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

@article{paperbot423,
  title = {Mixin Composition Synthesis based on Intersection Types},
  author = {Jan Bessai and Tzu-Chun Chen and Andrej Dudenhefner and Boris Düdder and Ugo de'Liguoro and Jakob Rehof},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 14, Issue 1},
  year = {2018},
  doi = {10.23638/lmcs-14(1:18)2018}
}