Polymorphic intersection type assignment for rewrite systems with abstraction and -rul

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

Constraint Handling Rules with Binders, Patterns and Generic Quantification

Constraint Handling Rules provide descriptions for constraint solvers. However, they fall short when those constraints specify some binding structure, like higher-rank types in a constraint-based type inference algorithm. In this paper, the term syntax of constraints is replaced by $\lambda$-tree syntax, in which binding is explicit; and a new $\nabla$ generic quantifier is introduced, which is used to create new fresh constants.Comment: Paper presented at the 33nd International Conference on Logic Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1, 2017 16 pages, LaTeX, no PDF figure