## Properties of Input-Consuming Derivations (1999)

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Citations: | 8 - 4 self |

### BibTeX

@MISC{Bossi99propertiesof,

author = {A. Bossi and S. Etalle and S. Rossi},

title = {Properties of Input-Consuming Derivations},

year = {1999}

}

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### Abstract

We study the properties of input-consuming derivations of moded logic programs. Input-consuming derivations do not employ a fixed selection rule, and can be used to model the behavior of logic programs using dynamic scheduling and employing constructs such as delay declarations. We consider the class of nicely-moded programs and queries. We show that for these programs one part of the well-known Switching Lemma holds also for input-consuming derivations. Furthermore, we provide conditions which guarantee that all input-consuming derivations starting in a Nicely-Moded query are finite. The method presented here is easy to apply and generalizes other related works.

### Citations

1921 | Foundations of Logic Programming - Lloyd - 1987 |

435 | Logic Programming - Apt - 1990 |

258 |
The Goedel Programming Language
- Hill, Lloyd
- 1994
(Show Context)
Citation Context ... concept of input-consuming derivation step we refer to the sequel: The resolution of an atom with a definition must not instantiate the input arguments of the resolved atom. On the other hand, Gödel =-=[HL94]-=- and ECLiPSe [WNS97] use delay declarations, and SICStus Prolog [SIC97] employs block declarations (which are a special kind of delay declarations). Both delay and block declarations check the partial... |

200 | The execution algorithm of Mercury, an efficient purely declarative logic programming language
- Somogyi, Henderson, et al.
- 1996
(Show Context)
Citation Context ...-moded, nicely-moded, simplymoded, etc.); see for example [AP94b, AM94], or more simply, the tables of programs we report in Section 7, or consider for instance the logic programming language Mercury =-=[SHC96]-=-, which requires that its programs are moded (and well-moded). Contributions of this paper In this paper we study some properties of input-consuming derivations. In the first place we show that, if we... |

196 |
From Logic Programming to Prolog
- Apt
- 1997
(Show Context)
Citation Context ...ven an atom A, we denote by Rel(A) the predicate symbol of A. A query is a finite, possibly empty, sequence of atoms A1, . . .,Am. The empty query is denoted by �. Following the convention adopted in =-=[Apt97]-=-, we use bold characters to denote queries. A clause is a formula H ← B where H is an atom (the head) and B is a query (the body). When B is empty, H ← B is written H ← and is called a unit clause. A ... |

176 | Acyclic programs, in - Apt, Bezem - 1990 |

143 |
Termination of logic programs: the never-ending story
- Schreye, Decorte
- 1994
(Show Context)
Citation Context ...ply any longer. The goal of our research is the study of termination properties. This is motivated by the fact that most of the literature on termination of logic programs (see De Schreye and Decorte =-=[DD94]-=- for a survey on this subject) assumes the 2sstandard Prolog selection rule, i.e., the leftmost one. Notable exceptions are Bezem [Bez93] and Cavedon [Cav89] who provide results for all selection rule... |

126 | Reasoning about termination of pure Prolog programs
- Apt, Pedreschi
- 1994
(Show Context)
Citation Context ...a linear sequence of variables. • A program P is simply-moded iff all of its clauses are simply-moded. It is important to notice that most programs are simply-moded (see the mini-survey at the end of =-=[AP93]-=-) and that often non simply-moded programs can naturally be transformed into simply-moded ones. Example 27 • The programs REVERSE of Example 5, MERGE of Example 7 and FLATTEN of Example 25 are all sim... |

110 | ECLiPSe: a Platform for Constraint Logic Programming
- Wallace, Novello, et al.
- 1997
(Show Context)
Citation Context ...onsuming derivation step we refer to the sequel: The resolution of an atom with a definition must not instantiate the input arguments of the resolved atom. On the other hand, Gödel [HL94] and ECLiPSe =-=[WNS97]-=- use delay declarations, and SICStus Prolog [SIC97] employs block declarations (which are a special kind of delay declarations). Both delay and block declarations check the partial instantiation of so... |

82 | Reasoning about Prolog programs: from Modes through Types to Assertions - Apt, Marchiori - 1994 |

82 | On the occur-check free Prolog programs - Apt, Pellegrini - 1994 |

56 | The execution algorithm of Mercury: an ecient purely declarative logic programming language - Somogyi, Henderson, et al. - 1996 |

53 | Strong termination of logic programs - Bezem - 1993 |

45 | Modular termination proofs for logic and pure Prolog programs
- Apt, Pedreschi
- 1994
(Show Context)
Citation Context ...order to prove that a program is input terminating, we use the concept of quasi recurrent program (similar to, but noticeably less restrictive than the concept of semi-recurrent program introduced in =-=[AP94a]-=-). We show that if P is nicely-moded and quasi recurrent then all its input-consuming derivations starting from a nicely-moded query terminate. Furthermore, we demonstrate that under mild additional c... |

38 |
Parallelizing NU-Prolog
- Naish
- 1988
(Show Context)
Citation Context ...n fact, dynamic scheduling has proven to be useful in a number of applications; among other things, it allows one to model coroutining, as shown in [Nai92, HL94], and parallel executions, as shown in =-=[Nai88]-=-. Let us use the following simple examples to show how dynamic scheduling can be enforced by using delay declarations and how it can prevent nontermination and unnecessary computations. Consider the p... |

38 | Automatic inference of norms: a missing link in automatic termination analysis - Decorte, Schreye, et al. - 1993 |

33 | Verification of logic programs with delay declarations, in A. Borzyszkowski and S. Sokolowski (eds
- Apt, Luitjes
- 1995
(Show Context)
Citation Context ...ho provide results for all selection rules. There are only few authors who tackled the specific problem of verifying the termination of logic programs with dynamic scheduling. Namely, Apt and Luitjes =-=[AL95]-=-, Marchiori and Teusink [MT95] and Smaus [Sma99b]. We compare our results with the ones in [AL95, MT95, Sma99b] in the concluding section. Another feature of logic programs which does not hold in pres... |

30 | Moded Flat GHC and its message-oriented implementation technique
- Ueda, Morita
- 1994
(Show Context)
Citation Context ...ly instantiated. Such a mechanism is in fact offered by most modern languages: In GHC [Ued88] programs are augmented with guards in order to control the selection of atoms dynamically. Moded Flat GHC =-=[UM94]-=- uses an extra condition on the input positions, which is extremely similar to the concept of input-consuming derivation step we refer to the sequel: The resolution of an atom with a definition must n... |

29 |
Continuity, consistency and completeness properties for logic programs
- Cavedon
- 1989
(Show Context)
Citation Context ... logic programs (see De Schreye and Decorte [DD94] for a survey on this subject) assumes the 2sstandard Prolog selection rule, i.e., the leftmost one. Notable exceptions are Bezem [Bez93] and Cavedon =-=[Cav89]-=- who provide results for all selection rules. There are only few authors who tackled the specific problem of verifying the termination of logic programs with dynamic scheduling. Namely, Apt and Luitje... |

28 | Termination of well-moded programs
- Etalle, Bossi, et al.
- 1999
(Show Context)
Citation Context ...tions started in a nicely-moded query are finite. The method we use in order to prove that a program is input terminating is based on the following concept of moded level mapping due to Etalle et al. =-=[EBC99]-=-. Definition 16 (Moded Level Mapping) Let P be a program and BE P be the extended Herbrand base3 for the language associated with P. A function | | is a moded level mapping for P iff: • it is a functi... |

26 | Coroutining and the construction of terminating logic programs - Naish - 1993 |

21 | Guarded Horn Clauses, a parallel logic programming language with the concept of a guard - Ueda - 1988 |

18 |
Acyclic programs and the completeness of SLDNF-resolution
- Cavedon
- 1991
(Show Context)
Citation Context ...ecurrent program. The first notion (which in the case of normal programs, i.e., programs with negation, coincides with the one of acyclic program) was introduced in [Bez93, AB91] and independently in =-=[Cav91]-=- in order to prove universal termination for all selection rules together with other properties of logic programs. Later, Apt and Pedreschi [AP94a] provided the new definition of semi-recurrent progra... |

16 | Termination of logic programs with delay declarations - Marchiori, Teusink - 1999 |

15 | Proving termination of input-consuming logic programs
- Smaus
- 1999
(Show Context)
Citation Context ...re are only few authors who tackled the specific problem of verifying the termination of logic programs with dynamic scheduling. Namely, Apt and Luitjes [AL95], Marchiori and Teusink [MT95] and Smaus =-=[Sma99b]-=-. We compare our results with the ones in [AL95, MT95, Sma99b] in the concluding section. Another feature of logic programs which does not hold in presence of dynamic scheduling is the well-known swit... |

13 | Proving termination of logic programs with delay declarations
- Marchiori, Teusink
- 1995
(Show Context)
Citation Context ...ection rules. There are only few authors who tackled the specific problem of verifying the termination of logic programs with dynamic scheduling. Namely, Apt and Luitjes [AL95], Marchiori and Teusink =-=[MT95]-=- and Smaus [Sma99b]. We compare our results with the ones in [AL95, MT95, Sma99b] in the concluding section. Another feature of logic programs which does not hold in presence of dynamic scheduling is ... |

13 | Two problems -- two solutions: One system -- ECLiPSe - Wallace, Veron - 1993 |

13 | Veri of logic programs with delay declarations - Apt, Luitjes - 1995 |

12 |
Modes and Types in Logic Programming
- Smaus
- 1999
(Show Context)
Citation Context ...computed answer substitution (c.a.s., for short). The length of a (partial) derivation δ, denoted by len(δ), is the number of derivation steps in δ. The following definition of B-step is due to Smaus =-=[Sma99a]-=-. Definition 1 (B-step) Let A, B,C θ =⇒ (A,B,C)θ be a derivation step. We say that each atom in Bθ is a direct descendant of B, and for each atom E in (A,C), Eθ is a direct descendant of E. We say tha... |

11 | A Transformation System for CLP with Dynamic Scheduling and CCP - Etalle, Gabbrielli, et al. - 1997 |

10 | Termination of logic programs with block declarations running in several modes
- Smaus, Hill, et al.
- 1998
(Show Context)
Citation Context ...etailed comparison is presented in the concluding section. We also show that the results presented in this paper can be extended to programs and queries which are permutation nicely- or simply-moded, =-=[SHK98]-=-. To evaluate the practicality of the results we present, we consider the programs from various well-known collections, and we check whether they satisfy the conditions of our main theorem. The paper ... |

9 | Mercury: an ecient purely declarative logic programming language - Somogyi, Henderson, et al. - 1995 |

8 | Constraint logic programming with dynamic scheduling: a semantics based on closure operators
- Falaschi, Gabbrielli, et al.
- 1997
(Show Context)
Citation Context ... the most popular mechanism for implementing dynamic scheduling. However, being a non-logical mechanism, they are difficult to model and there are few proposals concerning their semantics [Mar97] and =-=[FGMP97]-=-. An alternative approach to dynamic scheduling, which is much more declarative in nature, has been proposed by Smaus [Sma99b]. It consists in the use of input-consuming derivations. 7sThere is a main... |

4 | Moded GHC and its message-oriented implementation technique - Ueda, Morita - 1994 |

2 | Algebraic and logical semantics for CLP languages with dynamic scheduling - Marriott - 1997 |

2 | GHC - A language for a new age of parallel programming - Ueda - 1988 |

1 |
Algebraic and logical semantics for clp languages with dynamic scheduling
- Marriot
- 1997
(Show Context)
Citation Context ...s are by far the most popular mechanism for implementing dynamic scheduling. However, being a non-logical mechanism, they are difficult to model and there are few proposals concerning their semantics =-=[Mar97]-=- and [FGMP97]. An alternative approach to dynamic scheduling, which is much more declarative in nature, has been proposed by Smaus [Sma99b]. It consists in the use of input-consuming derivations. 7sTh... |