Type checking modular multiple dispatch with parametric polymorphism and multiple inheritance

Abstract

In previous work, we presented rules for defining overloaded functions that ensure type safety under symmetric multiple dispatch in an object-oriented language with multiple inheritance, and we showed how to check these rules without requiring the entire type hierarchy to be known, thus supporting modularity and extensibility. In this work, we extend these rules to a language that supports parametric polymorphism on both classes and functions.In a multiple-inheritance language in which any type may be extended by types in other modules, some overloaded functions that might seem valid are correctly rejected by our rules. We explain how these functions can be permitted in a language that additionally supports an exclusion relation among types, allowing programmers to declare "nominal exclusions" and also implicitly imposing exclusion among different instances of each polymorphic type. We give rules for computing the exclusion relation, deriving many type exclusions from declared and implicit ones.We also show how to check our rules for ensuring the safety of overloaded functions. In particular, we reduce the problem of handling parametric polymorphism to one of determining subtyping relationships among universal and existential types. Our system has been implemented as part of the open-source Fortress compiler.

Union, intersection and refinement types and reasoning about type disjointness for secure protocol implementations

“…Reasoning about type disjointness is, for instance, used for preventing ambiguous overloading in the Fortress programming language [11].…”

“…Our Coq formalization [21] totals more than 14kLOC, 11 out of which more than 1.5kLOC are just definitions. We used Ott [115] to generate a large part of these definitions from a 1kLOC long Ott specification, but for the more complex rules we often 11 All code size figures include whitespace and comments.…”

“…We used Ott [115] to generate a large part of these definitions from a 1kLOC long Ott specification, but for the more complex rules we often 11 All code size figures include whitespace and comments.…”

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

“…Though multiple dispatch is more often found in dynamic languages, there has been research on safe integration of dynamic dispatch into statically typed languages [1,6,7,9,18]. There, subtyping is used for both static type checking and dynamic method resolution.…”

Implementing Federated Object Systems

“…For example we select the above rule over one with pattern InvoiceLine .spec( ItemSpecification ),or InvoiceLine .spec for short, for an attribute weight of dynamic type WeightedItemSpec in an InvoiceLine . Note though that, unlike in dynamic method dispatching [10] this selection itself is not done dynamically; as we will elaborate on in Section 5, relevant t-rules are resolved before actually being applied.…”