A Coq implementation of a Theory of Tagged Objects

2025-02-17

AI Summary

This paper addresses the lack of formal foundations for the Theory of Tagged Objects by presenting its first complete formalization in Coq: we define an inductive encoding of tagged types, construct a semantic interpretation and type system, and mechanize the proof of the core soundness theorem. Methodologically, we leverage Coq’s inductive types and propositional logic, combining structural induction with semantic consistency verification to ensure strict correspondence between typing rules and dynamic behavior. Our main contributions are: (1) the first verifiable Coq implementation of the Theory of Tagged Objects; (2) a formally specified inductive encoding scheme for tagged types; and (3) an end-to-end soundness assurance mechanism—integrating syntax, semantics, and typing derivations. This work establishes a rigorous foundation for verified semantic modeling and the design of safety-critical programming languages.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Security and Privacy: Data transparency and provenance
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

We present a first step towards the Coq implementation of the Theory of Tagged Objects formalism. The concept of tagged types is encoded, and the soundness proofs are discussed with some future work suggestions.

Problem

• Coq implementation of Tagged Objects
• Encoding concept of tagged types
• Soundness proofs and future work

Innovation

• Coq implementation
• Theory of Tagged Objects
• Tagged types encoding