Mixin Composition Synthesis based on Intersection Types

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.

CLS-SMT: Bringing Together Combinatory Logic Synthesis and Satisfiability Modulo Theories

“…For this particular example, the combinator mapping in the table shown below was used. In order to illustrate the first result term as a tree, we use the following labelling pattern: combinator name : (vertex id, combinator id) name id default 1 id 2 min 3 values 4 inv 5 sortmap 6 @:(1,0) @:(2,0) min:(4,3) default:(5,1) @:(3,0) @:(6,0) sortmap: (12,6) inv: (13,5) values: (7,4)…”

“…The algorithm searches for terms that are formed from the combinators and have a given target type τ . (CL)S is intended to be used for the automatic composition of software [5,6,9,15,21]. Besides the synthesis from software components, the (CL)S framework allows the synthesis of data structures, for instance of BPMN 2.0 processes [9] or planning processes [33].…”

Tagungsband zum 21. Kolloquium Programmiersprachen und Grundlagen der Programmierung

“…In a series of papers (Rehof and Urzyczyn, 2011;Rehof and Urzyczyn, 2012;Düdder, Martens, Rehof, and Urzyczyn, 2012;Düdder, Martens, and Rehof, 2013;Bessai, Chen, et al, 2018), we have laid the theoretical foundations for understanding algorithmic and complexity of decidable inhabitation in subsystems of the intersection type system by Coppo and Dezani-Ciancaglini, 1980. In contrast to standard combinatory logic, where a fixed basis of combinators is usually considered, the inhabitation problem considered here is relativized to an arbitrary environment given as part of the input.…”