Sharing a Perspective on the 𝜆-Calculus

Abstract

The λ-calculus models the core of functional programming languages. This essay discusses a gap between the theory of the λ-calculus and functional languages, namely the fact that the former does not give a status to sharing, the essential ingredient for efficiency in the lattter.

The essay provides an overview of the perspective of the author, who has been and still is studying sharing from various angles. In particular, it explains how sharing impacts the equational and denotational semantics of the λ-calculus, breaking some expected properties, and demanding the development of new, richer semantics of the λ-calculus.