Manuel M. T. Chakravarty

System F with type equality coercions

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 top-level equality axioms. Unlike System F, FC is expressive enough to serve as a target for several different source-language features, including Haskells newtype, generalised algebraic data types, associated types, functional dependencies, and perhaps more besides.

Associated type synonyms

Haskell programmers often use a multi-parameter type class in which one or more type parameters are functionally dependent on the first. Although such functional dependencies have proved quite popular in practice, they express the programmers intent somewhat indirectly. Developing earlier work on associated data types, we propose to add functionally dependent types as type synonyms to type-class bodies. These associated type synonyms constitute an interesting new alternative to explicit functional dependencies.

Accelerating Haskell array codes with multicore GPUs

Current GPUs are massively parallel multicore processors optimised for workloads with a large degree of SIMD parallelism. Good performance requires highly idiomatic programs, whose development is work intensive and requires expert knowledge. To raise the level of abstraction, we propose a domain-specific high-level language of array computations that captures appropriate idioms in the form of collective array operations. We embed this purely functional array language in Haskell with an online code generator for NVIDIAs CUDA GPGPU programming environment. We regard the embedded languages collective array operations as algorithmic skeletons; our code generator instantiates CUDA implementations of those skeletons to execute embedded array programs. This paper outlines our embedding in Haskell, details the design and implementation of the dynamic code generator, and reports on initial benchmark results. These results suggest that we can compete with moderately optimised native CUDA code, while enabling much simpler source programs.

Data parallel Haskell: a status report

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 programming model 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.

Associated types with class

Haskells type classes allow ad-hoc overloading, or type-indexing, of functions. A natural generalisation is to allow type-indexing of data types as well. It turns out that this idea directly supports a powerful form of abstraction called associated types, which are available in C++ using traits classes. Associated types are useful in many applications, especially for self-optimising libraries that adapt their data representations and algorithms in a type-directed manner.In this paper, we introduce and motivate associated types as a rather natural generalisation of Haskells existing type classes. Formally, we present a type system that includes a type-directed translation into an explicitly typed target language akin to System F; the existence of this translation ensures that the addition of associated data types to an existing Haskell compiler only requires changes to the front end.

Regular, shape-polymorphic, parallel arrays in Haskell

We present a novel approach to regular, multi-dimensional arrays in Haskell. The main highlights of our approach are that it (1) is purely functional, (2) supports reuse through shape polymorphism, (3) avoids unnecessary intermediate structures rather than relying on subsequent loop fusion, and (4) supports transparent parallelisation. We show how to embed two forms of shape polymorphism into Haskells type system using type classes and type families. In particular, we discuss the generalisation of regular array transformations to arrays of higher rank, and introduce a type-safe specification of array slices. We discuss the runtime performance of our approach for three standard array algorithms. We achieve absolute performance comparable to handwritten C code. At the same time, our implementation scales well up to 8 processor cores.

Type checking with open type functions

We report on an extension of Haskell with open type-level functions and equality constraints that unifies earlier work on GADTs, functional dependencies, and associated types. The contribution of the paper is that we identify and characterise the key technical challenge of entailment checking; and we give a novel, decidable, sound, and complete algorithm to solve it, together with some practically-important variants. Our system is implemented in GHC, and is already in active use.

Nepal - Nested Data Parallelism in Haskell

This paper discusses an extension of Haskell by support for nested data-parallel programming in the style of the special-purpose language Nesl. The extension consists of a parallel array type, array comprehensions, and primitive parallel array operations. This extension brings a hitherto unsupported style of parallel programming to Haskell. Moreover, nested data parallelism should receive wider attention when available in a standardised language like Haskell.

Optimising purely functional GPU programs

Purely functional, embedded array programs are a good match for SIMD hardware, such as GPUs. However, the naive compilation of such programs quickly leads to both code explosion and an excessive use of intermediate data structures. The resulting slow-down is not acceptable on target hardware that is usually chosen to achieve high performance. In this paper, we discuss two optimisation techniques, sharing recovery and array fusion, that tackle code explosion and eliminate superfluous intermediate structures. Both techniques are well known from other contexts, but they present unique challenges for an embedded language compiled for execution on a GPU. We present novel methods for implementing sharing recovery and array fusion, and demonstrate their effectiveness on a set of benchmarks.

Running the manual: an approach to high-assurance microkernel development

We propose a development methodology for designing and prototyping high assurance microkernels, and describe our application of it. The methodology is based on rapid prototyping and iterative refinement of the microkernel in a functional programming language. The prototype provides a precise semi-formal model, which is also combined with a machine simulator to form a reference implementation capable of executing real user-level software, to obtain accurate feedback on the suitability of the kernel API during development phases. We extract from the prototype a machine-checkable formal specification in higher-order logic, which may be used to verify properties of the design, and also results in corrections to the design without the need for full verification. We found the approach leads to productive, highly iterative development where formal modelling, semi-formal design and prototyping, and end use all contribute to a more mature final design in a shorter period of time.