A common notation system for both lambda calculus and combinatory logic

Masahiko Sato

Graduate School of Informatics, Kyoto University

We present a notation system which can be used to faithfully represent both the terms of lambda calculus and combinatory logic. We show the faithfullness of the representations by observing that the representations respect the beta and eta reduction rules. We also argue that Curry's Last Problem (J.R.Hindley, Curry's Last Problem: Imitating lambda-beta-reduction in Combinatory Logic) in its original form is an ill-posed problem, and can be solved naturally by expressing the problem in our notation system.