Soundness of Abadi–Fiore’s axiomatized program logic for the iso-to-equi encoding

Prove the soundness of the axiomatized program logic introduced by Abadi and Fiore (1996) to justify that iso-recursive terms produced by their encoding with explicit coercions behave identically to the original equi-recursive terms. Establish a complete soundness proof for this logic to remove the reliance on an unproven conjecture in the absence of an operational semantics.

Background

Abadi and Fiore (1996) showed that iso- and equi-recursive types have the same expressive power by translating equi-recursive types into iso-recursive types using explicit coercions. To argue behavioral equivalence, they proposed an axiomatized program logic rather than giving an operational semantics.

However, within that framework the soundness of the program logic was not established; it was stated as a conjecture. Consequently, despite the widely cited expressiveness result, a complete, operationally justified proof of behavioral equivalence relying on that particular logic has not appeared in the literature. This paper cites that gap as motivation for introducing full iso-recursive types, which avoid explicit coercions and permit a complete proof via erasure-based reasoning.