A Logical Approach to Deciding Semantic Subtyping

Author:

Gesbert Nils1,Genevès Pierre2,Layaïda Nabil3

Affiliation:

1. Grenoble INP -- Ensimag

2. CNRS

3. Inria

Abstract

We consider a type algebra equipped with recursive, product, function, intersection, union, and complement types, together with type variables. We consider the subtyping relation defined by Castagna and Xu [2011] over such type expressions and show how this relation can be decided in EXPTIME, answering an open question. The novelty, originality and strength of our solution reside in introducing a logical modeling for the semantic subtyping framework. We model semantic subtyping in a tree logic and use a satisfiability-testing algorithm in order to decide subtyping. We report on practical experiments made with a full implementation of the system. This provides a powerful polymorphic type system aiming at maintaining full static type-safety of functional programs that manipulate trees, even with higher-order functions, which is particularly useful in the context of XML.

Funder

Agence Nationale de la Recherche

Publisher

Association for Computing Machinery (ACM)

Subject

Software

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