J.-G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, Proc. of the International Conference on Logic Programming, pages 335--349. MIT Press, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....as clearly described in [18] The rst one is intended to algebraically characterize classes of programs and queries terminating wrt. a speci c interpreter, such as termination wrt. SLD resolution [3, 11] LD resolution [10, 23] LDNF resolution [9, 12] SLD resolution with dynamic scheduling [14, 26] or with tabling [30, 29] The second one is intended to automatize the veri cation by de ning sucient conditions for termination wrt. a speci c interpreter, e.g. the standard Prolog interpreter [31, 20, 13, 22, 19, 21] In this paper we follow the rst approach: we de ne and characterize the ....

J.-G. Smaus. Proving termination of input-consuming logic programs. In D. D. Schreye, editor, Proceedings of the 16th International Conference on Logic Programming, pages 335-349. MIT Press, 1999.

....input consuming derivations of nicely moded programs and queries. Input consuming derivations do not employ a xed selection rule, the only requirement is that the input arguments of the selected atom do not become instantiated in the resolution step. This assumption, rst introduced by Smaus in [27] on which the paper [9] improves, is a natural abstraction of logic programs using dynamic scheduling and employing constructs such as delay declarations. The class of nicely moded programs and queries which is considered in [9] generalises the class of simply moded programs and queries in the ....

J.-G. Smaus. Proving Termination of Input-Consuming Logic Programs. In D. De Schreye, editor, Proceedings of the International Conference on Logic Programming, pages 335-349. The MIT Press, 1999.

....as clearly described in [18] The rst one is intended to algebraically characterize classes of programs and queries terminating wrt. a speci c interpreter, such as termination wrt. SLD resolution [3, 11] LD resolution [10, 22] LDNFresolution [9, 12] SLD resolution with dynamic scheduling [14, 25]. The second one is intended to automatize the veri cation by de ning sucient conditions for termination wrt. the standard Prolog interpreter [27, 20, 13, 21, 19] In this paper we follow the rst approach: we de ne and characterize the class of well typed typed terminating programs, namely ....

J.-G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, Proceedings of the 16th International Conference on Logic Programming, pages 335-349. MIT Press, 1999.

....paradigm. Contributions of the Paper In this paper we address the problem of providing a model theoretic semantics for programs using a dynamic selection rule. In order to do so, we need a declarative way of modeling them, and for this we restrict our attention to input consuming programs [12]. The de nition of inputconsuming program employs the concept of mode: We assume that programs are moded, that is, that the positions of each atom are partitioned into input and output ones. Then, input consuming derivation steps are precisely those in which the input arguments of the selected ....

....positions of predicates in Q. Moreover, when writing an atom as p(s; t) we are indicating with s the sequence of terms lling in the input positions of p and with t the sequence of terms lling in the output positions of p. The notion of input consuming derivation was introduced by Smaus in [12] and is de ned as follows. De nition 2.5 (Input Consuming) A derivation step A;B;C = c (A; B; C) is called input consuming i In(B) In(B) A derivation is called input consuming i all its derivation steps are inputconsuming. Thus, a derivation step is input consuming if the ....

J. G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, 16th International Conference on Logic Programming, Las Cruces, New Mexico, USA, The MIT Press, pages 335-349, 1999.

....paradigm. Contributions of the Paper In this paper we address the problem of providing a model theoretic semantics to programs using a dynamic selection rule. In order to do so, we need a declarative way of modeling them, and for this we restrict our attention to input consuming programs [18]. The de nition of inputconsuming program employs the concept of mode: We assume that programs are moded, that is, that the positions of each atom are partitioned into input and output ones. Then, input consuming derivation steps are precisely those in which the input arguments of the selected ....

....positions of predicates in Q. Moreover, when writing an atom as p(s; t) we are indicating with s the sequence of terms lling in the input positions of p and with t the sequence of terms lling in the output positions of p. The notion of input consuming derivation was introduced by Smaus in [18] and is de ned as follows. De nition 2.5 (Input Consuming) A derivation step A;B;C = c (A; B; C) is called input consuming i In(B) In(B) A derivation is called input consuming i all its derivation steps are inputconsuming. Thus, a derivation step is input consuming if the ....

J. G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, 16th International Conference on Logic Programming. MIT press, 1999.

....lling in the input (resp. output) positions of Q. Moreover, when writing an atom as p(s; t) we are indicating with s the sequence of terms lling in its input positions 4 and with t the sequence of terms lling in its output positions. The notion of input consuming derivation was introduced in [14] and is de ned as follows. De nition 5 (Input Consuming) A derivation step A;B;C = c (A; B;C) is called input consuming i In(B) In(B) A derivation is called input consuming i all its derivation steps are inputconsuming. Thus, a derivation step is input consuming if the ....

J. G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, 16th International Conference on Logic Programming. MIT press, 1999.

....to prove termination of logic programs augmented with delay declarations that imply determinacy and matching. Marchiori and Teusink s [20] introduces the class of delay recurrent programs and proves that programs in this class terminate for all local delay selection rule. More recently, Smaus s [21] studies the termination of input consuming derivations of well and nicely moded programs. We compare our results with the ones in [4,20,21] in the conclusions. During our study it became also clear that more fundamental properties of logic programs do not hold, or hold only partially, in this ....

....[20] introduces the class of delay recurrent programs and proves that programs in this class terminate for all local delay selection rule. More recently, Smaus s [21] studies the termination of input consuming derivations of well and nicely moded programs. We compare our results with the ones in [4,20,21] in the conclusions. During our study it became also clear that more fundamental properties of logic programs do not hold, or hold only partially, in this modi ed setting. Among them, the well known switching lemma, which is for instance at the base of the result on the independence of the ....

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J. G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, 16th International Conference on Logic Programming. MIT press, 1999.

....rule has the disadvantage that the most of the literature on termination (see [SD94] for a survey on the subject) does not apply to programs which employ them. Notable exceptions are Bezem s [Bez93] and and Cavedon s [Cav89] which provide result for unrestricted selection rules and Smaus [Sma99], on which this paper improves. Goal of this paper is to study the dynamic behaviour of programs using dynamic scheduling, and to provide sucient conditions which guarantee their termination. The rst obstacle we encounter is of providing an algebraic way of representing delay declarations. For ....

....is to study the dynamic behaviour of programs using dynamic scheduling, and to provide sucient conditions which guarantee their termination. The rst obstacle we encounter is of providing an algebraic way of representing delay declarations. For this purpose, we follow here the same approach of [Sma99] 1 and we substitute the use of delay declarations by the restriction to input consuming derivations. The de nition of input consuming derivation is done in two phases: rst we give the program a mode, that is, we partition the positions of each atom occurring in input and output positions. ....

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J. G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, 16th International Conference on Logic Programming. MIT press, 1999. 15

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J.-G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, Proc. of the International Conference on Logic Programming, pages 335--349. MIT Press, 1999.

....and enjoying a modeltheoretical reading as well as a natural bottom up constructive definition. We demonstrate that this semantics is correct and fully abstract with respect to the computed substitutions of partial derivations. A first attempt to tackle this problem has been presented in [27] and extended in [7] where we defined the class of input terminating programs, i.e. programs whose input consuming derivations are finite, and characterize the subclass of simply moded quasi recurrent programs. It is worth stressing that this latter class includes only programs whose termination ....

.... of termination of input consuming derivations, in a similar way as this has been done previously for LD derivations [5, 24] Input consuming derivations were originally conceived as an abstract and reasonably strong assumption about the selection rule in order to prove termination [27]. The first result in this area was a su#cient 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. The previous approaches are applicable as long as each ....

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J.-G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, Proceedings of the 16th International Conference on Logic Programming, pages 335--349, Las Cruces, New Mexico, USA, 1999. The MIT Press.

....heads is a severe restriction since it rules out input arguments of the selected atom being tested for equality. Lemma 3.4 Every resolvent of a nicely moded query Q and a nicely moded clause C, where the derivation step is input consuming and vars(C) vars(Q) is nicely moded. Proof see [21]. For a nicely moded program and query, it is guaranteed that every inputconsuming derivation step only instantiates other atoms in the query that occur to the right of the selected atom. Lemma 3.5 Let P be a nicely moded program, Q = Q 1 ; p(s; t) Q 2 a nicely moded query, and hQ; i; hQ 1 ....

....paper considerably. Lemma 4.1 Let P be a well and nicely moded program and F; b; H a well and nicely moded query where b is an atom terminating atom. An inputconsuming derivation of P [ fF; b; Hg can have in nitely many b steps only if it has in nitely many a steps, for some a 2 F . Proof see [21]. The following theorem is a consequence of Lemma 4.1 and states that atomterminating atoms on their own cannot produce an in nite derivation. Theorem 4.2 Let P be a well and nicely moded program and Q a well and nicely moded query. An input consuming derivation of P [ fQg can be in nite only ....

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J.-G. Smaus. Proving termination of input-consuming logic programs. Technical Report 10-99, Computing Laboratory, University of Kent at Canterbury, United Kingdom, 1999.

....all uni cations are solvable by moded uni cation is a moded derivation. Moded uni cation is a special case of double matching. How moded derivations are ensured is not our problem here, and we refer to [2] Note that the requirement of moded derivations is stronger than input consuming derivations [17] where it is only required that the MGU does not bind s. RR n 0123456789 18 Smaus Fages Deransart De nition 10 A query Q = p 1 ( s 1 ; t 1 ) pn ( s n ; t n ) is nicely moded if t 1 ; t n is a linear vector of terms and for all i 2 f1; ng vars( s i ) n ....

J.-G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, Proceedings of the 16th International Conference on Logic Programming, pages 335349. MIT Press, 1999.

....of dynamic scheduling. 1.2 The Contributions This paper contains essentially four contributions to solving the above problems. In order to provide a characterization of dynamic scheduling that is reasonably abstract and hence amenable to semantic analysis, we consider inputconsuming derivations [16], a formalism very similar to the one of Moded GHC [18] Roughly speaking, in an input consuming program only atoms whose input arguments are not instantiated through the uni cation step are allowed to be selected. Moreover, we restrict our attention to the class of simply moded programs, which ....

....In particular, every unit clause is simply moded. Example 2.3. Programs APPEND and IN ORDER are simply moded wrt. the modes append(In,In,Out) and in order(In,Out) ut 3 Input Consuming Programs Input consuming derivations are a formalism for describing dynamic scheduling in an abstract way [16]. De nition 3.1. A derivation step A;B;C = A; B; C) is input consuming i In(B) In(B) A derivation is input consuming i all its derivation steps are input consuming. ut 1 For the case that k = 0, the empty conjunction might be denoted as true, or the delay declaration might simply be ....

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J.-G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, Proceedings of the 16th International Conference on Logic Programming, pages 335-349. MIT Press, 1999.

....presence of dynamic scheduling. Contributions. This paper contains essentially four contributions tackling the above problems. In order to provide a characterisation of dynamic scheduling that is reasonably abstract and hence amenable to semantic analysis, we consider inputconsuming derivations [18], a formalism similar to Moded GHC [20] In an inputconsuming derivation, only atoms whose input arguments are not instantiated through the unification step may be selected. Moreover, we restrict our attention to the class of simply moded programs, which are programs that are, in a well defined ....

....In particular, every unit clause is simply moded. Notice also that programs APPEND and IN ORDER are simply moded wrt. the modes append(In,In,Out) and in order(In,Out) 3 Input Consuming Programs Input consuming derivations are a formalism for describing dynamic scheduling in an abstract way [18]. Definition 3.1. A derivation step A;B;C = A; B; C) is input consuming iff In(B) In(B) A derivation is input consuming iff all its derivation steps are input consuming. ut Thus, allowing only input consuming derivations is a form of dynamic scheduling, since selectability depends on ....

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J.-G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, Proceedings of ICLP'99, pages 335--349. MIT Press, 1999.

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J.-G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, Proc. of the International Conference on Logic Programming, pages 335--349. MIT Press, 1999.

No context found.

J.-G. Smaus. Proving termination of input-consuming logic programs. In D. De Schreye, editor, Proceedings of the 16th International Conference on Logic Programming, pages 335--349, Las Cruces, New Mexico, USA, 1999. The MIT Press.

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