We define two type assignment systems for first-order rewriting extended with application, -abstraction, and -reduction, using a combination of 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 inferre
