Abstract. We present FJig, a simple calculus where basic building blocks are classes in the style of Featherweight Java, declaring elds, methods and one constructor. However, inheritance has been generalized to the much more exible notion originally proposed in Bracha's Jigsaw framework. That is, classes play also the role of modules, that can be composed by a rich set of operators, all of which can be expressed by a minimal core. We keep the nominal approach of Java-like languages, that is, types are class names. However, a class is not necessarily a structural subtype of any class used in its dening expression. The calculus allows the encoding of a large variety of dierent mechanisms for software composition in class-based languages, including standard inheritance, mixin classes, traits and hiding. Hence, FJig can be used as a unifying framework for analyzing existing mechanisms and proposing new extensions.We provide two dierent semantics of an FJig program: attening and direct semantics. The dierence is analogous to that between two intuitive models to understand inheritance: the former where inherited methods are copied into heir classes, and the latter where member lookup is performed by ascending the inheritance chain. Here we address equivalence of these two views for a more sophisticated composition mechanism.

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We present a new language design which smoothly integrates modular composition and nesting of Java-like classes. That is, inheritance has been replaced by an expressive set of composition operators, inspired by Bracha's Jigsaw framework, and these operators allow to manipulate (e.g., rename or duplicate) a nested class at any level of depth. Typing is nominal as characteristic of Java-like languages, so types are paths of the form outer n .C 1 . . . . .C k which, depending on the class (node) where they occur, denote another node in the nesting tree. However, paths denoting the same class are not equivalent, since they behave differently w.r.t. composition operators.The resulting language, called DEEPFJIG, obtains a great expressive power, allowing, e.g., to solve the expression problem, encode basic AOP mechanisms, and bring some refactoring techniques at the language level, while keeping a very simple semantics and type system which represent a natural extension for, say, a Java programmer.

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