Sequence Types and Infinitary Semantics

02/15/2021

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by   Pierre Vial, et al.

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We introduce a new representation of non-idempotent intersection types, using sequences (families indexed with natural numbers) instead of lists or multisets. This allows scaling up intersection type theory to the infinitary lambda-calculus. We thus characterize hereditary head normalization (Klop's Problem) and we give a unique type to all hereditary permutators (TLCA Problem #20), which is not possible in a finite system. On our way, we use non-idempotent intersection to retrieve some well-known results on infinitary terms. This paper begins with a gentle, high-level introduction to intersection type theory and to the infinitary calculus.