Fully Abstract from Static to Gradual
summary
Proposes that the embedding from static into gradual languages must be fully abstract embedding — it preserves and reflects contextual equivalence — and shows this criterion catches gradualizations that pass Siek’s refined checks yet break parametricity or non‑interference (explicit counterexamples where embeddings map equal static terms to distinguishable gradual terms). Provides a mechanized GTLCμ mechanized proof for the simply‑typed λ‑calculus with equirecursive types, builds a back‑translation using a universal recursive back‑translation into a cast calculus with explicit casts and proves correctness via step‑indexed logical relations in Iris.
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