Anti-Unification with Unranked Terms and Hedges

We study anti-unification for unranked terms and hedges that may contain term and hedge variables. The anti-unification problem of two hedges s̃1 and s̃2 is concerned with finding their generalization, a hedge q̃ such that both s̃1 and s̃2 are instances of q̃ under some substitutions. Hedge variables help to fill in gaps in generalizations, while term variables abstract single (sub)terms with different top function symbols. First, we design a complete and minimal algorithm to compute least general generalizations. Then, we improve the efficiency of the algorithm by restricting possible alternatives permitted in the generalizations. The restrictions are imposed with the help of a rigidity function that is a parameter in the improved algorithm and selects certain common subsequences from the hedges to be generalized. Finally, we indicate a possible application of the algorithm in software engineering.