(To appear in Theory and Practice of Logic Programming (TPLP)) We introduce a systematic, concurrent execution scheme for Constraint Handling Rules (CHR) based on a previously proposed sequential goal-based CHR semantics. We establish strong correspondence results to the abstract CHR semantics, thus guaranteeing that any answer in the concurrent, goal-based CHR semantics is reproducible in the abstract CHR semantics. Our work provides the foundation to obtain efficient, parallel CHR execution schemes.
Production systems are an established method for encoding knowledge in an expert system. The semantics of production system languages and the concomitant algorithms for their evaluation, RETE and TREAT, enumerate the set of rule instantiations and then apply a strategy that selects a single instantiation for firing. Often rule instantiations are calculated and never fired. In a sense, the time and space required to eagerly compute these unfired instantiations is wasted. This paper presents preliminary results about a new match technique, lazy matching. The lazy match algorithm folds the selection strategy into the search for instantiations, such that only one instantiation is computed per cycle. The algorithm improves the worst-case asymptotic space complexity of incremental matching. Moreover, empirical and analytic results demonstrate that lazy matching can substantially improve the execution time of production system programs. Conflict resolution is a form of global control used in production systems to achieve an efficient sequential execution of a rule-based program. This type of control is not used in parallel production system models[6, 13]. Instead, only those programs are executed which make no assumptions regarding conflict resolution. Therefore, the initial sequential rule-based programs are either executed in parallel without their conflict resolution strategy, which normally results in incorrect behavior, or the programs are transformed in an ad hoc manner to execute on a particular parallel production system model. As a result, these programs do not exhibit the parallelism hoped for [10, 13]. We believe that a second reason behind the lack of parallelism is that no formal methods of verifying the correctness of rule-based programs are utilized. Correctness is especially important when conflict resolution is no longer utilized, because it necessary to transform sequential rule-based programs into equivalent programs without conflict resolution. Also, the parallel execution of a rule-based program is more complex and demands these formal methods even more than its sequential counterpart. We are concerned with designing and developing correct rule-based programs for parallel execution. In this paper, we show the difficulty in transforming a simple sequential rule-based program to a new version of the program with no conflict resolution. Also, we show that the use of a new programming paradigm and language may result in more efficient programs which are provably correct, and can be executed in parallel. 