Mixin Composition Synthesis based on Intersection Types

TL;DR

This paper introduces a novel method for synthesizing mixin compositions using intersection types and type inhabitation, translating class and mixin definitions into typed combinators for automated composition.

Contribution

It presents a new approach combining intersection types and lambda calculus to synthesize mixin compositions, with formal soundness and partial completeness proofs.

Findings

Successfully synthesizes mixin compositions using type inhabitation.

Establishes a formal relation between record types and intersection types.

Demonstrates practical application within an existing composition framework.

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 is a class typed by the goal type and generated by a mixin composition applied to an existing class.