Equational Anti-unification over Absorption Theories

Abstract

Interest in anti-unification, the dual problem of unification, is rising due to various new applications. For example, anti-unification-based techniques have been used recently in software analysis and related areas such as clone detection and automatic program repair. While syntactic forms of anti-unification have found many interesting uses, some aspects of modern applications are more appropriately modeled by reasoning modulo an equational theory. Thus, extending existing anti-unification methods to deal with important equational theories is the natural step forward. This paper considers anti-unification modulo pure absorption theories, i.e., where some function symbols are associated with a special constant satisfying the axiom $$f(x,\varepsilon _{f}) \,\approx \, f(\varepsilon _{f},x) \,\approx \, \varepsilon _{f}$$ f ( x , ε f ) ≈ f ( ε f , x ) ≈ ε f . We provide a sound and complete rule-based algorithm for such theories. Furthermore, we show that anti-unification modulo absorption is infinitary. Despite this, our algorithm terminates and produces a finitary algorithmic representation of the minimal complete set of solutions.