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

Sequence Types and Infinitary Semantics