Modular multiple dispatch with multiple inheritance

Abstract

Overloaded functions and methods with multiple dispatch are useful for extending the functionality of existing classes in an objectoriented language. However, such functions introduce the possibility of ambiguous calls that cannot be resolved at run time, and modular static checking that such ambiguity does not exist has proved elusive in the presence of multiple implementation inheritance. We present a core language for defining overloaded functions and methods that supports multiple dispatch and multiple inheritance, together with a set of restrictions on these definitions that can be statically and modularly checked. We have proved that these restrictions guarantee that no undefined nor ambiguous calls occur at run time, while still permitting various kinds of overloading.

Type checking modular multiple dispatch with parametric polymorphism and multiple inheritance

“…We prove that these rules guarantee type safety. This extends previous work [2] in which we gave analogous rules, and proved the analogous result, for a core of Fortress that does not support generics.…”

“…In our previous work on Fortress without generics [2], we provided a special rule-the Exclusion Rule-to exploit this information. However, the Exclusion Rule can also be viewed, as we do in this paper, as a special case of the Meet Rule, where there are no nontrivial types to which both definitions are applicable.…”

“…Hereafter we consider every function to have a single parameter; the appearance of multiple parameters denotes a single tuple parameter. 2 A type is a nontrivial subtype of another type if it is not the trivial "bottom" type defined in the next section. 3 Despite its name, this relation, like the subtype relation, is reflexive: two function definitions with the same domain type are each more specific than the other.…”

Magda: A New Language for Modularity

“…Initially they were introduced in a untyped setting as an extension of Smalltalk [22,46]. Later on they were studied also in typed (thus often restricted) settings [47,44,11,6]. One of the design goals of this approach was to overcome problems with mixins mentioned above.…”

“…This problem has already been spotted and worked around using different solutions. The first solution was developed in Chai, an extension of Java with traits [47], and independently in the Fortress language [6,4,5]. The second solution is in the work adapting traits to statically typed languages [44].…”