A. Bossi, S. Etalle, and S. Rossi. Properties of Input-Consuming Derivations. In J.-G. Smaus and S. Etalle, editors, Proceedings of the ICLP Workshop on Verication of Logic Programs, 1999. Home/Search Document Details and Download
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Termination of Simply-Moded Well-Typed Logic Programs.. - Verbaeten, De Schreye (2001) (Correct)
....level mapping is the Herbrand base (instead of the extended Herbrand base) and that a moded level mapping does not have to be of the speci ed form, j:j s , induced by some symbol mapping s. The moded level mappings of [18] are used to prove LD termination of well moded programs and queries. In [9], Bossi, Etalle and Rossi extended the de nition of moded level mapping by taking the extended Herbrand base as the domain of such a level mapping. This extended de nition of moded level mapping is used to prove termination of input consuming derivations of nicely moded programs and queries. We ....
....extended the de nition of moded level mapping by taking the extended Herbrand base as the domain of such a level mapping. This extended de nition of moded level mapping is used to prove termination of input consuming derivations of nicely moded programs and queries. We discuss the papers [18] and [9] in more detail in the conclusion section. Proposition 2 Let P be a well moded program and S B E P be a set of well moded queries. Let j:j s be a level mapping which measures only input positions in Call(P; S) Then, j:j s is rigid on Call(P; S) Proof Since well moded programs are ....
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A. Bossi, S. Etalle, and S. Rossi. Properties of Input-Consuming Derivations. In J.-G. Smaus and S. Etalle, editors, Proceedings of the ICLP Workshop on Verication of Logic Programs, 1999.
Semantics of Well-Moded Input-Consuming Programs - Bossi, Etalle, Rossi Self-citation (Bossi Etalle Rossi) (Correct)
....of the selected atom will not be instantiated by the uni cation with the clause s head. For example, when the program APPEND reported above is used for concatenating two lists, we assume that the rst two arguments ll in input positions while the third argument lls in an output position. In [5, 6] we showed that, assuming the above moding, for queries of the form app(s; t; X) with X being a variable disjoint from s and t) the delay declaration delay append(Ls, until nonvar(Ls) guarantees precisely that if an atom is selectable and resolvable, then it is so via an input consuming ....
....is a renaming for A. By Lemma 4.3, there exists an input consuming successful derivation : A # P of P [ fAg such that and 0 are similar. The thesis follows from Lemma 2.3. Now, we need to establish some properties of nicely moded programs. First, we recall the following result from [5, 6]. 14 Lemma 4.5 Let the program P and the query Q be nicely moded. Let : Q Q 0 be a partial input consuming derivation of P [ fQg. Then, for all x 2 Var(Q) and x 62 Var(Out(Q) x = x. Note that if Q is nicely moded then x 2 Var(Q) and x 62 Var(Out(Q) i x 2 VIn (Q) Now, we can ....
A. Bossi, S. Etalle, and S. Rossi. Properties of input-consuming derivations. Technical Report CS 99-06, Universiteit Maastricht, 1999.
Semantics and Termination of Simply-Moded Logic.. - Bossi, Etalle, Rossi.. (2001) Self-citation (Bossi Etalle Rossi) (Correct)
....of a simply moded query using a simply moded clause is simply moded [4] Example 3.2. Consider again the delay declaration delay append(Ls, until nonvar(Ls) 2 Notice that there is a difference between this notion of deadlock and the one used for programs with delay declarations; see [6] for a detailed discussion. It is easy to check that every derivation starting in a query append(t,s,X) where X is a variable disjoint from s and t, is input consuming wrt. append(In,In,Out) iff it respects the delay declaration. ut To show the correspondence between delay declarations and ....
....about the selection rule in order to prove termination [18] The first result in this area was a sufficient criterion applicable to well and nicely moded programs. This was improved upon by dropping the requirement of well modedness, which means that one also captures termination by deadlock [6]. In this section, we only consider simply moded programs and queries (simply moded and well moded programs form two largely overlapping, but distinct classes) and we provide a criterion for termination which is sufficient and necessary, and hence an exact characterisation of termination. We ....
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A. Bossi, S. Etalle, and S. Rossi. Properties of input-consuming derivations. ENTCS, 30(1), 1999. http://www.elsevier.nl/locate/entcs.
Semantics of Input-Consuming Logic Programs - Bossi, Etalle, Rossi (2000) (1 citation) Self-citation (Bossi Etalle Rossi) (Correct)
....order of PROLOG. While this allows for more exibility, it can easily yield to nontermination or to an inecient computation. For instance, if we consider the standard program APPEND app( Ys,Ys) app( H Xs] Ys, H Zs] app(Xs,Ys,Zs) we have that the query q1: app( 1,2] 3,4] Xs) app(Xs,[5,6],Ys) might easily loop in nitely (one just has to keep resolving the rightmost atom together with the second clause) To avoid this, most implementations use constructs such as delay declarations. In the case of APPEND when used for concatenating two lists the natural delay declaration is d1: ....
....that # 0 jIn(A) is a renaming for A. By Lemma 13, there exists an inputconsuming derivation A # P similar to 0 . The thesis follows by Lemma 3. ut Properties of Nicely Moded Programs Now, we need to establish some properties of nicely moded programs. First, we recall the following from [5, 6]. Lemma 15. Let the program P and the query Q be nicely moded. Let : Q Q 0 be a partial input consuming derivation of P [ fQg. Then, for all x 2 Var(Q) and x 62 Var(Out(Q) x = x. Note that if Q is nicely moded then x 2 Var(Q) and x 62 Var(Out(Q) i x 2 VIn (Q) Now, we can ....
A. Bossi, S. Etalle, and S. Rossi. Properties of input-consuming derivations. Technical Report CS 99-06, Universiteit Maastricht, 1999.
Properties of Input-Consuming Derivations - Bossi, Etalle, Rossi (1999) (1 citation) Self-citation (Bossi Etalle Rossi) (Correct)
....show that for nicely moded programs one side of the switching lemma still holds. First, we need one technical result, stating that the only variables of a query that can be a ected in the derivation process are those occurring in some output positions. The proof is omitted, and reported in [10]. Lemma 4.1 Let the program P and the query Q be nicely moded. Let : Q 7 Q 0 be a partial input consuming derivation of P [ fQg. Then, for all x 2 Var(Q) and x 62 Var(Out(Q) x = x. The following corollary is an immediate consequence of the above lemma and the de nition of ....
....s; t) where t is linear and variable disjoint from u and s are terminating. 5.3 Modular Termination This section contains a generalization of Theorem 5.6 to the modular case, as well as the complete proofs for it. The following lemma is a crucial one. The proof is omitted, and reported in [10]. Lemma 5.8 Let the program P and the query Q : A 1 ; A n be nicelymoded. Suppose that there exists an in nite input consuming derivation of 14 Bossi, Etalle, Rossi P [ fQg. Then, there exist an index i 2 f1; ng and substitution such that there exists an input consuming ....
A. Bossi, S. Etalle, and S. Rossi. Properties of input-consuming derivations. Technical Report CS 99-06, Universiteit Maascricht.
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