Analysing and Compiling Coroutines with Abstract Conjunctive Partial Deduction

Abstract

We provide an approach to formally analyze the computational behavior of coroutines in Logic Programs and to compile these computations into new programs, not requiring any support for coroutines. The problem was already studied near to 30 years ago, in an analysis and transformation technique called Compiling Control. However, this technique had a strong ad hoc flavor: the completeness of the analysis was not well understood and its symbolic evaluation was also very ad hoc. We show how Abstract Conjunctive Partial Deduction, introduced by Leuschel in 2004, provides an appropriate setting to redefine Compiling Control. Leuschel's framework is more general than the original formulation, it is provably correct, and it can easily be applied for simple examples. We also show that the Abstract Conjunctive Partial Deduction framework needs some further extension to be able to deal with more complex examples. Remark: Def.2 case 2 "subterm of t selected by..." is not defined. Answer: Reformulated. Remark: Ex.5 Explanation of the relations defined by the program would substantially help the reader. (Especially safe/2, allsafe/4; at least one of them). Answer: The example was removed. We included the meaning of the predicates in the new example. Remark: Def.6 is too clumsy, even for an informal presentation. Among others, nothing is said that AConAtom is being redefined. What about something like: We extend AConAtom by a new construct multi(C) (where C ∈ AConAtom) such that γ(multi(C)) = ... Answer: We did this in the way the reviewer suggested. Remark: What is gamma of ∧ with zero arguments? Can n really be 0? (Def.7 may suggest that n > 0.) Answer: We require more than zero arguments. Remark: Table 1 Seems unnecessary, as the speedup depends mainly on issues not discussed in the paper. Also: Fractional numbers of inferences seem incorrect. It is not clear whether "inferences original" are those of the original program under Prolog selection rule. Should not the performance of the original program with a special selection rule be included? Answer: We removed the table. Remark: Missing page numbers make a substantial inconvenience for reviewers. Answer: The guidelines for submission require that there are no page numbers. A.2 Review 2 Remark: The overall idea-introducing a more systematic approach to compiling control-seems quite interesting. The paper, however, is too preliminary to determine if the approach is viable in practice and whether some extension of the ACPD framework (namely, the multi abstraction, the main original contribution of the paper) is actually required to succeed. Nevertheless, the paper would surely give rise to an interesting talk for the LOPSTR audience. Answer: The multi-abstraction has been significantly extended in the new version. We can currently deal with all examples that were studied in the CC approach and cannot come up with any examples where is would not succeed. Most likely, there are going to be such cases, as we cannot prove as yet that we can now deal with all cases.

Transforming Coroutining Logic Programs into Equivalent CHR Programs

“…As in [14], we illustrate a use case of our technique by means of the permutation sort algorithm. Listing 1 shows a naive version of this algorithm.…”

“…But that bound increases with N, so that for an ACPD analysis in the style of Section 2, which is a safe approximation of every concrete computation, there cannot be a bound. To deal with this, [14] introduces the multi abstraction.…”

“…In [14], we introduced a new abstraction, multi. This new abstraction makes it possible to generalize the three goals above to the following new abstract goal: draw(g 1 , g 2 , a 1 ), multi(attack all(g i , g j , a 1 )), multi(attack all(g k , g l , [g 4 |a 1 ])), confused([g 4 |a 1 ]) 3 .…”

“…Recently, in [14] and [12], we revisited the CC technique. Our motivation was not efficiency, but program analysis: Coroutining computations -the main type of computations dealt with by CC -are notoriously difficult to analyze.…”

“…In [14], our work focused on the analysis phase of CC. We showed that the analysis could be reformulated and formalized using Abstract Conjunctive Partial Deduction (ACPD for short), a framework proposed by Leuschel in [9].…”