Decidable tag-based semantic subtyping for nominal types, tuples, and unions

Abstract

Semantic subtyping enables simple, set-theoretical reasoning about types by interpreting a type as the set of its values. Previously, semantic subtyping has been studied primarily in the context of statically typed languages with structural typing. In this paper, we explore the applicability of semantic subtyping in the context of a dynamic language with nominal types. Instead of static type checking, dynamic languages rely on run-time checking of type tags associated with values, so we propose using the tags for semantic subtyping. We base our work on a fragment of the Julia language and present tag-based semantic subtyping for nominal types, tuples, and unions, where types are interpreted set-theoretically as sets of type tags. The proposed subtyping relation is shown to be decidable, and a corresponding analytic definition is provided. The implications of using semantic subtyping for multiple dispatch are also discussed.CCS Concepts • Software and its engineering → Formal language definitions;

Decidable subtyping of existential types for the Julia language

“…In [Belyakova 2019], I proposed and mechanized in Coq a semantic interpretation of (a subset of) Julia types τ as sets of concrete value types σ (or type tags) rather than values, with semantic subtyping defined as τ ⊆ τ ′ . For the type language of non-parametric nominal types, tuples, and unions, a decidable syntactic subtype relation based on disjunctive normal form coincides with the set inclusion of interpretations.…”

“…In [Belyakova 2019], I show that the decidable syntactic subtype relation is sound and complete with respect to the interpretation.…”

A type system for Julia

“…al. [8]. This formalism captures the overwhelming majority of subtyping for Julia's type language (primarily excluding variadic length tuples).…”