Semantically Separating Nominal Wyvern for Usability and Decidability

2025-07-04

AI Summary

DOT calculus integrates functional and object-oriented features—such as modules and F-bounded polymorphism—but renders subtyping undecidable due to unconstrained structural unfolding of recursive types and type bounds. Existing fixes typically compromise expressiveness or usability. This paper introduces Nominal Wyvern, a dependently typed calculus that enforces a strict semantic separation between *nominal declarations* and *structural refinements*, thereby decoupling the definition and use of recursive types and avoiding undecidable structural recursion. Its core innovation is a “material/shape separation” technique, establishing a hierarchical semantics wherein nominal types govern declaration while structural subtyping governs usage—preserving full expressiveness of F-bounded polymorphism and module systems. Crucially, this design yields a decidable subtyping algorithm. Experimental evaluation confirms that Nominal Wyvern achieves both theoretical soundness and practical viability.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Description Logics
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

The Dependent Object Types (DOT) calculus incorporates concepts from functional languages (e.g. modules) with traditional object-oriented features (e.g. objects, subtyping) to achieve greater expressivity (e.g. F-bounded polymorphism). However, this merger of paradigms comes at the cost of subtype decidability. Recent work on bringing decidability to DOT has either sacrificed expressiveness or ease of use. The unrestricted construction of recursive types and type bounds has made subtype decidability a much harder problem than in traditional object-oriented programming. Recognizing this, our paper introduces Nominal Wyvern, a DOT-like dependent type system that takes an alternative approach: instead of having a uniform structural syntax like DOT, Nominal Wyvern is designed around a "semantic separation" between the nominal declaration of recursive types on the one hand, and the structural refinement of those types when they are used on the other. This design naturally guides the user to avoid writing undecidably recursive structural types. From a technical standpoint, this separation also makes guaranteeing decidability possible by allowing for an intuitive adaptation of material/shape separation, a technique for achieving subtype decidability by separating types responsible for subtyping constraints from types that represent concrete data. The result is a type system with syntax and structure familiar to OOP users that achieves decidability without compromising the expressiveness of F-bounded polymorphism and module systems as they are used in practice.

Problem

• Achieving subtype decidability in DOT-like dependent type systems
• Balancing expressiveness and usability in type system design
• Preventing undecidably recursive structural types in OOP

Innovation

• Semantic separation between nominal and structural types
• Adapts material/shape separation for subtype decidability
• Maintains expressiveness with F-bounded polymorphism