A Unification Algorithm for GP 2

The graph programming language GP 2 allows to apply sets of ruleschemata (or “attributed” rules) non-deterministically. To analyse conflicts of pro-grams statically, graphs labelled with expressisons are overlayed to construct criticalpairs of rule applications. Each overlay induces a system of equations whose solu-tions represent different conflicts. We present a rule-based unification algorithm forGP expressions that is terminating, sound and complete. For every input equation,the algorithm generates a finite set of substitutions. Soundness means that each ofthese substitutions solves the input equation. Since GP labels are lists constructed byconcatenation, unification modulo associativity and unit law is required. This prob-lem, which is also known as word unification, is infinitary in general but becomesfinitary due to GP’s rule schema syntax and the assumption that rule schemata areleft-linear. Our unification algorithm is complete in that every solution of an inputequation is an instance of some substitution in the generated set