Polymorphic Intersection Type Assignment for Rewrite Systems with Abstraction and β-Rule

Abstract

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.Partially supported by MURST COFIN’99 TOSCA Project.KeywordsIntersection TypeFree VariableFunction SymbolType InferencePrincipal TypeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.