Anti-unification for Unranked Terms and Hedges

Abstract

We study anti-unification for unranked terms and hedges that may contain term and hedge variables. The anti-unification problem of two hedgess 1 ands 2 is concerned with finding their generalization, a hedgeq such that boths 1 ands 2 are instances ofq 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, which is a parameter in the improved algorithm and selects certain common subsequences from the hedges to be generalized. The obtained rigid anti-unif ication algorithm is further made more precise by permitting combination of hedge and term variables in generalizations. Finally, we indicate a possible application of the algorithm in software engineering.

Anti-Unification and Natural Language Processing

“…Such sequences are called hedges. In anti-unification for such languages (see, e.g., [29]), they help to deal with position mismatches for similar argument pairs in terms to be generalized.…”

“…Our anti-unification algorithms are a part of RISC anti-unification algorithm library [6] and can be accessed from http://www.risc.jku.at/projects/stout/library.html. Particular algorithms from the library are described in [5,[7][8][9][10][11]29]. Yet another open-source anti-unification library, for order-sorted equational theories, has been described in [2] and is available online at http://safe-tools.dsic.upv.es/acuos/.…”

A Library of Anti-unification Algorithms

“…Unranked anti-unification is finitary, but it turned out that a minimal and complete algorithm may compute up to 3 n generalizations, where n is the size of the input. To deal with this problem, the notion of R T -generalization has been introduced in [16].…”

“…-first-order rigid unranked anti-unification from [16], -second-order unranked anti-unification from [5], -higher-order (pattern) anti-unification from [6] and -its subalgorithm for deciding α-equivalence, -nominal anti-unification from [7] and -its subalgorithm for deciding equivariance.…”

ACUOS: A System for Modular ACU Generalization with Subtyping and Inheritance

“…Experimental results given in Section 3 show that ACUOS performs efficiently in practice. For a discussion of the related literature, we refer to [2,3,1,4,10] 2 Use Case: Extracting Analogies…”