Church's lambda-calculus is modified by introducing a new mechanism, the lambda-bar operator #, which neutralizes the effect of one preceding lambda binding. This operator can be used in such a way that renaming of bound variables in any reduction sequence can be avoided, with the effect that efficient interpreters with comparatively simple machine organization can be designed. It is shown that any semantic model of the pure λ-calculus also serves as a model of this modified reduction calculus, which guarantees smooth semantic theories. The Berkling Reduction Language (BRL) is a new functional programming language based upon this modification. © 1982 Academic Press, Inc.
Berkling, K. J., & Fehr, E. (1982). A consistent extension of the lambda-calculus as a base for functional programming languages. Information and Control, 55(1–3), 89–101. https://doi.org/10.1016/S0019-9958(82)90458-2