M. Leuschel and D. De Schreye. Constrained Partial Deduction and the Preservation of Characteristic Trees. Technical report, Department of Computer Science, Katholieke Universiteit Leuven, June 1997. Accepted for publication in New Generation Computing.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... (sp, sage, paddy, mixtus, ecce) as well as semi automated ones (logimix, leupel, logen) have been developed and successfully applied to at least medium size applications [25, 15] 1 Another recent line of research has focussed on overcoming some of the inherent limitations of partial evaluation, [24] [26, 14] 23, 22] integrating ideas from constraint logic programming, unfold fold program transformation, and abstract interpretation respectively while keeping the above described advantages in terms of complexity and automatic controllability. Personal Details: The proposer has ....

M. Leuschel and D. De Schreye. Constrained partial deduction and the preservation of characteristic trees. New Generation Computing, 16:283--342, 1998.

....by requiring the set of atoms A to be independent and requiring the literals in the residual program and goal to be A closed. Partial deduction is naturally a unification based technique, although a technique using basic binding constraints to propagate negative information was developed by [LS97] Ensuring the termination of partial deduction is typically divided into local control and global control. Local control is concerned with the generation of finite incomplete SLDNF trees during spe 2.2 Constraint Solving 18 cialisation. On the other hand, the global control guarantees that the ....

....the transformation. For example, in supercompilation, negative information is propagated by restrictions, which can be represented by Herbrand (term) constraints [Tur86, GK93] The ability to propagate negative binding constraints during partial evaluation was explored by Leuschel et al. in [LS97] In addition, generalized partial computation has been defined using constraints and libraries of manipulation functions [Tak91] On the other hand, the integration of modern constraint solving in an algorithm for partial evaluation has been under exploited; exploring the use of advanced ....

M. Leuschel and D. De Schreye. Constrained Partial Deduction and the Preservation of Characteristic Trees. Technical report, Department of Computer Science, Katholieke Universiteit Leuven, June 1997. Accepted for publication in New Generation Computing.

....8, 10, 11] In these frameworks, search and or constraint solving facilities of the logic language provides the necessary machinery to avoid redundant computations. In this field, great efforts have been made to produce optimal specialisation, and at the same time to ensure termination, see e.g. [12, 13]. Acknowledgements. Thanks to Robert Gluck, Neil D. Jones, Laura Lafave and Michael Leuschel for discussions and comments. Thanks to Peter Sestoft for many insightful comments to [15] ....

Michael Leuschel and Danny De Schreye. Constrained partial deduction and the preservation of characteristic trees. New Generation Computing, 1997.

....strategies which provide an appropriate level of specialization while ensuring termination, is a crucial problem which has also received considerable attention. Much work has been devoted to the study of such control strategies in the context of on line partial evaluation of logic programs [MG95, LD97, LM96]. Usually, control is divided into components: local control, which controls the unfolding for a given atom, and global control, which ensures that the set of atoms for which a partial evaluation is to be computed remains finite. In most of the practical algorithms for program specialization, ....

....domain. However, if the abstract domain is infinite (as is required for partial evaluation) global control has to be augmented with a widening operator in order to ensure termination. The strategies for global control used in partial evaluation, such as those based on characteristic trees [GB91, LD97], on global trees [MG95] and on combinations of both [LM96] are then applicable to abstract interpretation. We have discussed different alternatives for introducing more powerful local unfolding strategies in abstract interpretation, such as unfolding the specialized program derived from ....

M. Leuschel and D. De Schreye. Constrained partial deduction and the preservation of characteristic trees. Technical Report CW 250, Departement Computerwetenschappen, K.U. Leuven, Belgium, June 1997. Accepted for Publication in New Generation Computing.

....strategies which provide an appropriate level of specialization while ensuring termination, is a crucial problem which has also received considerable attention. Much work has been devoted to the study of such control strategies in the context of on line partial evaluation of logic programs [MG95, LD97, LM96]. Usually, control is divided into components: local control, which controls the unfolding for a given atom, and global control, which ensures that the set of atoms for which a partial evaluation is to be computed remains finite. In most of the practical program specialization algorithms, the ....

M. Leuschel and D. De Schreye. Constrained partial deduction and the preservation of characteristic trees. Technical Report CW 250, Departement Computerwetenschappen, K.U. Leuven, Belgium, June 1997. Accepted for Publication in New Generation Computing.

....as they are called in partial evaluation once and for all, throw away the intermediate steps and just remember the results. Such local unfoldings will not only decrease the size of our process tress, they will also allow us to ensure that folding is not carried out prematurely. Inspired by [19], we will now formulate an improved driving mechanism that does not keep the intermediate paths and only put nodes in the process tree if they represent computations that are needed in the transformed program. This will furthermore have desirable effects when the transformed program is generated, ....

....for negative information, e.g. x 6= CONS; A 6= z] They show that this is in fact enough to pass the KMP test, but there is no termination guarantee for their transformer. For logic programs, Leuschel and De Schreye have presented a transformation technique called Constrained Partial Deduction [19], from which we have adopted the terminology of local and global trees. The aim of partial deduction is to specialize a goal which consists of a set of atoms. The global control decides which atoms should be partially deduced. The local control construct a fintite SLDNF tree for each atom ....

LEUSCHEL, M., AND DE SCHREYE, D. Constrained partial deduction and the preservation of characteristic trees. New Generation Computing (1997). To Appear.

....and De Schreye 1996] or well quasi relations on selected atoms ensures termination in a non ad hoc fashion, taking the structural properties of the program into account. Recently, well quasi relations such as the homeomorphic embedding relation, extended to improve the treatment of variables [Leuschel et al. 1998], have gained popularity. A suitable combination of determinacy and ordering leads to a practically viable local control. 2.2 Global Control The global control is usually embodied in a so called abstraction operator, which, given a set A, constructs a new set A 0 , generalising atoms in A, ....

....which capture the specialisation behaviour of atoms, and m trees [Martens and Gallagher 1995] which register their relationship. To avoid specialisation losses, it is important that characteristic trees be preserved upon abstraction. Prior techniques were incapable to achieve this. The method in [Leuschel et al. 1998] relies on imposing characteristic trees on the generalised atoms as well as adapting the homeomorphic embedding relation for characteristic trees. In this way, it is possible to spot sequences of growing characteristic trees and perform generalisation in order to avert the danger of ....

[Article contains additional citation context not shown here]

Leuschel, M. and De Schreye, D. 1998. Constrained partial deduction and the preservation of characteristic trees. New Gen. Comput. . To Appear.

....particular idempotent and relevant 4 mgu of fA; B 0 g, where B 0 is obtained from B by renaming apart (wrt A) If no such unifier exists then mgu (A; B) fail. The operation mgu has the interesting property that mgu (A; B) fail iff A and B have no common instance (for a proof see e.g. [52]) Definition 2.3. Given a database update U = hDb ; Db = Db Gamma i, we define the set of positive potential updates pos(U) and the set of negative potential updates neg(U) inductively as follows: pos 0 (U) fA j A Body 2 Db g neg 0 (U) fA j A Body 2 Db Gamma g ....

....a simple solve meta interpreter, like the one of Figure 5. In that case, the assumption that the integrity constraints were satisfied before the update has to be handed to the specialiser, for instance in the form of a constraint. The framework of constrained partial deduction, developed in [52], could be used to that effect. In such a setting, self applicable constrained partial deduction could be used to obtain specialised update procedures by performing the second Futamura projection [28, 26] and update procedure compilers by performing the third Futamura projection. ....

M. Leuschel and D. De Schreye. Constrained partial deduction and the preservation of characteristic trees. New Generation Computing. To Appear.

....opposed to offline) in the sense that control decisions are taken during the construction of fl and not beforehand. It is also rather naive (e.g. it does not use characteristic trees [23] also the generic Algorithm 3. 1 does not include recent improvements such as conjunctions [5] constraints [21, 16] or abstract interpretation [18] However, it is easier to comprehend (and analyse) and will actually be sufficiently powerful for our purposes (i.e. decide covering problems of reset Petri nets and other WSTS s) Unfolding Rule In this paper we will use a very simple method for ensuring that ....

M. Leuschel and D. De Schreye. Constrained partial deduction and the preservation of characteristic trees. New Gen. Comput. , 16:283--342, 1998.

....Algorithms We now present several concrete partial deduction algorithms. These algorithms are online (as opposed to o#ine) in the sense that they take their control decisions during the construction of # and not beforehand. They are also rather nave (e.g. they do not use the refinements in [35, 10, 33, 26, 29]) However, they are easier to comprehend (and analyse) and will actually be su#ciently powerful to solve several interesting problems. Unfolding Rule In this paper we will use a very simple method for ensuring that each individual SLD tree constructed by U is finite: we always do just a single ....

M. Leuschel and D. De Schreye. Constrained partial deduction and the preservation of characteristic trees. New Generation Computing, 16:283--342, 1998. 14

.... can be found in [4] 49] and [46] Renaming is often combined with argument filtering to improve the efficiency of the specialised program (see e.g. 20, 4] and also [50] Closedness can be ensured by using the following outline of a partial deduction algorithm (similar to the ones used in e.g. [18, 19, 39, 44]) 5 Algorithm3. Partial deduction) Input: a program P and an initial set S0 of atoms to be specialised Output: a set of atoms S Initialisation: Snew : abstract(S0 ) repeat Sold : Snew Snew : fsn j sn 2 leaves(UP (so) so 2 Sold g Snew : abstract(Sold [ Snew ) until Sold = Snew ....

M. Leuschel and D. De Schreye. Constrained partial deduction and the preservation of characteristic trees. New Generation Computing, 16:283--342, 1998.

....ensured and the degree of polyvariance is decided: For which atoms should partial deductions be produced Obviously, again, termination is an important issue, as well as obtaining a good overall specialisation. The following ingredients are important in recent approaches: ffl characteristic trees [23, 22, 45, 40] A characteristic tree is an abstraction of an SLD tree. It registers which atoms have been selected and which clauses were used for resolution. As such, it provides a good characterisation of the computation and specialisation connected with a certain atom (or goal) Its use in partial deduction ....

M. Leuschel and D. De Schreye. Constrained partial deduction and the preservation of characteristic trees. New Generation Computing, 16(3):283--342, 1998.

....respective programs. An abstraction operator which takes these trees into account will notice their similar behaviour in the context of P 1 and their dissimilar behaviour within P 2 , and can therefore take appropriate actions in the form of different generalisations. Unfortunately, as shown in [30], it is in general impossible to preserve characteristic trees upon generalisation in the context of ordinary partial deduction. This can lead to severe specialisation losses, as well as to non termination of certain partial deduction algorithms. A solution to this entanglement is presented in ....

.... : plusconj2(X1,X2,X3,X4,X4) plusconj2(0,X1,X2,X3,X3) plusconj3(X1,X2,X3,X3) plusconj2(s(X1) X2,X3,s(X4) s(X4) plusconj2(X1,X2,X3,X4,X4) plusconj3(0,X1,X1,X1) plusconj3(s(X1) X2,s(X3) s(X3) plusconj3(X1,X2,X3,X3) In future work we plan to integrate constrained partial deduction [30] as well as the more refined algorithm of [29] which interleaves bottom up abstract interpretation steps with top down conjunctive partial deduction unfolding steps, into the ecce system. First investigations indicate that this will make it possible to prove much more sophisticated inductive ....

M. Leuschel and D. De Schreye. Constrained partial deduction and the preservation of characteristic trees. New Generation Computing. To appear. Preliminary version as Technical Report CW 250, Departement Computerwetenschappen, K.U. Leuven, Belgium, June 1997. Accessible via http://www.cs.kuleuven.ac.be/~lpai.

....answers and the closedness condition guarantees that all calls, which might occur during the execution of the specialised program, are covered by some definition. 2 Motivations One drawback of (ordinary) partial deduction is that every atom in A stands for all of its instances. As identified in [22] this limits the precision and specialisation that a concrete partial deduction algorithm can attain. The basic idea of [22] which we summarise in this paper, is to move to a setting of constrained partial deduction, which will allow us to enhance precision and specialisation by incorporating ....

....program, are covered by some definition. 2 Motivations One drawback of (ordinary) partial deduction is that every atom in A stands for all of its instances. As identified in [22] this limits the precision and specialisation that a concrete partial deduction algorithm can attain. The basic idea of [22], which we summarise in this paper, is to move to a setting of constrained partial deduction, which will allow us to enhance precision and specialisation by incorporating constraints. More precisely, constrained partial deduction works on a set A of constrained atoms: couples of the form c 2A ....

[Article contains additional citation context not shown here]

M. Leuschel and D. De Schreye. Constrained partial deduction and the preservation of characteristic trees. Technical Report CW 250, Departement Computerwetenschappen, K.U. Leuven, Belgium, June 1997. Accepted for Publication in New Generation Computing. Accessible via http://www.cs.kuleuven.ac.be/~lpai.

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M. Leuschel and D. De Schreye. Constrained Partial Deduction and the Preservation of Characteristic Trees. Technical report, Department of Computer Science, Katholieke Universiteit Leuven, June 1997. Accepted for publication in New Generation Computing.

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