Mixin Composition Synthesis based on Intersection Types

Abstract

We present a method for synthesizing compositions of mixins using typeinhabitation in intersection types. First, recursively defined classes andmixins, which are functions over classes, are expressed as terms in a lambdacalculus with records. Intersection types with records and record-merge areused to assign meaningful types to these terms without resorting to recursivetypes. Second, typed terms are translated to a repository of typed combinators.We show a relation between record types with record-merge and intersectiontypes with constructors. This relation is used to prove soundness and partialcompleteness of the translation with respect to mixin composition synthesis.Furthermore, we demonstrate how a translated repository and goal type can beused as input to an existing framework for composition synthesis in boundedcombinatory logic via type inhabitation. The computed result is a class typedby the goal type and generated by a mixin composition applied to an existingclass