Polymorphic type inference with overloading and subtyping

Structural semantics for polymorphic data types (preliminary report)

Consistent subtyping is employed in some gradual type systems to validate type conversions. The original definition by Siek and Taha serves as a guideline for designing gradual type systems with subtyping. Polymorphic types à la System F also induce a subtyping relation that relates polymorphic types to their instantiations. However, Siek and Taha’s definition is not adequate for polymorphic subtyping. The first goal of this article is to propose a generalization of consistent subtyping that is adequate for polymorphic subtyping and subsumes the original definition by Siek and Taha. The new definition of consistent subtyping provides novel insights with respect to previous polymorphic gradual type systems, which did not employ consistent subtyping. The second goal of this article is to present a gradually typed calculus for implicit (higher-rank) polymorphism that uses our new notion of consistent subtyping. We develop both declarative and (bidirectional) algorithmic versions for the type system. The algorithmic version employs techniques developed by Dunfield and Krishnaswami for higher-rank polymorphism to deal with instantiation. We prove that the new calculus satisfies all static aspects of the refined criteria for gradual typing. We also study an extension of the type system with static and gradual type parameters, in an attempt to support a variant of the dynamic criterion for gradual typing. Assuming a coherence conjecture for the extended calculus, we show that the dynamic gradual guarantee of our source language can be reduced to that of λ B, which, at the time of writing, is still an open question. Most of the metatheory of this article, except some manual proofs for the algorithmic type system and extensions, has been mechanically formalized using the Coq proof assistant.

Consistent subtyping is employed in some gradual type systems to validate type conversions. The original definition by Siek and Taha serves as a guideline for designing gradual type systems with subtyping. Polymorphic types à la System F also induce a subtyping relation that relates polymorphic types to their instantiations. However Siek and Taha’s definition is not adequate for polymorphic subtyping. The first goal of this paper is to propose a generalization of consistent subtyping that is adequate for polymorphic subtyping, and subsumes the original definition by Siek and Taha. The new definition of consistent subtyping provides novel insights with respect to previous polymorphic gradual type systems, which did not employ consistent subtyping. The second goal of this paper is to present a gradually typed calculus for implicit (higher-rank) polymorphism that uses our new notion of consistent subtyping. We develop both declarative and (bidirectional) algorithmic versions for the type system. We prove that the new calculus satisfies all static aspects of the refined criteria for gradual typing, which are mechanically formalized using the Coq proof assistant.

This article presents a polymorphic modal type system and its principal type inference algorithm that conservatively extend ML by all of Lisp's staging constructs (the quasi-quotation system). The combination is meaningful because ML is a practical higher-order, impure, and typed language, while Lisp's quasi-quotation system has long evolved complying with the demands from multi-staged programming practices. Our type system supports open code, unrestricted operations on references, intentional variable-capturing substitution as well as capture-avoiding substitution, and lifting values into code, whose combination escaped all the previous systems.

This article presents a polymorphic modal type system and its principal type inference algorithm that conservatively extend ML by all of Lisp's staging constructs (the quasi-quotation system). The combination is meaningful because ML is a practical higher-order, impure, and typed language, while Lisp's quasi-quotation system has long evolved complying with the demands from multi-staged programming practices. Our type system supports open code, unrestricted operations on references, intentional variable-capturing substitution as well as capture-avoiding substitution, and lifting values into code, whose combination escaped all the previous systems.

This paper presents a polymorphic type inference algorithm for a small subset of JavaScript. The goal is to prevent accessing undefined members of objects. We define a type system that allows explicit extension of objects through add operation and implicit extension through method calls. The type system also permits strong updates and unrestricted extensions to new objects. The type inference algorithm is modular so that each function definition is only analyzed once and larger programs can be checked incrementally.

From a software engineering point of view, logic programming lacks many properties allowing secure development of large programs by many programmers. In this paper we try to improve these properties by proposing a polymorphic type system for Prolog. Our type system is able to deal with subtype relations if information about dataflow within clauses is available. This information can be given by a mode system. We give an outline of a type checking algorithm for this type system and discuss several problems which do not arise in type systems without subtypes.

Advanced polymorphic type systems have come to play an important role in the world of functional programming. But, curiously, these type systems have so far had little impact upon widely-used imperative programming languages like C and C++. We show that ML-style polymorphism can be integrated smoothly into a dialect of C, which we call Polymorphic C. It has the same pointer operations as C, including the address-of operator &, the dereferencing operator*, and pointer arithmetic. Our type system allows these operations in their full generality, so that programmers need not give up the flexibility of C to gain the benefits of ML-style polymorphism. We prove a type soundness theorem that gives a rigorous and useful characterization of well-typed Polymorphic C programs in terms of what can go wrong when they are evaluated.

We present Skil, an imperative language enhanced with higher order functions and currying, as well as with a polymorphic type system. The high level of Skil allows the integration of algorithmic skeletons, i.e. of higher order functions representing parallel computation patterns. At the same time, the language can be efficiently implemented. After describing a series of skeletons which work with distributed arrays, we give two examples of parallel programs implemented on the basis of skeletons, namely shortest paths in graphs and Gaussian elimination. Run time measurements show that we approach the efficiency of message passing C up to a factor between 1 and 2.5.

A logic language is suitable for specification if it is equipped with features for data abstraction and modularization. In this paper, an effective mechanism to incorporate function and type into logic programming is presented as the means to embed data abstraction mechanism into logic programming. This incorporation is essentially based on Horn clause logic with equality and a polymorphic type system that is an extension of Mycroft and O’Keefe’s system. This paper also presents an implementation based on Warren Abstract Machine (WAM) and shows the performance, along with a comparison with WAM.

A Syntactic Approach to Type Soundness

At the Integrated Publication and Information Systems Institute (IPSI) of the GMD (Gesellschaft für Mathematik und Datenverarbeitung) database research is focused towards distributed database management systems to support the integration of heterogeneous multi-media information bases needed in an integrated publishing environment. The objective is to investigate advanced object-oriented and active data modelling concepts together with the principles of distributed data stores and data management. The unifying basis for the database research is the object-oriented data model VML developed in the project VODAK over the last four years. The data model is based on recursively defined meta classes, classes and instance hierarchies paired with a strict separation of structural and operational definitions in a polymorphic type system. This report describes the highlights of the work on the VODAK database system, the research efforts in heterogeneous database integration and the research plans of the multimedia database project as well as applications of our system in different environments such as hypertext and office automation.

A record data type can be extended by addition of more fields. The extended type is a subtype of the original, in that any value of the extended type can be regarded as a value of the original type by ignoring the additional fields. This results in a type hierarchy. Milner [3] has proposed a polymorphic type system. With the Milner approach, the type of a function may contain type variables. This also results in a type hierarchy. In a language with a polymorphic type system, if it is anticipated that a record type will need to be extended, then the record type can be defined to have a dummy extension field . In the parent type, the extension field will have null contents of type void . The type of the extension field can differ with different subtypes. The approach can be extended to allow a type to be subtype of two or more parent types. To a limited extent, this approach can be used in Ada and other languages with generic program units.

International audience

Enhancements to a visual dataflow language called Show-and-Tell (STL) are described. These enhancements enrich STL by a polymorphic-type system similar to the one used in ML, and they introduce user-definable higher-order functions. A short overview of STL is given, and the concept of higher-order functions is discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>