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We provide a type-theoretical characterization of weakly-normalizing terms inan infinitary lambda-calculus. We adapt for this purpose the standardquantitative (with non-idempotent intersections) type assignment system of thelambda-calculus to our infinite calculus. Our work provides a new answer toKlop's HHN-problem, namely, finding out if there is a type systemcharacterizing the hereditary head-normalizing (HHN) lambda-terms. Tatsutashowed that HHN could not be characterized by a finite type system. We provethat an infinitary type system endowed with a validity condition calledapproximability can achieve it.

Infinitary Intersection Types as Sequences: a New Answer to Klop's Question