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We study the problem of type inference for a family of polymorphic type disciplines containing the power of Core-ML. This family comprises all levels of the stratiication of the second-order lambda-calculus by \ r a n k " o f t ypes. We s h o w that typability is an undecidable problem at every rank k 3 of this stratiication. While it was already known that(More)
Principality of typings is the property that for each typable term, there is a typing from which all other typings are obtained via some set of operations. Type inference is the problem of finding a typing for a given term, if possible. We define an intersection type system which has principal typings and types exactly the strongly normalizable ¿-terms.(More)
We embed the standard λ-calculus, denoted Λ, into two larger λ-calculi, denoted Λ ∧ and &Λ ∧. The standard notion of β-reduction for Λ corresponds to two new notions of reduction, β ∧ for Λ ∧ and &β ∧ for &Λ ∧. A distinctive feature of our new calculus Λ ∧ (resp., &Λ ∧) is that, in every function application, an argument is used at most once (resp., exactly(More)
We investigate finite-rank intersection type systems, analyzing the complexity of their type inference problems and their relation to the problem of recognizing semantically equivalent terms. Intersection types allow something of type &amp;tau;<inf>1</inf> &amp;Lambda; &amp;tau;<inf>2</inf> to be used in some places at type &amp;tau;<inf>1</inf> and in(More)
The Semi-Unification Problem (SUP) is a natural generalization of both first-order unification and matching. The problem arises in various branches of computer science and logic. Although several special cases of SUP are known to be decidable, the problem in general has been open for several years. We show that SUP in general is undecidable, by reducing(More)