Abstract
We show that the standard method of saturated sets for proving strong normalization of β-reduction in the simply typed and second-order polymorphic lambda calculus incorporates non-structural subtyping systems in a natural way. This shows that strong normalization for non-structural subtyping proved by Wand, O'Keefe and Palsberg (1995) via coercion interpretations can be obtained in a straightforward extension of the standard method. The proof presented here is compared to other proofs of strong normalization for subtyping systems.
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