Semantic Types and Approximation for Featherweight Java

We consider semantics for the class-based object-oriented calculus Featherweight Java (without casts) based upon approximation. We also define an intersection type assignment system for this calculus and show that it satisfies subject reduction and expansion, i.e. types are preserved under reduction and its converse. We establish a link between type assignment and the approximation semantics by showing an approximation result, which leads to a sufficient condition for the characterisation of head-normalisation and termination. We show the expressivity of both our calculus and our type system by defining an encoding of Combinatory Logic into our calculus and showing that this encoding preserves typeability. We also show that our system characterises the normalising and strongly normalising terms for this encoding. We thus demonstrate that the great analytic capabilities of intersection types can be applied to the context of class-based object orientation

Semantic Types for Class-based Objects

We investigate semantics-based type assignment for class-based object-oriented programming. Our motivation is developing a theoretical basis for practical, expressive, type-based analysis of the functional behaviour of object-oriented programs. We focus our research using Featherweight Java, studying two notions of type assignment:- one using intersection types, the other a ‘logical’ restriction of recursive types. We extend to the object-oriented setting some existing results for intersection type systems. In doing so, we contribute to the study of denotational semantics for object-oriented languages. We define a model for Featherweight Java based on approximation, which we relate to our intersection type system via an Approximation Result, proved using a notion of reduction on typing derivations that we show to be strongly normalising. We consider restrictions of our system for which type assignment is decidable, observing that the implicit recursion present in the class mechanism is a limiting factor in making practical use of the expressive power of intersection types. To overcome this, we consider type assignment based on recursive types. Such types traditionally suffer from the inability to characterise convergence, a key element of our approach. To obtain a semantic system of recursive types for Featherweight Java we study Nakano’s systems, whose key feature is an approximation modality which leads to a ‘logical’ system expressing both functional behaviour and convergence. For Nakano’s system, we consider the open problem of type inference. We introduce insertion variables (similar to the expansion variables of Kfoury and Wells), which allow to infer when the approximation modality is required. We define a type inference procedure, and conjecture its soundness based on a technique of Cardone and Coppo. Finally, we consider how Nakano’s approach may be applied to Featherweight Java and discuss how intersection and logical recursive types may be brought together into a single system

Typing Context-Dependent Behavioural Variation

Context Oriented Programming (COP) concerns the ability of programs to adapt to changes in their running environment. A number of programming languages endowed with COP constructs and features have been developed. However, some foundational issues remain unclear. This paper proposes adopting static analysis techniques to reason on and predict how programs adapt their behaviour. We introduce a core functional language, ContextML, equipped with COP primitives for manipulating contexts and for programming behavioural variations. In particular, we specify the dispatching mechanism, used to select the program fragments to be executed in the current active context. Besides the dynamic semantics we present an annotated type system. It guarantees that the well-typed programs adapt to any context, i.e. the dispatching mechanism always succeeds at run-time.Comment: In Proceedings PLACES 2012, arXiv:1302.579

Semantic Predicate Types and Approximation for Class-based Object Oriented Programming

We apply the principles of the intersection type discipline to the study of class-based object oriented programs and; our work follows from a similar approach (in the context of Abadi and Cardelli's Varsigma-object calculus) taken by van Bakel and de'Liguoro. We define an extension of Featherweight Java, FJc and present a predicate system which we show to be sound and expressive. We also show that our system provides a semantic underpinning for the object oriented paradigm by generalising the concept of approximant from the Lambda Calculus and demonstrating an approximation result: all expressions to which we can assign a predicate have an approximant that satisfies the same predicate. Crucial to this result is the notion of predicate language, which associates a family of predicates with a class.Comment: Proceedings of 11th Workshop on Formal Techniques for Java-like Programs (FTfJP'09), Genova, Italy, July 6 200

Mixin Composition Synthesis based on Intersection Types

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

Featherweight VeriFast

VeriFast is a leading research prototype tool for the sound modular verification of safety and correctness properties of single-threaded and multithreaded C and Java programs. It has been used as a vehicle for exploration and validation of novel program verification techniques and for industrial case studies; it has served well at a number of program verification competitions; and it has been used for teaching by multiple teachers independent of the authors. However, until now, while VeriFast's operation has been described informally in a number of publications, and specific verification techniques have been formalized, a clear and precise exposition of how VeriFast works has not yet appeared. In this article we present for the first time a formal definition and soundness proof of a core subset of the VeriFast program verification approach. The exposition aims to be both accessible and rigorous: the text is based on lecture notes for a graduate course on program verification, and it is backed by an executable machine-readable definition and machine-checked soundness proof in Coq

Towards a Java Subtyping Operad

The subtyping relation in Java exhibits self-similarity. The self-similarity in Java subtyping is interesting and intricate due to the existence of wildcard types and, accordingly, the existence of three subtyping rules for generic types: covariant subtyping, contravariant subtyping and invariant subtyping. Supporting bounded type variables also adds to the complexity of the subtyping relation in Java and in other generic nominally-typed OO languages such as C# and Scala. In this paper we explore defining an operad to model the construction of the subtyping relation in Java and in similar generic nominally-typed OO programming languages. Operads, from category theory, are frequently used to model self-similar phenomena. The Java subtyping operad, we hope, will shed more light on understanding the type systems of generic nominally-typed OO languages.Comment: 13 page