Elena Zucca

A calculus of module systems

We present CMS, a simple and powerful calculus of modules supporting mutual recursion and higher order features, which can be instantiated over an arbitrary core calculus satisfying standard assumptions. The calculus allows expression of a large variety of existing mechanisms for combining software components, including parameterized modules similar to ML functors, extension with overriding as in object-oriented programming, mixin modules and extra-linguistic mechanisms like those provided by a linker. Hence CMS can be used as a paradigmatic calculus for modular languages, in the same spirit the lambda calculus is used for functional programming. We first present an untyped version of the calculus and then a type system; we prove confluence, progress, and subject reduction properties. Then, we define a derived calculus of mixin modules directly in terms of CMS and show how to encode other primitive calculi into CMS (the lambda calculus and the Abadi-Cardelli object calculus). Finally, we consider the problem of introducing a subtype relation for module types.

A theory of mixin modules: basic and derived operators

Mixins are modules in which some components are deferred, that is, their definition has to be provided by another module. Moreover, in contrast to parameterized modules (like ML functors), mixin modules can be mutually dependent and their composition supports the redefinition of components (overriding). In this paper, we present a formal model of mixins and their basic composition operators. These operators can be viewed as a kernel language with clean semantics in which one can express more complex operators of existing modular languages, including variants of inheritance in object-oriented programming. Our formal model is given in an ‘institution independent’ way, that is, it is parameterized by the semantic framework modelling the underlying core language.

A Primitive Calculus for Module Systems

We present a simple and powerful calculus of modules supporting mutual recursion and higher order features. The calculus allows to encode a large variety of existing mechanisms for combining software components, including parameterized modules, extension with overriding of object-oriented programming, mixin modules and extra-linguistic mechanisms like those provided by a linker. As usual, we first present an untyped version of our calculus and then a type system which is proved sound w.r.t. the reduction semantics; moreover we give a translation of other primitive calculi.

Polymorphic bytecode: compositional compilation for Java-like languages

We define compositional compilation as the ability to typecheck source code fragments in isolation, generate corresponding binaries,and link together fragments whose mutual assumptions are satisfied, without reinspecting the code. Even though compositional compilation is a highly desirable feature, in Java-like languages it can hardly be achieved. This is due to the fact that the bytecode generated for a fragment (say, a class) is not uniquely determined by its source code, but also depends on the compilation context.We propose a way to obtain compositional compilation for Java, by introducing a polymorphic form of bytecode containing type variables (ranging over class names) and equipped with a set of constraints involving type variables. Thus, polymorphic bytecode provides a representation for all the (standard) bytecode that can be obtained by replacing type variables with classes satisfying the associated constraints.We illustrate our proposal by developing a typing and a linking algorithm. The typing algorithm compiles a class in isolation generating the corresponding polymorphic bytecode fragment and constraints on the classes it depends on. The linking algorithm takes a collection of polymorphic bytecode fragments, checks their mutual consistency, and possibly simplifies and specializes them. In particular, linking a self-contained collection of fragments either fails, or produces standard bytecode (the same as would have been produced by standard compilation of all fragments).

D-oids: a model for dynamic data-types †

We propose a semantic framework for dynamic systems, which, in a sense, extends the well-known algebraic approach for modelling static data structures to the dynamic case. The framework is based on a new mathematical structure, called a d-oid, consisting of a set of instant structures and a set of dynamic operations. An instant structure is a static structure, e.g. an algebra; a dynamic operation is a transformation of instant structures with an associated point to point map, which allows us to keep track of the transformations of single objects and thus is called a tracking map. By an appropriate notion of morphism, the d-oids over a dynamic signature constitute a category.It is shown that d-oids can model object systems and support an abstract notion of possibly unique object identity; moreover, for a d-oid satisfying an identity preserving condition, there exists an essentially equivalent d-oid where the elements of instant structures are just names.

True separate compilation of Java classes

We define a type system modeling true separate compilation for a small but significant Java subset, in the sense that a single class declaration can be intra-checked (following the Cardellis terminology) and compiled providing a minimal set of type requirements on missing classes. These requirements are specified by a local type environment associated with each single class, while in the existing formal definitions of the Java type system classes are typed in a global type environment containing all the type information on a closed program. We also provide formal rules for static inter-checking and relate our approach with compilation of closed programs, by proving that we get the same results.

Parametric channels via label expressions in CCS

Abstract CCS, the Calculus of Communicating Systems devised by Milner, has proved extremely successful for providing, via translation, a sound mathematical basis for a wide class of concurrent languages. Nevertheless, as it stands, it suffers from a limitation: it is impossible to determine at run time the channel on which to send or receive a communication. There are various possibilities for giving CCS such ability, but the price can be a drastic change in the language and the theory of CCS. Here we present a simple solution to this problem, which keeps language and theory almost unchanged, at least in fundamental aspects: the essential idea is to extend CCS by allowing (channel-) label expressions. We also show various applications of this extended version of CCS.

Principal typings for Java-like languages

The contribution of the paper is twofold. First, we define a general notion of type system equipped with an entailment relation between type environments; this generalisation serves as a pattern for instantiating type systems able to support separate compilation and inter-checking of Java-like languages, and allows a formal definition of soundess and completeness of inter-checking w.r.t. global compilation. These properties are important in practice since they allow selective recompilation. In particular, we show that they are guaranteed when the type system has principal typings and provides sound and complete entailment relation between type environments.The second contribution is more specific, and is an instantiation of the notion of type system previously defined for Featherweight Java with method overloading and field hiding. The aim is to show that it is possible to define type systems for Java-like languages, which, in contrast to those used by standard compilers, have principal typings, hence can be used as a basis for selective recompilation.

A core calculus for Java exceptions

In this paper we present a simple calculus (called CJE) in ourder to fully investigate the exception mechanism of Java, and in particular its interaction with inheritance, which turns out to be non trivial. Moreover, we show that the type system for the calculus directly dirven by the Java language specification (called FULL) uses too many types, in the sense that there are different types which rpovide exactly the same information. Hence, we obtain from FULL a simplified type system called MIN where equivalent types have been identified. We show that is useful both for type-checking optimization and for clarifying the static semantics of the language. The two type systems are proved to satisfy the subject reduction property

Featherweight Jigsaw: A Minimal Core Calculus for Modular Composition of Classes

We present FJig, a simple calculus where basic building blocks are classes in the style of Featherweight Java, declaring fields, methods and one constructor. However, inheritance has been generalized to the much more flexible notion originally proposed in Brachas 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 defining expression. The calculus allows the encoding of a large variety of different 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 different semantics of an FJig program: flattening and direct semantics. The difference 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.