## Modular Termination Proofs for Logic and Pure Prolog Programs (1993)

Venue: | ADVANCES IN LOGIC PROGRAMMING THEORY |

Citations: | 44 - 5 self |

### BibTeX

@INPROCEEDINGS{Apt93modulartermination,

author = {Krzysztof R. Apt and Dino Pedreschi},

title = {Modular Termination Proofs for Logic and Pure Prolog Programs},

booktitle = {ADVANCES IN LOGIC PROGRAMMING THEORY},

year = {1993},

pages = {183--229},

publisher = {Oxford University Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

We provide a uniform and simplified presentation of the methods of Bezem [Bez93] (first published as [Bez89]) and of Apt and Pedreschi [AP93] (first published as [AP90]) for proving termination of logic and Prolog programs. Then we show how these methods can be refined so that they can be used in a modular way.

### Citations

1876 |
Foundations of Logic Programming
- Lloyd
- 1987
(Show Context)
Citation Context ...tion of pure Prolog programs. Then in Sections 4 and 5 we refine these methods so that they can be used in a modular way. 1.2 Preliminaries Throughout this paper we use the standard notation of Lloyd =-=[Llo87]-=- and Apt [Apt90]. In particular, for a logic program P (or simply a program) we denote the Herbrand Base of P by BP and the least Herbrand model of P by MP . Also, we use Prolog's convention identifyi... |

630 | The Art of Prolog - Sterling, Shapiro - 1986 |

456 | Termination of Rewriting
- Dershowitz
- 1987
(Show Context)
Citation Context ... b 2 Z; where X;Y; Z are finite multisets of elements of W , and then define the multiset ordering OE m over (W; !) as the transitive closure of the relation OE. It is well-known (see e.g. Dershowitz =-=[Der87]-=-) that multiset ordering over a well-founded ordering is again well-founded. In particular, the multiset ordering over the set of natural numbers with their usual ordering is well-founded. 2 Terminati... |

424 |
Logic programming
- Apt
- 1990
(Show Context)
Citation Context ...log programs. Then in Sections 4 and 5 we refine these methods so that they can be used in a modular way. 1.2 Preliminaries Throughout this paper we use the standard notation of Lloyd [Llo87] and Apt =-=[Apt90]-=-. In particular, for a logic program P (or simply a program) we denote the Herbrand Base of P by BP and the least Herbrand model of P by MP . Also, we use Prolog's convention identifying in the contex... |

213 |
Unfold/fold transformation of logic programs
- Tamaki, Sato
- 1984
(Show Context)
Citation Context ...nating, and that for a list s, all LD-derivations of QUICKSORT [ f / qs(s; t)g are finite. (To be more precise, we obtain QUICKSORT from the above program by unfolding in the sense of Tamaki and Sato =-=[TS84]-=-.) A generate & test scheme Consider the following one-clause program GT, representing a generate and test schema; it is parametric with respect to the generate and test relations. gtsolve(X, Y) / gen... |

126 | Reasoning about termination of pure prolog programs
- Apt, Pedreschi
- 1993
(Show Context)
Citation Context ... Universit`a di Pisa Corso Italia 40, 56125 Pisa, Italy Abstract We provide a uniform and simplified presentation of the methods of Bezem [Bez93] (first published as [Bez89]) and of Apt and Pedreschi =-=[AP93]-=- (first published as [AP90]) for proving termination of logic and Prolog programs. Then we show how these methods can be refined so that they can be used in a modular way. 1991 Mathematics Subject Cla... |

68 |
EĆcient tests for top-down termination of logical rules
- Ullman, Gelder
- 1988
(Show Context)
Citation Context ...e easily applied to various Prolog programs. The level mapping can be usually defined as a simple function of the terms of the ground atom. The following natural concept, due to Ullman and Van Gelder =-=[UvG88]-=-, will often be useful. Define by induction a function j j, called listsize, which assigns natural numbers to ground terms: j[xjxs]j = jxsj + 1; jf(x 1 ; : : :; xn )j = 0 if f 6= [ : j : ]: Note that ... |

51 | Strong termination of Logic Programs
- Bezem
- 1991
(Show Context)
Citation Context ...m, The Netherlands Dino Pedreschi Dipartimento di Informatica, Universit`a di Pisa Corso Italia 40, 56125 Pisa, Italy Abstract We provide a uniform and simplified presentation of the methods of Bezem =-=[Bez93]-=- (first published as [Bez89]) and of Apt and Pedreschi [AP93] (first published as [AP90]) for proving termination of logic and Prolog programs. Then we show how these methods can be refined so that th... |

50 |
Studies in Pure Prolog: Termination
- Apt, Pedreschi
- 1990
(Show Context)
Citation Context ...Italia 40, 56125 Pisa, Italy Abstract We provide a uniform and simplified presentation of the methods of Bezem [Bez93] (first published as [Bez89]) and of Apt and Pedreschi [AP93] (first published as =-=[AP90]-=-) for proving termination of logic and Prolog programs. Then we show how these methods can be refined so that they can be used in a modular way. 1991 Mathematics Subject Classification: 68Q40, 68T15. ... |

46 |
Characterizing termination of logic programs with level mapping
- Bezem
- 1992
(Show Context)
Citation Context ...eschi Dipartimento di Informatica, Universit`a di Pisa Corso Italia 40, 56125 Pisa, Italy Abstract We provide a uniform and simplified presentation of the methods of Bezem [Bez93] (first published as =-=[Bez89]-=-) and of Apt and Pedreschi [AP93] (first published as [AP90]) for proving termination of logic and Prolog programs. Then we show how these methods can be refined so that they can be used in a modular ... |

29 | Continuity, consistency, and completeness properties for logic programs - Cavedon - 1999 |

26 |
On the Relationship between Logic and Functional Languages," Draft of article to appear
- Reddy
- 1984
(Show Context)
Citation Context ... defining ms requires a more artificial level mapping in which ---ms(xs, ys, ls)--- = ---ls---+1. 23 Curry's type assignment Consider the following program for Curry's type assignment (see e.g. Reddy =-=[Red86]-=-). In Curry's type system, a type assignment E ` M : T expresses the fact that -term M is assigned type T w.r.t. environment E. Here, -terms are represented using the function symbols var (for variabl... |

23 |
A framework for analyzing the termination of definite logic programs with respect to call patterns
- SCHREYE, VERSCHAETSE, et al.
- 1992
(Show Context)
Citation Context ...rce the decrease in the second clause. Both drawbacks pose serious limitations for the practical applicability of the proposed proof method. First, as argued by De Schreye, Verschaetse and Bruynooghe =-=[SVB92]-=-, unnatural level mappings are difficult to discover by automated tools. Secondly, modularity is essential in mastering the complexity of largescaled programs. These drawbacks share their originating ... |

2 |
Uber eine Schluweise aus dem Endlichen ins Unendliche
- Konig
- 1927
(Show Context)
Citation Context ... P [ fGg are finite. Proof. By the fact that we fixed the choice of mgu's and the fact that logic programs are finite, the S-trees are finitely branching. The claim now follows by Konig's Lemma Konig =-=[Kon27]-=-. 2 This lemma allows us to concentrate on S-trees. For a program P and a goal G, we denote by nodesP (G) the number of nodes in the S-tree for P [ fGg. Lemma 2.10 Let P be a program and G a goal such... |