A new translation algorithm from Lambda Calculus into Combinatory Logic

Sabine Broda and Luís Damas



Systems of lambda calculus are of importance for most knowledge representation theories and in particular for several systems for Natural Language Processing. During the implementation of lambda systems several problems arise, which are directly related to the presence of bounded variables. These problems can be avoided using translations from lambda calculus into combinatory systems, which give origin to extremely simple reduction machines. In this article we present and prove the correctness of a translation algorithm, that, when compared with other systems, has quite good properties in terms of memory space as well as in terms of length of evaluations.