LAMBDA(BETA') - A LAMBDA-CALCULUS WITH A GENERALIZED BETA-REDUCTION RULE

Abstract

The classical notion of beta-reduction in the lambda-calculus has an arbitrary syntactically-imposed sequentiality. A new notion of reduction beta' is defined which is a generalization of beta-reduction. This notion of reduction is shown to satisfy the Church-Rosser property as well as some other fundamental properties, leading to the conclusion that this generalized notion of beta'-reduction can be used in place of beta-reduction without sacrificing any of the fundamental properties.