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Types for Nominal Rewriting ?

We define a type inference system for Nominal Rewriting where the types associated to terms are polymorphic (built from a set of base data sorts, type variables, and user-defined type constructors). In contrast with standard term rewriting systems or the λ-calculus, a typing environment for nominal rewriting includes type information for atoms, variables and function symbols. We give a syntax-directed system of typing rules associating types to terms, and show that every typable term has a principal type in a given environment. Type inference is decidable; moreover, rewriting preserves types when rules are typable.