This paper is an exploration of the parallel graph reduction approach to parallel functional programming, illustrated by a particular example: pipelined, dynamically-scheduled implementation of search, updates and read-modify-write transactions on an in-store binary search tree. We use program transformation, execution-driven simulation and analytical modelling to expose the maximum potential parallelism, the minimum communication and synchronisation overheads, and to control the overall space requirement. We begin with a lazy functional program specifying a series of transactions on a binary tree, each involving several searches and updates, in a side-effect-free fashion. Transformation of the source code produces a formulation of the program with greater locality and larger grain size than can be achieved using naive parallelization methods, and we show that, with care, these tasks can be scheduled effectively. Even with a workload using random keys, significant spatial locality is found, and we evaluate a modified cache coherency protocol which avoids false sharing so that large cache lines can be used to minimise the number of messages required. As expected with a pipeline, the application should reach a steady state as soon as the first transaction is completed. However, if the network latency is too large, the rate of completion lags behind the rate at which work is admitted, and internal queues grow without bound. We determine the conditions under which this occurs, and show how it can be avoided while maximising speedup.

From the points of view of programming pragmatics, rewriting and operational semantics, the syntactic construct used for exception handling in ML-like programming languages, and in much theoretical work on exceptions, has subtly undesirable features. We propose and discuss a more well-behaved construct.

Here are two puzzles for you to solve. First, consider the binary tree in figure 1. Take a pencil (I am assuming that this is your personal copy of JFP!) and mark some of the nodes in such a way that the sum of the values of marked nodes is as large as possible. The catch is that you cannot mark all the nodes: if you mark a node, then you are not allowed to mark its parent. Equivalently, no two marked nodes can be contiguous in the tree.

The second puzzle is similar though both the datatype and constraint are different. Consider the rose tree of figure 2 (a rose tree is a tree with arbitrary branching structure). Mark some of the nodes so that all marked nodes are now contiguous in the tree. For example, if you mark the root value 4 and the leaf value 1, then you must also mark the values 5 and −3 along the path from 4 to 1. Again the idea is to maximise the sum of the marked nodes. Of course, if all values were nonnegative, the best solution would be to mark all nodes. But they aren't and the maximum sum is obtained only by a judicious choice of marking. Answers to both puzzles are given at the end of the paper.

The Maximum Marking Problem (MMP) is the problem of marking the entries of some given data structure in such a way that a given constraint is satisfied and the sum of the values associated with marked entries is as large as possible. By the end of this pearl, you will be convinced that there is a linear-time solution for both the puzzles described above.

Chris Okasaki showed how to implement red-black trees in a functional programming language. Ralf Hinze incorporated even the invariants of such data structures into their types, using higher-order nested datatypes. We show how one can achieve something very similar without the usual performance penalty of such types, by combining the features of nested datatypes, phantom types and existential type variables.

Modern programming languages rely on advanced type systems that detect errors at compile-time. While the benefits of type systems have long been recognized, there are some areas where the standard systems in programming languages are not expressive enough. Language designers usually trade expressiveness for decidability of the type system. Some interesting programs will always be rejected (despite their semantical soundness) or be assigned uninformative types.

There are several remedies to this situation. Dependent type systems, which allow the formation of types that explicitly depend on other types or values, are one of the most promising approaches. These systems are well-investigated from a theoretical point of view by logicians and type theorists. For example, dependent types are used in proof assistants to implement various logics and there are sophisticated proof editors for developing programs in a dependently typed language.

To the present day, the impact of these developments on practical programming has been small, partially because of the level of sophistication of these systems and of their type checkers. Only recently, there have been efforts to integrate dependent systems into intermediate languages in compilers and programming languages. Additional uses have been identified in high-profile applications such as mobile code security, where terms of a dependently typed lambda calculus to encode safety proofs.

A special issue of the Journal of Functional Programming will be devoted to the interplay between dependent type theory and programming practice. We welcome technical contributions in the field, as well as position papers that:

[bull ] make researchers in programming languages aware of new developments and research directions on the theory side;

[bull ] point out to theorists practical uses of advanced type systems and urge them to address theoretical problems arising in emerging applications.

Authors who are concerned about the appropriateness of a topic are welcome to contact the guest editors. Manuscripts should be unpublished works and not submitted elsewhere. Revised and enhanced versions of papers published in conference proceedings that have not appeared in archival journals are eligible for submission. All submissions will be reviewed according to the usual standards of scholarship and originality.

Submissions should be sent to Gilles Barthe ([email protected]), with a copy to Nasreen Ahmad ([email protected]). Submitted articles should be sent in postscript format, preferably gzipped and uuencoded. In addition, please send, as plain text, title, abstract and contact information.

The submission deadline is December 1st, 2001.