Independence in CLP languages

Abstract

Studying independence of goals has proven very useful in the context of logic programming. In particular, it has provided a formal basis for powerful automatic parallelization tools, since independence ensures that two goals may be evaluated in parallel while preserving correctness and efficiency. We extend the concept of independence to constraint logic programs (CLP) and prove that it also ensures the correctness and efficiency of the parallel evaluation of independent goals. Independence for CLP languages is more complex than for logic programming as search space preservation is necessary but no longer sufficient for ensuring correctness and efficiency. Two additional issues arise. The first is that the cost of constraint solving may depend upon the order constraints are encountered. The second is the need to handle dynamic scheduling. We clarify these issues by proposing various types of search independence and constraint solver independence, and show how they can be combined to allow different optimizations, from parallelism to intelligent backtracking. Sufficient conditions for independence which can be evaluated "a priori" at run-time are also proposed. Our study also yields new insights into independence in logic programming languages. In particular, we show that search space preservation is not only a sufficient but also a necessary condition for ensuring correctness and efficiency of parallel execution.

Parallel execution of prolog programs

“…This notion is also close to the firstfail principle widely used in constraint programming [Haralick and Elliot 1980]. The importance of determining goals which will not fail and/or are deterministic was studied also in [Hermenegildo 1986a;Pontelli et al 1996;Hermenegildo and Rossi 1995;García de la Banda et al 2000], and techniques have been devised for detecting deterministic and non-failing computations at comple-time [Debray and Warren 1989;.…”

“…This effectively eliminates the dichotomy between manual and automatic parallelization. Hermenegildo, Nasr, Rossi, and García de la Banda formalized and enhanced the Restricted And-Parallelism model further by providing backtracking semantics, a formal model, and correctness and efficiency results, showing the conditions under which the "no-slowdown" property (i.e., that parallel execution is no slower than sequential execution) holds [Hermenegildo 1986a;Hermenegildo and Nasr 1986;Hermenegildo and Rossi 1995;García de la Banda et al 2000]. A typical CGE has the form:…”

“…The issue of speculative computation also arises in independent and-parallel systems [Tebra 1987;Hermenegildo and Rossi 1995;García de la Banda et al 2000]. Given two independent goals a(X), b(Y) that are being executed in and-parallel, if a eventually fails, then work put in for solving b will go wasted (in sequential Prolog the goal b will not ever get executed).…”

“…In fact, it is possible to detect this automatically [Cabeza and Hermenegildo 1994]. A number of (also correct and efficient) further generalizations of the concept of non-strict independence have been proposed, based on notions of equivalence of search spaces [Hermenegildo and Rossi 1995;García de la Banda et al 2000;. These ehancements allow goals to share variables and bind them, provided the bindings made by these goals are either deterministic (in a similar way to the "Andorra" models reviewed below) or consistent (in the constraint logic programming sense).…”

“…These ehancements allow goals to share variables and bind them, provided the bindings made by these goals are either deterministic (in a similar way to the "Andorra" models reviewed below) or consistent (in the constraint logic programming sense). These enhancements have allowed extending independence to logic programs with delays [García de la Banda et al 1996; and constraint logic programs [García de la Banda et al 2000], as shown in Sec. 8.…”