A formalization of System I with type Top in Agda

2026-03-24

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Multiagent Systems: Other Foundations of Multi Agent Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Security and Privacy: Data transparency and provenance

Abstract

System I is a recently introduced simply-typed lambda calculus with pairs where isomorphic types are considered equal. In this work we propose a variant of System I with the type Top, and present a complete formalization of this calculus in Agda, which includes the proofs of progress and strong normalization.

Problem

• System I
• type Top
• isomorphic types
• lambda calculus
• formalization

Innovation

• System I
• Top type
• Agda formalization
• strong normalization
• type isomorphism