Well-typed Programs Research Articles

Guest editorial

The Eighth International Workshop on Foundations of Object-Oriented Languages (FOOL 8) was held on January 20, 2001, colocated with the ACM Symposium on Principles of Programming Languages in London. Kathleen Fisher chaired the program committee. Six contributed papers were presented. After the workshop, extended versions of three were solicited for this special issue of TOPLAS ; the two articles that were ultimately submitted were reviewed, revised, and accepted following standard TOPLAS procedures.The special issue opens with Type-Preserving Compilation of Featherweight Java by Christopher League, Zhong Shao, and Valery Trifonov. The goal of the authors is to establish a foundation for certifying compilation of Java-like class-based languages. To this end, the authors give an encoding of core Java features in a typed intermediate language suitable for use within a type-preserving compiler. Because of its intended use, the authors focus on developing an efficient encoding. They show that the type erasure of their implementation matches the standard vtable self-application semantics of message sending.The authors use Featherweight Java (FJ), which models the core features of Java, as their source language. Their translation targets a variant of F ω , already implemented as part of the SML/NJ compiler, using its row polymorphism and existential and recursive types to encode FJ. The authors show that the translation from FJ to their target preserves types.In the issue's second article, More Dynamic Object Reclassification: Fickle II , Sophia Drossopoulou, Ferruccio Damiani, Mariangiola Dezani-Ciancaglini, and Paola Giannini explore the issue of dynamic reclassification, by which an object changes its class membership at runtime while retaining its identity. This ability helps model real-world situations where an object has different roles over time---for example, a person who is first a student and then graduates to become a teacher.The authors focus their study on the design of a language, Fickle II , which extends an imperative, typed, class-based, object-oriented language with a reclassification operation. To specify the behavior of their language, the authors give an operational semantics. They then develop a type and effect system and show that the type system is sound, in the sense that a well-typed program cannot get stuck under the operational semantics.We would like to thank our colleagues who served on the FOOL 8 program committee and those who participated in the anonymous reviewing process for TOPLAS . Their efforts contributed greatly to the quality of this special issue.

A parameterized type system for race-free Java programs

This paper presents a new static type system for multithreaded programs; any well-typed program in our system is free of data races. Our type system is significantly more expressive than previous such type systems. In particular, our system lets programmers write generic code to implement a class, then create different objects of the same class that have different objects of the same class that have different protection mechanisms. This flexibility enables programmers to reduce the number of unnecessary synchronizationoperations in a program without risking data races. We also support default types which reduce the burden of writing extra type annotations. Our experience indicates that our system provides a promising approach to make multithreaded programs more reliable and efficient

Termination of Simply-Moded Well-Typed Logic Programs under a Tabled Execution Mechanism

Tabled logic programming is receiving increasing attention in the Logic Programming community. It avoids many of the shortcomings of SLD(NF) execution and provides a more flexible and often extremely efficient execution mechanism for logic programs. In particular, tabled execution of logic programs terminates more often than execution based on SLD-resolution. So, if a program can be proven to terminate under SLD-resolution, then the program will trivially also terminate under SLG-resolution, the resolution principle of tabling. But, since there are SLG-terminating programs which are not SLD-terminating, more effective proof techniques can be found. One of the few approaches studying termination of tabled logic programs was developed by Decorte et al. They present necessary and sufficient conditions for two notions of termination under LG-resolution, i.e. SLG-resolution with left-to-right selection rule: quasi-termination and (the stronger notion of) LG-termination. Starting from these necessary and sufficient conditions, we introduce sufficient conditions for quasi-termination and LG-termination which are stated fully at the clause level and are easy to automatize. To this end, we use mode and type information: we consider simply-moded, well-typed programs and queries. We point out how our termination conditions can be automatized, by extending the recently developed, constraint-based, automatic termination analysis for SLD-resolution of Decorte and De Schreye. Finally, we present a result on substitution-closedness of quasi-termination and LG-termination for the class of simply-moded, well-typed programs and queries.

From system F to typed assembly language

We motivate the design of typed assembly language (TAL) and present a type-preserving ttranslation from Systemn F to TAL. The typed assembly language we pressent is based on a conventional RISC assembly language, but its static type sytem provides support for enforcing high-level language abstratctions, such as closures, tuples, and user-defined abstract data types. The type system ensures that well-typed programs cannot violatet these abstractionsl In addition, the typing constructs admit many low-level compiler optimiztaions. Our translation to TAL is specified as a sequence of type-preserving transformations, including CPS and closure conversion phases; type-correct source programs are mapped to type-correct assembly language. A key contribution is an approach to polymorphic closure conversion that is considerably simpler than previous work. The compiler and typed assembly lanugage provide a fully automatic way to produce certified code, suitable for use in systems where unstrusted and potentially malicious code must be checked for safety before execution.

Ownership types for flexible alias protection

Object-oriented programming languages allow inter-object aliasing. Although necessary to construct linked data structures and networks of interacting objects, aliasing is problematic in that an aggregate object's state can change via an alias to one of its components, without the aggregate being aware of any aliasing. Ownership types form a static type system that indicates object ownership. This provides a flexible mechanism to limit the visibility of object references and restrict access paths to objects, thus controlling a system's dynamic topology. The type system is shown to be sound, and the specific aliasing properties that a system's object graph satisfies are formulated and proven invariant for well-typed programs.

Resource Access Control in Systems of Mobile Agents: (Extended Abstract)

We describe a typing system for a distributed π-calculus which guarantees that distributed agents cannot access the resources of a system without first being granted the capability to do so. The language studied allows agents to move between distributed locations and to augment their set of capabilities via communication with other agents. The type system is based on the novel notion of a location type, which describes the set of resources available to an agent at a location. Resources are themselves equipped with capabilities, and thus an agent may be given permission to send data along a channel at a particular location without being granted permission to read data along the same channel. We also describe a tagged version of the language, where the capabilities of agents are made explicit in the syntax. Using this tagged language we define access violations as runtime errors and prove that well-typed programs are incapable of such errors.

Programming in Three Dimensions

Cube is a three-dimensional, visual, statically typed, higher-order logic programming language, designed to be used in a virtual-reality-based programming environment. In this paper, we give an informal overview of the language and describe a prototype implementation.

Type inference for objects

Type inference. Types are useful because they can help a compiler generate good code and because “well-typed programs cannot go wrong.” In languages such as Pascal and Ada, variables must be declared with a type, and the compiler can then verify whether a given program is indeed well-typed. This verification is called type checking. Type inference is the computation of missing type annotations. It allows us to omit some or all of the type annotations in our programs, and it is successfully used in functional languages such as ML and Haskell.

Operational interpretations of an extension of Fω with control operators

AbstractWe study the operational semantics of an extension of Girard's System Fω with two control operators: an abort operation that abandons the current control context, and a callcc operation that captures the current control context. Two classes of operational semantics are considered, each with a call-by-value and a call-by-name variant, differing in their treatment of polymorphic abstraction and instantiation. Under the standard semantics, polymorphic abstractions are values and polymorphic instantiation is a significant computation step; under the ML-like semantics evaluation proceeds beneath polymorphic abstractions and polymorphic instantiation is computationally insignificant. Compositional, type-preserving continuation-passing style (cps) transformation algorithms are given for the standard semantics, resulting in terms on which all four evaluation strategies coincide. This has as a corollary the soundness and termination of well-typed programs under the standard evaluation strategies. In contrast, such results are obtained for the call-by-value ML-like strategy only for a restricted sub-language in which constructor abstractions are limited to values. The ML-like call-by-name semantics is indistinguishable from the standard call-by-name semantics when attention is limited to complete programs.

A sound type system for secure flow analysis

Ensuring secure information flow within programs in the context of multiple sensitivity levels has been widely studied. Especially noteworthy is Denning’s work in secure flow analysis and the lattice model [6][7]. Until now, however, the soundness of Denning’s analysis has not been established satisfactorily. We formulate Denning’s approach as a type system and present a notion of soundness for the system that can be viewed as a form of noninterference. Soundness is established by proving, with respect to a standard programming language semantics, that all well-typed programs have this noninterference property.

An interpretation of typed OOP in a language with state

In this paper we give semantics toLoop, an expressive typed object-oriented programming language with updatable instance variables.Loop has a rich type system that allows for the typing of methods operating over an open-ended “self” type. We prove the type system given is sound;i.e., well-typed programs do not experience “message not understood” errors. The semantics ofLoop is given by a translation into a state-based language,Soop, that contains reference cells, records, and a form of F-bounded polymorphic type.

A meta-language for typed object-oriented languages

In [12] we defined the λ&-calculus, a simple extension of the typed λ-calculus to model typed object-oriented languages. This paper is the continuation or, rather, the companion of [12] since it analyzes the practical counterpart of the theoretical issues introduced there. Indeed, to develop a formal study of type systems for object-oriented languages we define a meta-language based on λ& and we show, by a practical example, how it can be used to prove properties of a language. To this purpose, we define a toy object-oriented language and its type-checking algorithm; then we translate this toy language into our meta-language. The translation gives the semantics of the toy language and a theorem on the translation of well-typed programs proves the correctness of the type-checker of the toy language. As an aside we also illustrate the expressivity of the λ&-based model by showing how to translate existing features like multiple inheritance and multiple dispatch, but also by integrating in the toy language new features directly suggested by the model, such as first-class messages, a generalization of the use of super and the use of explicit coercions. An important novelty with respect to previous systems is that we show how to model multiple dispatch also in the presence of a notion of receiver (i.e. of a privileged argument to which the message is passed), a notion that is absent in languages like CLOS.

The structure of typed programming languages

From the Publisher: The Structure of Typed Programming Languages describes the fundamental syntactic and semantic features of modern programming languages, carefully spelling out their impacts on language design. Using classical and recent research from lambda calculus and type theory, it presents a rational reconstruction of the Algol-like imperative languages such as Pascal, Ada, and Modula-3, and the higher-order functional languages such as Scheme and ML. David Schmidt's text is based on the premise that although few programmers ever actually design a programming language, it is important for them to understand the structuring techniques. His use of these techniques in a reconstruction of existing programming languages and in the design of new ones allows programmers and would-be programmers to see why existing languages are structured the way they are and how new languages can be built using variations on standard themes. The text is unique in its tutorial presentation of higher-order lambda calculus and intuitionistic type theory. The latter in particular reveals that a programming language is a logic in which its typing system defines the propositions of the logic and its well-typed programs constitute the proofs of the propositions.

Projective ML

We propose a projective lambda calculus as the basis for operations on records. Projections operate on elevations, that is, records with defaults. This calculus extends lambda calculus while keeping its essential properties. We build projective ML from this calculus by adding the ML Let typing rule to the simply typed projective calculus. We show that projective ML possesses the subject reduction property, which means that well-typed programs can be reduced safely. Elevations are practical data structures that can be compiled efficiently. Moreover, standard records are difinable in terms of projections.

A type system for logic programs

A theory for a type system for logic programs is developed which addressesthe question of well-typing, type inference, and compile-time and run-time type checking. A type is a recursively enumerable set of ground atoms, which is tuple-distributive. The association of a type to a program is intended to mean that only ground atoms that are elements of the type may be derived from the program. A declarative definition of well-typed programs is formulated, based on an intuitive approach related to the fixpoint semantics of logic programs. Whether a program is well typed is undecidable in general. We define a restricted class of types, called regular types, for which type checking is decidable. Regular unary logic programs are proposed as a specification language for regular types. An algorithm for type-checking a logic program with respect to a regular type definition is described, and its complexity is analyzed. Finally, the practicality of the type system is discussed, and some examples are shown. The type system has been implemented in FCP for FCP and is incorporated in the Logix system.

Type declarations as subtype constraints in logic programming

This paper presents a type system for logic programs that supports parametric polymorphism and subtypes. This system follows most knowledge representation and object-oriented schemes in that subtyping is name-based , i.e., τ 1 is considered to be a subtype of τ 2 iff it is declared as such. We take this as a fundamental principle in the sense that type declarations have the form of subtype constraints. Types are assigned meaning by viewing such constraints as Horn clauses that, together with a few basic axioms, define a subtype predicate. This technique provides a (least) model for types and, at the same time, a sound and complete proof system for deriving subtypes. Using this proof system, we define well-typedness conditions which ensure that a logic program/query respects a set of predicate types. We prove that these conditions are consistent in the sense that every atom of every resolvent produced during the execution of a well-typed program is consistent with its type.

Terminating general recursion

In Martin-Lof's type theory, general recursion is not available. The only iterating constructs are primitive recursion over natural numbers and other inductive sets. The paper describes a way to allow a general recursion operator in type theory (extended with propositions). A proof rule for the new operator is presented. The addition of the new operator will not destroy the property that all well-typed programs terminate. An advantage of the new program construct is that it is possible to separate the termination proof of the program from the proof of other properties.

A polymorphic type system for prolog

We describe a polymorphic type scheme for Prolog which makes static type checking possible. Polymorphism gives a good degree of flexibility to the type system, and makes it intrude very little on a user's programming style. The only additions to the language are type declarations, which an interpreter can ignore if it so desires, with the guarantee that a well-typed program will behave identically with or without type checking. Our implementation is discussed and we observe that the type resolution problem for a Prolog program is another Prolog (meta)program.