Enhancing Show-and-Tell with a polymorphic type system and higher-order functions

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.

Efficient high-level parallel programming

Algorithmic skeletons are polymorphic higher-order functions representing common parallelization patterns and implemented in parallel. They can be used as the building blocks of parallel and distributed applications by integrating them into a sequential language. In this paper, we present a new approach to programming with skeletons. We integrate the skeletons into an imperative host language enhanced with higher-order functions and currying, as well as with a polymorphic type system. We thus obtain a high-level programming language which can be implemented very efficiently. After describing a series of skeletons which work with distributed arrays, we give two examples of parallel algorithms implemented in our language, namely matrix multiplication and a statistical numerical algorithm for solving partial differential equations. Run-time measurements show that we approach the efficiency of message-passing C up to a factor between 1 and 1.75.

Structural semantics for polymorphic data types (preliminary report)

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.

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.

We show how the Hindley/Milner polymorphic type system can be extended to incorporate overloading and subtyping, by using constrained quantification. We describe an algorithm for inferring principal types and outline a proof of its soundness and completeness. We find that it is necessary in practice to simplify the inferred types, and we describe techniques for type simplification that involve shape unification, strongly connected components, transitive reduction, and the monotonicities of type formulas.

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.

Visual programming language research has evolved greatly since its early days. At first, attempts at visual programming mostly took the form of flowchart-like diagrams. But in recent years, a wide number of innovative approaches have been incorporated into visual languages, including object-oriented programming, form-based programming, programming by demonstration, and dataflow programming. Unfortunately, while many of these systems represent important ideas, only a few have been successful as complete visual programming languages. This tutorial explains why this is true, and describes ways in which the problem can be addressed. This tutorial explores the issues behind the successes and failures of earlier approaches from a design perspective. It identifies characteristics of successful visual programming languages, and explains how to design an object-oriented language that maintains those characteristics. It shows solutions to a number of problems by looking at existing visual programming languages, including Prograph.

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.

VPL is a visual programming language and environment for interactive image processing. VPL uses a novel system architecture which separates interaction and computation components in order to provide a highly interactive visual programming user-interface. VPL is based on a declarative, demand driven dataflow model of computation. It is a practical, usable visual programming system, integrating tools for browsing, inspecting and editing components and documentation. VPL also provides data persistence and data import/export mechanisms. The visual programming model supports both function extensibility and higher order functions, allowing users to build their own program dataflow structures within the VPL environment. >

International audience

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.

An efficient spatial smoothing algorithm for filtering data while preserving spatial detail is obtained using the system (impulse response) function of the sensor. In contrast to the normal procedure for determining the filter coefficients for an arbitrary system function, this technique does not involve the use of Fourier transforms. The algorithm results in optimal smoothing within the constraints of retaining good vertical detail after only three or four iterations. A refinement of this procedure involving higher-order filter functions produced the equivalent operation in a single pass. The spatial filtering coefficients are obtained analytically for the frequently applicable Gaussian system function. The efficiency of this procedure is illustrated by filtering simulation, logs, and spectral data. For real-time smoothing of nuclear log data, a filter length of five times the vertical resolution is required. >