Abstract

Gradual typing is an effective approach to integrate static and dynamic typing, which supports the smooth transition between both extremes via the imprecision of type annotations. Gradual typing has been applied in many scenarios such as objects, subtyping, effects, ownership, typestates, information-flow typing, parametric polymorphism, etc. In particular, the combination of gradual typing and mutable references has been explored by different authors, giving rise to four different semantics-invariant, guarded, monotonic and permissive references. These semantics were specially crafted to reflect different design decisions with respect to precision and efficiency tradeoffs. Since then, progress has been made in the formulation of methodologies to systematically derive gradual counterparts of statically-typed languages, but these have not been applied to study mutable references.