Academy & Industry Research Collaboration Center (AIRCC)

Volume 9, Number 3, March 2019

Intersection Type System and Lambda Calculus with Director Strings


Xinxin Shen and Kougen Zheng, Zhejiang University, China


The operation of substitution in 𝜆-calculus is treated as an atomic operation. It makes that substitution operation is complex to be analyzed. To overcome this drawback, explicit substitution systems are proposed. They bridge the gap between the theory of the 𝜆-calculus and its implementation in programming languages and proof assistants. 𝜆𝑜-calculus is a name-free explicit substitution. Intersection type systems for various explicit substitution calculi, not including λo-calculus, have been studied by researchers. In this paper, we put our attention to 𝜆𝑜-calculus. We present an intersection type system for 𝜆𝑜-calculus and show it satisfies the subject reduction property.


Intersection type, Lambda calculus, Director strings, Subject reduction