas01terminationof,

author = {Salvador Lucas},

title = {Termination of on-demand rewriting and termination of OBJ programs},

booktitle = {In Proc. of 3rd International Conference on Principles and Practice of Declarative Programming, PPDP'01},

year = {2001},

pages = {82--93},

publisher = {ACM Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

Declarative languages such as OBJ*, CafeOBJ, and Maude use syntactic annotations to introduce replacement restrictions aimed at improving termination or efficiency of computations. Unfortunately, there is a lack of formal techniques for proving such benefits. We show that context-sensitive rewriting and on-demand rewriting provide a suitable framework to address this problem. We provide methods to analyze termination of on-demand rewriting and apply them to analyze termination of OBJ*, CafeOBJ, and Maude programs. Keywords Program analysis, replacement restrictions, term rewriting, termination 1.

### Citations

950 |
Term Rewriting and All That
- Baader, Nipkow
- 1998
(Show Context)
Citation Context ...ictions (like those enumerated for `::') modifies termination of OBJ (like) programs. Term rewriting systems (TRSs) provide a suitable computational model for more sophisticated programming languages =-=[2]-=-. Syntactic replacement restrictions can be associated to symbols f of a signature \Sigma by means of a replacement maps: \Sigma ! P(N) [14] that discriminates the argument positions (f) ` f1; : : : ;... |

453 | Termination of rewriting
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(Show Context)
Citation Context ...g that there is no infinite chain of dependency pairs associated to R 1s[1]. It is not difficult to see that more conventional techniques such as Knuth-Bendix, polynomial, or recursive path orderings =-=[4]-=- do not apply to this example. Given replacement mapssand D , ODR permits reductions on positions that are not replacing (according to ); this is not captured by the transformation of Definition 2. In... |

214 | Termination of term rewriting using dependency pairs
- Arts, Giesl
- 2000
(Show Context)
Citation Context ... x Remark 1. R 1sin Example 4 is proved to be terminating by using Arts and Giesl's dependency pairs technique, i.e., by checking that there is no infinite chain of dependency pairs associated to R 1s=-=[1]-=-. It is not difficult to see that more conventional techniques such as Knuth-Bendix, polynomial, or recursive path orderings [4] do not apply to this example. Given replacement mapssand D , ODR permit... |

124 | Principles of Maude
- Clavel, Eker, et al.
- 2000
(Show Context)
Citation Context ...g to evaluate expressions. A frequent problem here is nontermination.sSyntactic annotations (i.e., associated to the arguments of symbols) have been used in OBJ2 [8], OBJ3 [11], CafeOBJ [9], or Maude =-=[3]-=- as replacement restrictions to (hopefully) avoid nontermination. They are often specified as sequences of integers in parentheses called local strategies (see Figure 1). Local strategies guide the ev... |

102 |
et a!. Principles of OBJ2
- Futatsugi
(Show Context)
Citation Context ... ELAN, or Maude use innermost rewriting to evaluate expressions. A frequent problem here is nontermination.sSyntactic annotations (i.e., associated to the arguments of symbols) have been used in OBJ2 =-=[8]-=-, OBJ3 [11], CafeOBJ [9], or Maude [3] as replacement restrictions to (hopefully) avoid nontermination. They are often specified as sequences of integers in parentheses called local strategies (see Fi... |

69 | Context-sensitive computations in functional and functional logic programs
- Lucas
- 1998
(Show Context)
Citation Context ...utational model for more sophisticated programming languages [2]. Syntactic replacement restrictions can be associated to symbols f of a signature \Sigma by means of a replacement maps: \Sigma ! P(N) =-=[14]-=- that discriminates the argument positions (f) ` f1; : : : ; ar(f)g on which we can perform rewriting steps. Negative integers in local strategies can be managed using an additional replacement map D ... |

43 | Context-sensitive rewriting strategies
- Lucas
- 2002
(Show Context)
Citation Context ...ave: g(f(a),b) ,! g(c,b) which is a -normal form (note that 2 62 (g)). According to Theorem 7, the formalization of !' above could be seen as the description of a context-sensitive rewritingsstrategy =-=[15]-=- which is specified by means of local strategies. Computations yielding partially evaluated results can also be used to achieve full evaluations: if a term t has a (possibly infinite) normal form, it ... |

32 | Termination of context-sensitive rewriting
- Zantema
- 1997
(Show Context)
Citation Context ...f OBJ programs specifying local strategies without negative indices. We demonstrate that termination of such OBJ programs can be analyzed as termination of CSR. Termination of CSR has been studied in =-=[10, 13, 19, 20, 6]-=-. Concerning arbitrary local strategies, we introduce on-demand rewriting (ODR, using two replacement mapssand D ) as an extension of CSR. In [10], Giesl and Middeldorp provide transformations of TRSs... |

28 |
Term Rewriting with Operator Evaluation Strategy
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(Show Context)
Citation Context .... attempted. Negative indices indicate that the corresponding argument is evaluated `on-demand', where a `demand' is an attempt to match a pattern to the term that occurs in such an argument position =-=[5, 11, 18]-=-. For instance, the local strategy for `::' in Example 1 specifies that its second argument is evaluated `on-demand'. A local strategy such as (1) disables the evaluation of 2nd(0::from(s(0))) into s(... |

27 |
Termination of context-sensitive rewriting by rewriting
- Lucas
(Show Context)
Citation Context ...f OBJ programs specifying local strategies without negative indices. We demonstrate that termination of such OBJ programs can be analyzed as termination of CSR. Termination of CSR has been studied in =-=[10, 13, 19, 20, 6]-=-. Concerning arbitrary local strategies, we introduce on-demand rewriting (ODR, using two replacement mapssand D ) as an extension of CSR. In [10], Giesl and Middeldorp provide transformations of TRSs... |

25 |
An overview of CAFE specification environment – an algebraic approach for creating, verifying, and maintaining formal specifications over networks
- Futatsugi, Nakagawa
- 1997
(Show Context)
Citation Context ...rmost rewriting to evaluate expressions. A frequent problem here is nontermination.sSyntactic annotations (i.e., associated to the arguments of symbols) have been used in OBJ2 [8], OBJ3 [11], CafeOBJ =-=[9]-=-, or Maude [3] as replacement restrictions to (hopefully) avoid nontermination. They are often specified as sequences of integers in parentheses called local strategies (see Figure 1). Local strategie... |

25 | Transforming context-sensitive rewrite systems
- Giesl, Middeldorp
- 1999
(Show Context)
Citation Context ...f OBJ programs specifying local strategies without negative indices. We demonstrate that termination of such OBJ programs can be analyzed as termination of CSR. Termination of CSR has been studied in =-=[10, 13, 19, 20, 6]-=-. Concerning arbitrary local strategies, we introduce on-demand rewriting (ODR, using two replacement mapssand D ) as an extension of CSR. In [10], Giesl and Middeldorp provide transformations of TRSs... |

23 | Lazy rewriting on eager machinery
- Fokkink, Kamperman, et al.
- 2000
(Show Context)
Citation Context ...et R = (\Sigma; R) be a TRS and ; D 2 M \Sigma . Then, ,!`,! h; D i `,!tD . Proof. Immediate, by definition of ODR. The definition of ODR follows lazy rewriting of [12]. The more recent definition of =-=[7]-=- is aimed at dealing with graphs, rather than terms. Moreover, it uses decorations of nodes that incorporate the replacing/non-replacing character of each node inside the syntactic structure of graphs... |

20 |
Context-sensitive AC-rewriting
- Ferreira, Ribeiro
- 1999
(Show Context)
Citation Context |

17 | The evaluation strategy for head normal form with and without on-demand flags, in: K. Futatsugi (Ed
- Nakamura, Ogata
- 2001
(Show Context)
Citation Context ...upported by Spanish CICYT and Conselleria de Cultura y Educaci'o de la Generalitat Valenciana. 1 As in [11], by OBJ we mean OBJ2, OBJ3, CafeOBJ, or Maude. The following CafeOBJ program (borrowed from =-=[17]-=-): mod! TEST -- [T] op 0 : -? T op s : T -? T --strat: (1) op :: : T T -? T --strat: (1-2) op 2nd : T -? T --strat: (1 0) op from : T -? T --strat: (0) vars X Y Z : T eq from(X) = X::from(s(X)) . eq 2... |

12 | Reduction strategies for term rewriting systems - Nagaya - 1999 |

12 |
Operational semantics of rewriting with the on-demand evaluation strategy, in
- Ogata, Futatsugi
- 2000
(Show Context)
Citation Context ...ary E-strategy maps Ogata and Futatsugi have provided an operational description of the on-demand evaluation strategy used in OBJ3 and CafeOBJ, where negative integers are allowed in local strategies =-=[18]-=-. Nakamura and Ogata [17] have described the corresponding evaluation mapping eval' by using a reduction relation. Unfortunately, such a description is recursive and the definition of a single reducti... |

4 | Freezing - termination proofs for classical, context-sensitive and innermost rewriting
- Steinbach, Xi
- 1998
(Show Context)
Citation Context |

1 |
Introducing OBJ, volume Software Engineering with OBJ: algebraic specification in action
- Goguen, Winkler, et al.
- 2000
(Show Context)
Citation Context ...st.ac.jp/ masaki-n/correction.html for a corrigendum of the published version of the paper that concerns this theorem. 4 Actually, this depends on the form of default strategies for OBJ3 programs. In =-=[11]-=-, they are described in such a way that are compatible with the canonical replacement map of the program. Proof. By contradiction. If tj p is not a h; D i-normal form, then tj p ,! h; D i s for some s... |