Various algorithms for achieving different levels of local consistency (i.e., constraint propagation algorithms), even diverse ones for the same kind of local consistency, are present in the literature and built into existing systems. Due to their variety and diversity, a natural quest is to search for a common framework. In this article, we approach constraint propagation from a general perspective, by enlarging on previous algorithm schemata and augmenting their expressive power: in that, further constraint propagation algorithms are instances of our schema. This is due to new relations that we establish among function sets and use to instantiate our algorithm schema; these relations result from abstracting common properties of the surveyed constraint propagation algorithms. Hence, our general approach is expressive enough to bring out the common properties of most of the constraint propagation algorithms, as well as their distinctions.