Patricia Johann

• This paper develops a sound and complete transformation-based algorithm forunification in an extensional order-sorted combinatory logic supporting constantoverloading and a higher-order sort concept. Appropriate notions of order-sortedweak equality and extensionality - reflecting order-sorted fij-equality in thecorresponding lambda calculus given by Johann and Kohlhase - are defined, andthe typed combinator-based higher-order unification techniques of Dougherty aremodified to accommodate unification with respect to the theory they generate. Thealgorithm presented here can thus be viewed as a combinatory logic counterpartto that of Johann and Kohlhase, as well as a refinement of that of Dougherty, andprovides evidence that combinatory logic is well-suited to serve as a framework forincorporating order-sorted higher-order reasoning into deduction systems aimingto capitalize on both the expressiveness of extensional higher-order logic and theefficiency of order-sorted calculi.