We introduce a new representation of non-idempotent intersection types, using \textbf{ sequences} (families indexed with natural numbers) instead of lists or multisets. This allows scaling up \textbf{ intersection type} theory to the infinitary $\lambda$-calculus. We thus characterize hereditary head normalization, which gives a positive answer to a question known as \textbf{ Klop's Problem}. On our way, we use \textbf{ non-idempotent intersection} to retrieve some well-known results on infinitary terms.
Categories: cs.LO cs.PL