Functional programming languages are informally classified into pure and impure languages. The precise meaning of this distinction has been a matter of controversy. We therefore investigate a formal definition of purity. We begin by showing that some proposed definitions which rely on confluence, soundness of the beta axiom, preservation of pure observational equivalences and independence of the order of evaluation, do not withstand close scrutiny. We propose instead a definition based on parameter-passing independence. Intuitively, the definition implies that functions are pure mappings from arguments to results; the operational decision of how to pass the arguments is irrelevant. In the context of Haskell, our definition is consistent with the fact that the traditional call-by-name denotational semantics coincides with the traditional call-by-need implementation. Furthermore, our definition is compatible with the stream-based, continuation-based and monad-based integration of computational effects in Haskell. Finally, we observe that call-by-name reasoning principles are unsound in compilers for monadic Haskell.

The process of writing large parallel programs is complicated by the need to specify both the parallel behaviour of the program and the algorithm that is to be used to compute its result. This paper introduces evaluation strategies: lazy higher-order functions that control the parallel evaluation of non-strict functional languages. Using evaluation strategies, it is possible to achieve a clean separation between algorithmic and behavioural code. The result is enhanced clarity and shorter parallel programs. Evaluation strategies are a very general concept: this paper shows how they can be used to model a wide range of commonly used programming paradigms, including divide-and-conquer parallelism, pipeline parallelism, producer/consumer parallelism, and data-oriented parallelism. Because they are based on unrestricted higher-order functions, they can also capture irregular parallel structures. Evaluation strategies are not just of theoretical interest: they have evolved out of our experience in parallelising several large-scale parallel applications, where they have proved invaluable in helping to manage the complexities of parallel behaviour. Some of these applications are described in detail here. The largest application we have studied to date, Lolita, is a 40,000 line natural language engineering system. Initial results show that for these programs we can achieve acceptable parallel performance, for relatively little programming effort.

Lazy functional languages seem to be unsuitable for programming embedded computers because their implementations require so much memory for program code and graph. In this paper we describe a new abstract machine for the implementation of lazy functional languages on embedded computers called the X-machine. The X-machine has been designed so that program code can be stored compactly as byte code, yet run quickly using dynamic compilation. Our first results are promising – programs typically require only 33% of the code space of an ordinary implementation, but run at 75% of the speed. Future work needs to concentrate on reducing the size of statically-allocated data and the run-time system, and on developing a more detailed understanding of throw-away compilation.

Meertens number is a number with a very peculiar property. I had the idea in 1991, when I was invited to celebrate the occasion of Lambert Meertens' 25 years at the CWI, Amsterdam. Lambert has been a good friend and colleague for a number of years, and rather than bring the usual bottle of Glenlivet as a gift, I decided to give him a number.

Expansion postponement is a tantalisingly simple conjecture about pure type systems which has so far resisted all attempts to prove it for any interesting class of systems. We prove the property for all normalising pure type systems, and discuss the connection with typechecking.