Proposed Type System Research Articles

A gradual type system for Elixir

Elixir is a functional programming language with dynamic typing. We propose a gradual type system that makes it possible to perform type-checking on a significant fragment of the language. An important feature of the type system is that it does not require any syntactic change to Elixir. Type information is provided by means of function signatures which are declared in terms of Elixir typespec directives. The proposed type system is based on subtyping and is backward compatible, as it allows the presence of untyped code fragments. We have a prototype implementation of the type-checker in Elixir itself and a formalization in Idris of the fragment considered.

Probabilistic Termination by Monadic Affine Sized Typing

We introduce a system of monadic affine sized types, which substantially generalizes usual sized types and allows in this way to capture probabilistic higher-order programs that terminate almost surely. Going beyond plain, strong normalization without losing soundness turns out to be a hard task, which cannot be accomplished without a richer, quantitative notion of types, but also without imposing some affinity constraints. The proposed type system is powerful enough to type classic examples of probabilistically terminating programs such as random walks. The way typable programs are proved to be almost surely terminating is based on reducibility but requires a substantial adaptation of the technique.

Static analysis of cloud elasticity

We propose a static analysis technique that computes upper bounds of virtual machine usages in a concurrent language with explicit acquire and release operations of virtual machines. In our language it is possible to delegate other (ad-hoc or third party) concurrent code to release virtual machines (by passing them as arguments of invocations). Our technique is modular and consists of ( i ) a type system associating programs with behavioural types that record relevant information for resource usage (creations, releases, and concurrent operations), ( ii ) a translation function that takes behavioural types and returns cost equations, and ( iii ) an automatic off-the-shelf solver for the cost equations. A soundness proof of the type system establishes the correctness of our technique with respect to the cost equations. We have experimentally evaluated our technique using a cost analysis solver and we report some results. • A technique for the static analysis of resource utilization is proposed. • The analysis relies on a static type system that records program's resources behaviour. • The proposed approach supports concurrency and explicit release operations. • A proof of soundness of the proposed type system and of the analysis is provided.

Privacy protection by typing in ubiquitous computing systems

Ubiquitous computing systems collect and share a great deal of information upon the users and their environment; including private or highly sensitive personal information. Unless users are confident enough that their privacy is protected, many will be deterred from using such systems. This paper proposes a privacy type system that controls the behaviour of concurrent, context-aware and mobile processes to ensure that private information is not accidentally disclosed. We prove the subject reduction property and the soundness of the proposed type system; which guarantee that a well-typed process cannot accidentally disclose private information. We demonstrate the pragmatics of our approach with a case study.

Typed context awareness Ambient Calculus for pervasive applications

Abstract The idea of pervasive computing is that information processing will become part of everyday life, and will be available everywhere, making computing so natural to the point of being invisible in the ambient. An important concept that arises with pervasive computing is context awareness . Context is any information that can be used to characterize an entity. Based on contextual information, applications can dynamically adapt themselves to the environments in which they operate. The Calculus of Context-aware Ambients (CCA) is an untyped formal language used to describe mobile and context-aware pervasive applications. The CCA extends the Ambient Calculus by providing new features, such as context-guarded action and process abstraction, allowing to model contexts and context-aware computations. In this work, we define a type system for the CCA, called CCA T , with the focus in the communication between processes and in the correct use of process abstraction and contexts, extending previous works on the definition of type systems for mobile computing. Moreover, we prove that the proposed type system has the subject reduction property (or type preservation). We also model a hospital scenario using CCA T to demonstrate the use of the proposed type system.

A Sound Type System for Typing Runtime Errors

Dynamically typed languages such as Scheme are widely adopted because of their rich expressiveness. However, there is the drawback that dynamic typing cannot detect runtime errors at compile time. In this paper, we propose a type system which enables static detection of runtime errors. The key idea of our approach is to introduce a special type, called the error type, for expressions that cause runtime errors. The proposed type system brings out the benefit of the error type with set-theoretic union, intersection and complement types, recursive types, parametric polymorphism and subtyping. While existing type systems usually ensure that evaluation never causes runtime errors for typed expressions, our system ensures that evaluation always causes runtime errors for expressions typed with the error type. Likewise, our system also ensures that evaluation never causes errors for expressions typed with any type that does not contain the error type. Under the usual definition of subtyping, it is difficult to syntactically prove the soundness of our type system. We redefine subtyping by introducing the notion of intransitive subtyping, and syntactically prove the soundness under the new definition.

A Type System for Unstructured Locking that Guarantees Deadlock Freedom without Imposing a Lock Ordering

Deadlocks occur in concurrent programs as a consequence of cyclic resource acquisition between threads. In this paper we present a novel type system that guarantees deadlock freedom for a language with references, unstructured locking primitives, and locks which are implicitly associated with references. The proposed type system does not impose a strict lock acquisition order and thus increases programming language expressiveness.

A Type System for Tom

Extending a given language with new dedicated features is a general and quite used approach to make the programming language more adapted to problems. Being closer to the application, this leads to less programming flaws and easier maintenance. But of course one would still like to perform program analysis on these kinds of extended languages, in particular type checking and inference. In this case one has to make the typing of the extended features compatible with the ones in the starting language. The Tom programming language is a typical example of such a situation as it consists of an extension of Java that adds pattern matching, more particularly associative pattern matching, and reduction strategies. This paper presents a type system with subtyping for Tom, that is compatible with Java's type system, and that performs both type checking and type inference. We propose an algorithm that checks if all patterns of a Tom program are well-typed. In addition, we propose an algorithm based on equality and subtyping constraints that infers types of variables occurring in a pattern. Both algorithms are exemplified and the proposed type system is showed to be sound and complete.

A hybrid type system for lock-freedom of mobile processes

We propose a type system for lock-freedom in the π-calculus, which guarantees that certain communications will eventually succeed. Distinguishing features of our type system are: it can verify lock-freedom of concurrent programs that have sophisticated recursive communication structures; it can be fully automated; it is hybrid, in that it combines a type system for lock-freedom with local reasoning about deadlock-freedom, termination, and confluence analyses. Moreover, the type system is parameterized by deadlock-freedom/termination/confluence analyses, so that any methods (e.g. type systems and model checking) can be used for those analyses. A lock-freedom analysis tool has been implemented based on the proposed type system, and tested for nontrivial programs.

A Compositional Behavioral Modeling Framework for Embedded System Design and Conformance Checking

We propose a framework based on a synchronous multi-clocked model of computation to support the inductive and compositional construction of scalable behavioral models of embedded systems engineered with de facto standard design and programming languages. Behavioral modeling is seen under the paradigm of type inference. The aim of the proposed type system is to capture the behavior of a system under design and to re-factor it by performing global optimizing and architecture-sensitive transformations on it. It allows to modularly express a wide spectrum of static and dynamic behavioral properties and automatically or manually scale the desired degree of abstraction of these properties for efficient verification. The type system is presented using a generic and language-independent static single assignment intermediate representation.

Type inference with rank 1 polymorphism for type-directed compilation of ML

This paper defines an extended polymorphic type system for an ML-style programming language, and develops a sound and complete type inference algorithm. Different frdm the conventional ML type discipline, the proposed type system allows full rank 1 polymorphism , where polymorphic types can appear in other types such as product types, disjoint union types and range types of function types. Because of this feature, the proposed type system significantly reduces the value-only restriction of polymorphism, which is currently adopted in most of ML-style impure languages. It also serves as a basis for efficient implementation of type-directed compilation of polymorphism. The extended type system achieves more efficient type inference algorithm, and it also contributes to develop more efficient type-passing implementation of polymorphism. We show that the conventional ML polymorphism sometimes introduces exponential overhead both at compile-time elaboration and run-time type-passing execution, and that these problems can be eliminated by our type inference system. Compared with a more powerful rank 2 type inference systems based on semi-unification, the proposed type inference algorithm infers a most general type for any typable expression by using the conventional first-order unification, and it is therefore easily adopted in existing implementation of ML family of languages.