We introduce System FC, which extends System F with support for non-syntactic type equality. There are two main extensions: (i) explicit witnesses for type equalities, and (ii) open, non-parametric type functions, given meaning by toplevel equality axioms. Unlike System F, FC is expressive enough to serve as a target for several different source-language features, including Haskell’s newtype, generalised algebraic data types, associated types, functional dependencies, and perhaps more besides.

We describe the design and current status of our effort to implement the programming model of nested data parallelism into the Glasgow Haskell Compiler. We extended the original programmingmodel and its implementation, both of which were first popularised by the NESL language, in terms of expressiveness as well as efficiency. Our current aim is to provide a convenient programming environment for SMP parallelism, and especially multicore architectures. Preliminary benchmarks show that we are, at least for some programs, able to achieve good absolute performance and excellent speedups.

“Concepts ” are an essential language feature needed to support generic programming in the large. Concepts allow for succinct expression of bounds on type parameters of generic algorithms, enable systematic organization of problem domain abstractions, and make generic algorithms easier to use. In this paper we formalize the design of a type system and semantics for concepts that is suitable for non-type-inferencing languages. Our design shares much in common with the type classes of Haskell, though our primary influence is from best practices in the C ++ community, where concepts are used to document type requirements for templates in generic libraries. The technical development in this paper defines an extension to System F and a type-directed translation from the extension back to System F. The translation is proved sound; the proof is written in the human readable but machine checkable Isar language and has been automatically verified by the Isabelle proof assistant. This document was generated directly from the Isar theory files using Isabelle’s support for literate proofs.

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ABSTRACT. If you want to program a parallel computer, a purely functional language like Haskell is a promising starting point. Since the language is pure, it is by-default safe for parallel evaluation, whereas imperative languages are by-default unsafe. But that doesn’t make it easy! Indeed it has proved quite difficult to get robust, scalable performance increases through parallel functional programming, especially as the number of processors increases. A particularly promising and well-studied approach to employing large numbers of processors is data parallelism. Blelloch’s pioneering work on NESL showed that it was possible to combine a rather flexible programming model (nested data parallelism) with a fast, scalable execution model (flat data parallelism). In this paper we describe Data Parallel Haskell, which embodies nested data parallelism in a modern, general-purpose language, implemented in a state-of-the-art compiler, GHC. We focus particularly on the vectorisation transformation, which transforms nested to flat data parallelism. 1

ML modules and Haskell type classes have proven to be highly effective tools for program structuring. Modules emphasize explicit configuration of program components and the use of data abstraction. Type classes emphasize implicit program construction and ad hoc polymorphism. In this paper, we show how the implicitlytyped style of type class programming may be supported within the framework of an explicitly-typed module language by viewing type classes as a particular mode of use of modules. This view offers a harmonious integration of modules and type classes, where type class features, such as class hierarchies and associated types, arise naturally as uses of existing module-language constructs, such as module hierarchies and type components. In addition, programmers have explicit control over which type class instances are available for use by type inference in a given scope. We formalize our approach as a Harper-Stone-style elaboration relation, and provide a sound type inference algorithm as a guide to implementation.

Recent research has shown how boilerplate code, or repetitive code for traversing datatypes, can be eliminated using generic programming techniques already available within some implementations of Haskell. One particularly intractable kind of boilerplate is nameplate, or code having to do with names, name-binding, and fresh name generation. One reason for the difficulty is that operations on data structures involving names, as usually implemented, are not regular instances of standard map, fold , or zip operations. However, in nominal abstract syntax, an alternative treatment of names and binding based on swapping, operations such as #-equivalence, capture-avoiding substitution, and free variable set functions are much better-behaved.

First and foremost I thank my parents for all their love and for teaching me to enjoy learning. I especially thank my wife Katie for her support and understanding through this long and sometimes stressful process. I also thank Katie for insisting on good error messages for G! My advisor, Andrew Lumsdaine, deserves many thanks for his support and guidance and for keeping the faith as I undertook this long journey away from scientific computing and into the field of programming languages. I thank my thesis committee: R. Kent Dybvig, Daniel P. Friedman, Steven D. Johnson, and Amr Sabry for their advice and encouragement. A special thanks goes to Ronald Garcia, Christopher Mueller, and Douglas Gregor for carefully editing and catching the many many times when I accidentally skipped over the important stuff. Thanks to Jaakko and Jeremiah for hours of stimulating discussions and arguments concerning separate compilation and concept-based overloading. Thanks to David Abrahams for countless hours spent debating the merits of one design over another while jogging through the hinterlands of Norway. Thanks to Alexander Stepanov and David Musser for getting all this started, and thank you for the encouragement over the years. Thanks to Matthew Austern, his book Generic Programming in the STL was both an inspiration

Abstract. With Java 5 and C # 2.0, first-order parametric polymorphism was introduced in mainstream object-oriented programming languages under the name of generics. Although the first-order variant of generics is very useful, it also imposes some restrictions: it is possible to abstract over a type, but the resulting type constructor cannot be abstracted over. This can lead to code duplication. We removed this restriction in Scala, by allowing type constructors as type parameters and abstract types. This paper presents the design and implementation of the resulting type constructor polymorphism. It combines type constructor polymorphism with implicit parameters to yield constructs similar to, and at times more expressive than, Haskell’s constructor type classes. The paper also studies interactions with other object-oriented language constructs, and discusses the gains in expressiveness. 1

Datatype-generic programming is defining functions that depend on the structure, or “shape”, of datatypes. It has been around for more than 10 years, and a lot of progress has been made, in particular in the lazy functional programming language Haskell. There are more than 10 proposals for generic programming libraries or language extensions for Haskell. To compare and characterize the many generic programming libraries in a typed functional language, we introduce a set of criteria and develop a generic programming benchmark: a set of characteristic examples testing various facets of datatype-generic programming. We have implemented the benchmark for nine existing Haskell generic programming libraries and present the evaluation of the libraries. The comparison is useful for reaching a common standard for generic programming, but also for a programmer who has to choose a particular approach for datatype-generic programming.