Object Closure Conversion

An integral part of implementing functional languages is closure conversion—the process of converting code with free variables into closed code and auxiliary data structures. Closure conversion has been extensively studied in this context, but also arises in languages with first-class objects. In fact, one variant of Java’s inner classes are an example of objects that need to be closure converted, and the transformation for converting these inner classes into Java Virtual Machine classes is an example of closure conversion. This paper argues that a direct formulation of object closure conversion is interesting and gives further insight into general closure conversion. It presents a formal closure-conversion translation for a second-order object language and proves it correct. The translation and proof generalise to other object-oriented languages, and the paper gives some examples to support this statement. Finally, the paper discusses the well known connection between function closures and single-method objects. This connection is formalised by showing that an encoding of functions into objects, object closure conversion, and various object encodings compose to give various closure-conversion translations for functions.