## Transforming Acyclic Programs (1993)

Venue: | ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS |

Citations: | 10 - 3 self |

### BibTeX

@ARTICLE{Bossi93transformingacyclic,

author = {Annalisa Bossi and Sandro Etalle},

title = {Transforming Acyclic Programs},

journal = {ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS},

year = {1993},

volume = {16}

}

### Years of Citing Articles

### OpenURL

### Abstract

An Unfold/Fold transformation system is a source-to-source rewriting methodology devised to improve the efficiency of a program. Any such transformation should preserve the main properties of the initial program: among them, termination. To this end, in the field of logic programming, the class of acyclic programs plays an important role, as it is closely related to the one of terminating programs. The two classes coincide when negation is not allowed in the bodies of the clauses. In this paper it is proven that the Unfold/Fold transformation system defined by Tamaki and Sato preserves the acyclicity of the initial program. As corollaries, it follows that when the transformation is applied to an acyclic program, then finite failure set for definite programs is preserved; in the case of normal programs, all major declarative and operational semantics are preserved as well. These results cannot be extended to the class of left terminating programs without modifying the definitio...

### Citations

1855 |
Foundations of Logic Programming
- Lloyd
- 1987
(Show Context)
Citation Context ...are preserved through the transformation. 1.3 Preliminaries We assume that the reader is familiar with the basic concepts of logic programming; throughout the paper we use the standard terminology of =-=[Llo87]-=- and [Apt90]. We consider normal programs, that is finite collections of normal rules, A / L 1 ; : : : ; Lm . where A is an atom and L 1 ; : : : ; Lm are literals. We say that a clause is definite if ... |

416 |
Introduction to Logic Programming
- Apt
- 1990
(Show Context)
Citation Context ...d through the transformation. 1.3 Preliminaries We assume that the reader is familiar with the basic concepts of logic programming; throughout the paper we use the standard terminology of [Llo87] and =-=[Apt90]-=-. We consider normal programs, that is finite collections of normal rules, A / L 1 ; : : : ; Lm . where A is an atom and L 1 ; : : : ; Lm are literals. We say that a clause is definite if the body con... |

381 | Bilattices and the semantics of logic programming
- Fitting
- 1991
(Show Context)
Citation Context ...s context, we have that a three valued (or partial) interpretation, is a mapping from the ground atoms of L into the set ftrue, false, undefinedg. We can now give the definition of Fitting's operator =-=[Fit85]-=-. Definition 5.1 Let P be a normal program, I a three valued interpretation, A a ground atom; \Phi P (I) is the three valued interpretation defined as follows: ffl A is true in \Phi P (I), iff there e... |

221 |
Unfounded Sets and Well-founded Semantics for General Logic
- Gelder, Ross, et al.
- 1989
(Show Context)
Citation Context ...es of variables of the appropriate arity. 2 Now we summarize some of the semantic properties of acyclic programs. For the definition and the properties of the Well-Founded model semantics we refer to =-=[GRS88]. The-=-orem 5.3 Let P be an acyclic program, and let M = \Phi "! P . Then M is total, that is, no atom is undefined in it, moreover (i) M is the unique fixpoint of \Phi P ; hence it is the unique three-... |

213 |
Unfold/fold transformations of logic programs
- Tamaki, Sato
- 1984
(Show Context)
Citation Context ...Sistemi Informatici e Calcolo Parallelo" of CNR under grant n. 89.00026.69. 1. Introduction 1.1 Motivation In this paper we focus on the unfold/fold transformation systems proposed by Tamaki and =-=Sato [TS84]-=-. As the large literature shows [TS84, KK88, Sek90, Sek91, Sek93, AD93], a lot of research has been devoted to proving the correctness of the system wrt the various semantics proposed for logic progra... |

172 |
M.: Acyclic programs
- Apt, Bezem
- 1991
(Show Context)
Citation Context ...am has not yet been tackled. Recall that a program is called terminating if all its SLDNF derivations starting in a ground goal are finite. Here we follow the approach to termination of Apt and Bezem =-=[AB91]-=-. They investigate the class of acyclic programs (introduced by Cavedon [Cav91]) and prove that it is closely related to the one of terminating programs. In fact we have that every acyclic program is ... |

137 | Every logic program has a natural strati cation and an iterated least xed point model
- Przymusinski
- 1989
(Show Context)
Citation Context ...w, acyclic programs enjoy the following important property: the two most prominent approaches, namely the SLDNF resolution (see Lloyd [Llo87] and Apt [Apt90]) and the SLS resolution from Przymusinski =-=[Prz89]-=-, coincide when applied to acyclic programs. For the semantic properties of acyclic programs we refer to section 5. 3 Unfold/Fold transformations We now give the definition of unfold/fold transformati... |

126 | Reasoning about termination of pure prolog programs
- Apt, Pedreschi
- 1993
(Show Context)
Citation Context ...4 Let j j be a level mapping. A literal L is called bounded wrt j j if j j is bounded on the set [L] of ground instances of L. A goal is called bounded wrt j j iff all its literals are. 2 Example 2.5 =-=[AP93]-=- Consider the program member. P = f member(X; [Y jXs]) / member(X;Xs): member(X; [X jXs]): g We adopt the standard list notation and define the function j j l , called listsize which assigns natural n... |

51 | Strong termination of Logic Programs
- Bezem
- 1991
(Show Context)
Citation Context ...v91]) and prove that it is closely related to the one of terminating programs. In fact we have that every acyclic program is terminating [AB91] and that every definite, terminating program is acyclic =-=[Bez93]-=-; however, when negation is allowed in the bodies of the clauses, there are programs which are terminating but not acyclic. This is caused either by the presence of floundering derivations or by the f... |

43 |
Unfold/fold transformation of stratified programs
- Seki
- 1991
(Show Context)
Citation Context ...f the correctness of the operation wrt the Finite Failure Set was pointed out by Seki, who modified the applicability conditions of the folding operation as follows. Definition 3.7 (modified folding) =-=[Sek91]-=- The modified folding operation is defined exactly as in Definition 3.5, with the exception of condition (F4), which is replaced by the following (F4') one of the following two conditions holds 1. the... |

29 |
Preservation of Stronger Equivalence in Unfold/Fold Logic Programming Transformation
- Kawamura, Kanamori
- 1988
(Show Context)
Citation Context ...ant properties. Theorem 3.6 Let P 0 ; : : : ; Pn be a transformation sequence. ffl If P 0 is a definite program then -- [TS84] The least Herbrand models of the initial and final programs coincide. -- =-=[KK88]-=- The computed answers substitution semantics of the initial and final programs coincide. ffl If P 0 is a normal program, then -- [Sek90] The Stable models of the initial and final programs coincide. -... |

26 | Basic transformation operations which preserve computed answer substitutions of logic programs - Bossi, Cocco - 1993 |

25 | On the correctness of unfold/fold transformation of normal and extended logic programs
- Aravindan, Dung
- 1995
(Show Context)
Citation Context ...l programs coincide. -- [Sek89] Under a further mild assumption on the initial program; if the initial program is stratified then the final program is stratified and their Perfect models coincide. -- =-=[AD93]-=- The semantic kernels of the initial and final program coincide; this implies also that the Stable model semantics, the preferred extension semantics, the stationary semantics and the stable theory se... |

21 | Correctness of a Logic Program Transformation System - Maher - 1987 |

20 |
Unfold/Fold Transformation of General Logic Programs for the Well-founded Semantics
- Seki
- 1993
(Show Context)
Citation Context ...on of unfold/fold transformation sequence that was first given by Tamaki and Sato [TS84] for definite programs and then used by Seki [Sek90, Sek93] for normal programs. Here we present it as it is in =-=[Sek93]-=-. All definitions are given modulo reordering of the bodies of the clauses, and standardization apart is always assumed. Definition 3.1 (initial program) We call a normal program P 0 an initial progra... |

17 |
Acyclic programs and the completeness of SLDNF-resolution
- Cavedon
- 1991
(Show Context)
Citation Context ...l its SLDNF derivations starting in a ground goal are finite. Here we follow the approach to termination of Apt and Bezem [AB91]. They investigate the class of acyclic programs (introduced by Cavedon =-=[Cav91]-=-) and prove that it is closely related to the one of terminating programs. In fact we have that every acyclic program is terminating [AB91] and that every definite, terminating program is acyclic [Bez... |

10 |
Negation as failure rule
- Clark
- 1978
(Show Context)
Citation Context ...ified language L that we assume contains all the functions symbols and the predicate symbols of the programs that we consider. We refer also to the usual definition of program's completion, Comp(P ), =-=[Cla78] which con-=-sists of the completed definition of each predicate together with CET, Clark's Equality Theory, which is needed in order to interpret "=" correctly. When working with 3-valued logic, the sam... |

10 |
An Equivalence Preserving First Order Unfold/Fold Transformation System
- Sato
- 1992
(Show Context)
Citation Context ... operation. Seki proved that modified folding preserves the Finite Failure set of a definite program [Sek89, Sek91]; later on Sato, on a work that extends this definition to full first order programs =-=[Sat90]-=-, proved the correctness of the system wrt Kunen's semantics. 4 Transforming Acyclic Programs We now show that if the initial program of a transformation sequence is acyclic then the resulting program... |

6 |
A Comparative Study of the Well-Founded and the Stable Model Semantics: Transformation's Viewpoint
- Seki
- 1990
(Show Context)
Citation Context ...t Herbrand models of the initial and final programs coincide. -- [KK88] The computed answers substitution semantics of the initial and final programs coincide. ffl If P 0 is a normal program, then -- =-=[Sek90]-=- The Stable models of the initial and final programs coincide. -- [Sek93] The Well-Founded models of the initial and final programs coincide. -- [Sek89] Under a further mild assumption on the initial ... |