A formalization of System I with type Top in Agda

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.

💡 Research Summary

The paper presents a formalization in Agda of an extension of System I, a simply‑typed λ‑calculus with pairs in which isomorphic types are identified as equal. The authors add the unit type ⊤ (Top) as a base type, thereby introducing three new type isomorphisms (A × ⊤ ≡ A, ⊤ → A ≡ A, and A → ⊤ ≡ ⊤) together with the corresponding term‑level transformations. To keep the system amenable to mechanised reasoning, they make every type isomorphism explicit by attaching a witness ρ to the conversion rule; the term constructor `