This article presents a critical–propositional analysis of Sandro Stucki and Paolo G. Giarrusso’s A Theory of Higher-Order Subtyping with Type Intervals (2021), published in Proceedings of the ACM on Programming Languages and accompanied by its Agda formalization on Zenodo. The study examines the article’s theory of higher-order subtyping with type intervals in dialogue with the Theory of Objectivity (TO), especially regarding boundary, admissibility, relation, formal discipline, contextual memory, and the distinction between syntactic possibility and coherent instantiation.
The analysis argues that Stucki and Giarrusso’s formal treatment of intervals, bounds, subtyping, normalization, safety, undecidability, and mechanized proof offers an important methodological interlocution for TO. Although the analyzed article does not address cosmology, physics, the origin of the universe, atomic radiation, gravitational waves, or empirical observational data, it contributes indirectly to TO by showing how expressive systems require explicit rules of validity, limits, contexts, and proof conditions.
In dialogue with the modal axioms, phenomenic elements, Inducer Effects, cosmogonic theorem, and cosmological Eras of TO, the article proposes that type intervals may be read analogically as formal structures of admissibility. This analogy does not constitute empirical corroboration of TO, but it strengthens the philosophical and methodological demand for formal rigor in any theory that claims modal necessity.
This analytical text received analytical support from ChatGPT.
Keywords: Theory of Objectivity; Vidamor Cabannas; Denivaldo Silva; Sandro Stucki; Paolo G. Giarrusso; type intervals; higher-order subtyping; dependent object types; Scala; Agda; formalization; modal ontology; boundary; admissibility; formal rigor; Inducer Effects; cosmogonic theorem; computational logic; philosophy of computation.
Publication Date: 2026-06-20