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Mixin Composition Synthesis Based on Intersection Types

Authors Jan Bessai, Andrej Dudenhefner, Boris Düdder, Tzu-Chun Chen, Ugo de’Liguoro, Jakob Rehof

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Jan Bessai
Andrej Dudenhefner
Boris Düdder
Tzu-Chun Chen
Ugo de’Liguoro
Jakob Rehof

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Jan Bessai, Andrej Dudenhefner, Boris Düdder, Tzu-Chun Chen, Ugo de’Liguoro, and Jakob Rehof. Mixin Composition Synthesis Based on Intersection Types. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 76-91, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.TLCA.2015.76

Abstract

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 corresponds to a mixin composition typed by the goal type.
Keywords
  • Record Calculus
  • Combinatory Logic
  • Type Inhabitation
  • Mixin
  • Intersection Type

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