Capturing Strong Reduction in Director String Calculus

Abstract

A modified version of Director String Calculus (MDSC) is introduced which preserves the applicative structure of the original lambda terms and captures the strong reduction as opposed to weak reduction of the original Director String Calculus (DSC). Futhermore, MDSC provides an environment which supports the nonatomic nature of the substitution operation and hence can lend itself to parallel and optimal reduction.