## On termination of constraint logic programs (1995)

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Venue: | In Proc. CP'95, LNCS 976 |

Citations: | 13 - 2 self |

### BibTeX

@INPROCEEDINGS{Colussi95ontermination,

author = {Livio Colussi and Elena Marchiori and Massimo Marchiori},

title = {On termination of constraint logic programs},

booktitle = {In Proc. CP'95, LNCS 976},

year = {1995},

pages = {431--448},

publisher = {Springer}

}

### Years of Citing Articles

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### Abstract

Abstract. This paper introduces a necessary and sufficient condition for termination of constraint logic programs. The method is based on assigning a dataflow graph to a program, whose nodes are the program points and whose arcs are abstractions of the rules of a transition system, describing the operational behaviour of constraint logic programs. Then termination is proven using a technique inspired by the seminal approach of Floyd for proving termination of flowchart programs. 1

### Citations

563 |
Assigning meanings to programs
- Floyd
- 1967
(Show Context)
Citation Context ...ions are combined in the de nition of termination triple, which provides a characterization of terminating clp's (w.r.t. a precondition). Our approach is inspired by the technique introduced by Floyd =-=[Flo67]-=- toprove termination of owchart programs. Intuitively, in a termination triple the invariants and the W-functions are chosen in such away that every computation of the program is mapped into a decreas... |

138 |
Termination of logic programs: The never-ending story
- Schreye, Decorte
- 1994
(Show Context)
Citation Context ... termination of constraint logic programs (clp's for short). Termination of clp's is a fairly recent topic, and the only contribution we are aware of is by Mesnard [Mes93], cited in the recent survey =-=[DSD94]-=- on termination of logic programs. However, the aim of that work is di erent, namely to provide su cient conditions for the termination problem of clp's, based on approximation techniques. Here we aim... |

55 | Inductive Assertion Method for Logic Programs
- Drabent, Maluszynski
- 1988
(Show Context)
Citation Context ... unify. In this representation the rst type of arc abstracts a clause, and the second one the ow ofcontrol. Then, the graph is used to detect possible divergences, and other proof methods ([BC89] and =-=[DM88]-=-) are used to obtain the information on the operational behaviour of the program which is needed to perform the termination analysis on the graph. However, for our purpose, namely to give acharacteriz... |

41 | Norms on terms and their use in proving universal termination of a logic program - BOSSI, COCCO, et al. - 1994 |

40 |
Verifying correctness of logic programs
- Bossi, Cocco
- 1989
(Show Context)
Citation Context .... n1 and n2 unify. In this representation the rst type of arc abstracts a clause, and the second one the ow ofcontrol. Then, the graph is used to detect possible divergences, and other proof methods (=-=[BC89]-=- and [DM88]) are used to obtain the information on the operational behaviour of the program which is needed to perform the termination analysis on the graph. However, for our purpose, namely to give a... |

10 | A methodology for proving termination of logic programs
- Wang, Shyamasundar
- 1994
(Show Context)
Citation Context ...imate the real computation of the program, by possibly introducing extra computations, in the case that :A would have failed. Note that this technique is also implicitly used in Wang and Shyamasundar =-=[WS94]-=-. Using this de nition of data ow graph,we can obtain a sound description of an invariant for P: Theorem 15 can be restated as su cient condition, where in case 1. a negative literal is treated as an ... |

6 | A declarative approach for first-order built-in’s in Prolog. Applicable Algebra
- APT, MARCHIORI, et al.
- 1994
(Show Context)
Citation Context ...e of some constraints can turn an execution into a (finite) failure, because the actual state does not satisfy a constraint. A similar behaviour can be observed in some built-in's of Prolog (see e.g. =-=[AMP94]-=-). Moreover, in most CLP systems, the state is divided into two components containing the so-called active and passive constraint, and only the consistency of the active constraint is checked. Then th... |

5 |
Etude de la terminaison des programmes logiques avec constraintes aux moyens d'approximations
- Mesnard
- 1993
(Show Context)
Citation Context ...su cient and necessary condition for termination of constraint logic programs (clp's for short). Termination of clp's is a fairly recent topic, and the only contribution we are aware of is by Mesnard =-=[Mes93]-=-, cited in the recent survey [DSD94] on termination of logic programs. However, the aim of that work is di erent, namely to provide su cient conditions for the termination problem of clp's, based on a... |

4 |
Constraint Logic Programming: A Survey. JLP
- Jaffar, Maher
- 1994
(Show Context)
Citation Context ...enoted by r, s, t. A sequence El,..., Ek of syntactic objects is denoted by E or (El,..., E~)I and (sl = tl/~... Ask = tk) is abbreviated by ~ = ~. Constraint Logic Programs The reader is referred to =-=[JM94]-=- for a detailed introduction to Constraint Logic Programming. Here we present only those concepts and notation that we shall need in the sequel. A constraint c is a (first-order) formula on Term(VAR) ... |

3 |
Logic Programming and Negation: A Survey. JLP
- Apt, Bol
- 1994
(Show Context)
Citation Context ...y contain negated atoms :A.We suppose that negated atoms are solved using the negation as nite failure procedure or one of its modi cations which allow to deal also with non-ground literals (see e.g. =-=[AB94]-=-). Adata ow graph is assigned to a normal clp P, constructed by means of the following steps:s1. consider every negated atom :A of the program P as an atom A and build the data ow graph using De nitio... |

3 | A dataflow semantics for constraint logic programs
- Colussi, Marchiori, et al.
- 1995
(Show Context)
Citation Context ...~(A) contains those states obtained by applying the transition rule C to ((A) 9 A, a), for every a E r This theorem is derived from a fixpoint semantics which has been introduced in a companion paper =-=[CMM95]-=-. The conditions 1-3 of Theorem 15 correspond to the three cases of the definition of an operator F on n-tuples of assertions whose least fixpoint # F yields a semantics equal to (Z1(7), r Z,~(7), r F... |

1 |
A declarative approach for rst-order built-in's of Prolog
- Apt, Marchiori, et al.
- 1994
(Show Context)
Citation Context ...ce of some constraints can turn an execution into a ( nite) failure, because the actual state does not satisfy a constraint. A similar behaviour can be observed in some built-in's of Prolog (see e.g. =-=[AMP94]-=-). Moreover, in most CLP systems, the state is divided into two components containing the so-called active and passive constraint, and only the consistency of the active constraint ischecked. Then the... |

1 |
A data ow semantics for constraint logic programs
- Colussi, Marchiori, et al.
- 1995
(Show Context)
Citation Context ...s(A) contains those states obtained by applying the transition rule C to (hAi A� ), for every 2 call(A). This theorem is derived from a xpoint semantics which has been introduced in a companion paper =-=[CMM95]-=-. The conditions 1-3 of Theorem 15 correspond to the three cases of the de nition of an operator F on n-tuples of assertions whose least xpoint F yields a semantics equal to (I1(P� )�:::�In(P� )). For... |

1 |
Termination of Programs Represented as Interpreted Graphs
- Manna
- 1970
(Show Context)
Citation Context ... in i is shown to be strictly greater than the W-function of j applied to output( � ). To examine only a nite number of paths, we adapt a technique introduced by Floyd [Flo67] and formalized by Manna =-=[Man70]-=- to prove termination of owchart programs: only those nodes of the graph which `cut' some cycle are considered (see De nition 9), and only suitable paths connecting such nodes, called smart, are exami... |