Short-cut rules: Sequential composition of rules avoiding unnecessary deletions

Abstract

Sequences of rule applications in high-level replacement systems are difficult to adapt. Often, replacing a rule application at the beginning of a sequence, i.e., reverting a rule and applying another one instead, is prevented by structure created via rule applications later on in the sequence. A trivial solution would be to roll back all applications and reapply them in a proper way. This, however, has the disadvantage of being computationally expensive and, furthermore, may cause the loss of information in the process. Moreover, using existing constructions to compose the reversal of a rule with the application of another one, in particular the concurrent and amalgamated rule constructions, does not prevent the loss of information in case that the first rule deletes elements being recreated by the second one. To cope with both problems, we introduce a new kind of rule composition through ‘short-cut rules’. We present our new kind of rule composition for monotonic rules in adhesive HLR systems, as they provide a well-established generalization of graph-based transformation systems, and motivate it on the example of Triple Graph Grammars, a declarative and rule-based bidirectional transformation approach.