Practical usefulness of explicit weakening (lambda-up)

Ascertain whether the explicit weakening calculus (lambda-up) for simply-typed lambda calculus with de Bruijn indices, as developed and mechanized in Agda in this work, is useful in practice beyond the presented examples and case studies.

Background

The paper introduces a new formulation of substitution for simply-typed lambda calculus with de Bruijn indices, centered on making weakening explicit (the lambda-up calculus) while keeping substitution and composition as meta operations. This design aims to make many substitution properties hold by definitional equality, drastically simplifying mechanized proofs in Agda.

Throughout the paper, the author demonstrates that results which previously required extensive auxiliary lemmas become trivial through the new approach. However, in the conclusion the author flags a practical concern: the technique distinguishes terms that are typically considered equivalent in traditional notation. Although normalization strategies may mitigate this, the author emphasizes that further experience is needed to evaluate real-world utility, posing a direct question about the practical usefulness of explicit weakening.