Polymorphic Intersection Type Assignment for Rewrite Systems with Abstractions and beta-Rule

We define two type assignment systems for first-order rewriting extended with application, λ-abstraction, and β-reduction, using a combination of (Ω-free) intersection types and second-order polymorphic types. The first system is the general one, for which we prove subject reduction, and strong normalisation of typeable terms. The second is a decidable subsystem of the first, by restricting to Rank 2 (intersection and quantified) types. For this system we define, using an extended notion of unification, a notion of principal typing which is more general than ML's principal type property, since also the types for the free variables of terms are inferred.

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