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.

A functional programming language can be taught successfully as a first language, but if there is no follow up the students do not appreciate the functional approach. Following discussions concerning this issue at the 1995 FPLE conference (Hartel & Plasmeijer, 1995), we decided to develop such a follow up by writing a book that teaches C to students who can write simple functional programs. This paper summarises the essence of our approach, which is based on program transformation, and presents our experience teaching functional C at the Universities of Southampton and Bristol.

This issue of the Journal of Functional Programming marks a point of transition. Our long-time Chief Editors, Simon Peyton Jones and Philip Wadler, are stepping down. Most of us are aware of the amazing research contributions that Simon and Phil have made to functional programming. But you may not be aware how much these two have put in behind the scenes.

We describe an approach to introducing non-science majors to programming and computation in part by teaching them applets, servlets, and groupware applications. The course uses a dialect of didactic Scheme that is implemented in, and tightly integrated with, Java. The declarative nature of our approach allows non-science majors with no programming background to develop surprisingly complex web applications in about half a semester. This level of programming provides a context for a deeper understanding of computation than is usually feasible in a Computer Literacy course.

You are holding a necklace in your hands, composed of no fewer than thirteen exquisite pearls. The pearls are from all over the world, selected for the finest quality, smoothness and lustre. For your viewing pleasure, the necklace emphasizes variety, stringing pearls of wildly different color, shape and size. Satisfaction is guaranteed.

In this Pearl we illustrate with an example that modern functional programming languages like Haskell can be used effectively for programming search problems, in contrast to the widespread belief that Prolog is much better suited for tasks like these.

In a call-by-value language, representing objects as recursive records requires using an unsafe fixpoint. We design, for a core language including extensible records, a type system which rules out unsafe recursion and still supports the construction of a principal type for each typable term. We illustrate the expressive power of this language with respect to object-oriented programming by introducing a sub-language for “mixin-based” programming.

Twenty years ago Abelson and Sussman's Structure and Interpretation of Computer Programs radically changed the intellectual landscape of introductory computing courses. Instead of teaching some currently fashionable programming language, it employed Scheme and functional programming to teach important ideas. Introductory courses based on the book showed up around the world and made Scheme and functional programming popular. Unfortunately, these courses quickly disappeared again due to shortcomings of the book and the whimsies of Scheme. Worse, the experiment left people with a bad impression of Scheme and functional programming in general. In this pearl, we propose an alternative role for functional programming in the first-year curriculum. Specifically, we present a framework for discussing the first-year curriculum and, based on it, the design rationale for our book and course, dubbed How to Design Programs. The approach emphasizes the systematic design of programs. Experience shows that it works extremely well as a preparation for a course on object-oriented programming.

Static type systems in programming languages allow many errors to be detected at compile time that wouldn't be detected until runtime otherwise. Dependent types are more expressive than the type systems in most programming languages, so languages that have them should allow programmers to detect more errors earlier. In this paper, using the Twelf system, we show that dependent types in the logic programming setting can be used to ensure partial correctness of programs which implement theorem provers, and thus avoid runtime errors in proof search and proof construction. We present two examples: a tactic-style interactive theorem prover and a union-find decision procedure.

The Burrows–Wheeler Transform is a string-to-string transform which, when used as a preprocessing phase in compression, significantly enhances the compression rate. However, it often puzzles people how the inverse transform is carried out. In this pearl we to exploit simple equational reasoning to derive the inverse of the Burrows–Wheeler transform from its specification. We also outline how to derive the inverse of two more general versions of the transform, one proposed by Schindler and the other by Chapin and Tate.

Grammatical Framework (GF) is a special-purpose functional language for defining grammars. It uses a Logical Framework (LF) for a description of abstract syntax, and adds to this a notation for defining concrete syntax. GF grammars themselves are purely declarative, but can be used both for linearizing syntax trees and parsing strings. GF can describe both formal and natural languages. The key notion of this description is a grammatical object, which is not just a string, but a record that contains all information on inflection and inherent grammatical features such as number and gender in natural languages, or precedence in formal languages. Grammatical objects have a type system, which helps to eliminate run-time errors in language processing. In the same way as a LF, GF uses dependent types in abstract syntax to express semantic conditions, such as well-typedness and proof obligations. Multilingual grammars, where one abstract syntax has many parallel concrete syntaxes, can be used for reliable and meaning-preserving translation. They can also be used in authoring systems, where syntax trees are constructed in an interactive editor similar to proof editors based on LF. While being edited, the trees can simultaneously be viewed in different languages. This paper starts with a gradual introduction to GF, going through a sequence of simpler formalisms till the full power is reached. The introduction is followed by a systematic presentation of the GF formalism and outlines of the main algorithms: partial evaluation and parser generation. The paper concludes by brief discussions of the Haskell implementation of GF, existing applications, and related work.

Haskell today provides good support not only for a functional programming style, but also for an imperative one. Elements of imperative programming are needed in applications such as web servers, or to provide efficient implementations of well-known algorithms, such as many graph algorithms. However, one element of imperative programming, the global variable, is surprisingly hard to emulate in Haskell. We discuss several existing methods, none of which is really satisfactory, and finally propose a new approach based on implicit parameters. This approach is simple, safe, and efficient, although it does reveal weaknesses in Haskell's present type system.

Many functional programs with accumulating parameters are contained in the class of macro tree transducers. We present a program transformation technique that can be used to solve the efficiency problems due to creation and consumption of intermediate data structures in compositions of such functions, where classical deforestation techniques fail. To do so, given two macro tree transducers under appropriate restrictions, we construct a single macro tree transducer that implements the composition of the two original ones. The imposed restrictions are more liberal than those in the literature on macro tree transducer composition, thus generalising previous results.

Haskell code is developed for two ways to list the strings of the language defined by a regular expression: directly by set operations and indirectly by converting to and simulating an equivalent automaton. The exercise illustrates techniques for dealing with infinite ordered domains and leads to an effective standard form for nondeterministic finite automata.

Context-sensitive rewriting is a computational restriction of term rewriting used to model non-strict (lazy) evaluation in functional programming. The goal of this paper is the study and development of techniques to analyze the termination behavior of context-sensitive rewrite systems. For that purpose, several methods have been proposed in the literature which transform context-sensitive rewrite systems into ordinary rewrite systems such that termination of the transformed ordinary system implies termination of the original context-sensitive system. In this way, the huge variety of existing techniques for termination analysis of ordinary rewriting can be used for context-sensitive rewriting, too. We analyze the existing transformation techniques for proving termination of context-sensitive rewriting and we suggest two new transformations. Our first method is simple, sound, and more powerful than the previously proposed transformations. However, it is not complete, i.e., there are terminating context-sensitive rewrite systems that are transformed into non-terminating term rewrite systems. The second method that we present in this paper is both sound and complete. All these observations also hold for rewriting modulo associativity and commutativity.

Teacher: Good morning class. Today I would like you to construct a program for finding out how many ways a chessboard can be tiled with dominoes. For those who don't play games, a chessboard is a 8×8 board divided into 64 squares, and a domino is a 2×1 tile which can cover two squares of the board either vertically or horizontally. For example, a 2×2 board can be covered with two dominoes in exactly two ways, with both dominoes horizontal or both vertical.

Proof systems for expressive type theories provide a foundation for the verification and synthesis of programs. But despite their successful application to numerous programming problems there remains an issue with scalability. Are proof environments capable of reasoning about large software systems? Can the support they offer be useful in practice? In this article we answer this question by showing how the NUPRL proof development system and its rich type theory have contributed to the design of reliable, high-performance networks by synthesizing optimized code for application configurations of the ENSEMBLE group communication toolkit. We present a type-theoretical semantics of OCAML, the implementation language of ENSEMBLE, and tools for automatically importing system code into the NUPRL system. We describe reasoning strategies for generating verifiably correct fast-path optimizations of application configurations that substantially reduce end-to-end latency in ENSEMBLE. We also discuss briefly how to use NUPRL for checking configurations against specifications and for the design of reliable adaptive network protocols.

Compilers for ML and Haskell typically go to a good deal of trouble to arrange that multiple arguments can be passed efficiently to a procedure. For some reason, less effort seems to be invested in ensuring that multiple results can also be returned efficiently. In the context of the lazy functional language Haskell, we describe an analysis, Constructed Product Result (CPR) analysis, that determines when a function can profitably return multiple results in registers. The analysis is based only on a function's definition, and not on its uses (so separate compilation is easily supported) and the results of the analysis can be expressed by a transformation of the function definition alone. We discuss a variety of design issues that were addressed in our implementation, and give measurements of the effectiveness of our approach across a substantial benchmark set. Overall, the price/performance ratio is good: the benefits are modest in general (though occasionally dramatic), but the costs in both complexity and compile time, are low.

Pattern matching has proved an extremely powerful and durable notion in functional programming. This paper contributes a new programming notation for type theory which elaborates the notion in various ways. First, as is by now quite well-known in the type theory community, definition by pattern matching becomes a more discriminating tool in the presence of dependent types, since it refines the explanation of types as well as values. This becomes all the more true in the presence of the rich class of datatypes known as inductive families (Dybjer, 1991). Secondly, as proposed by Peyton Jones (1997) for Haskell, and independently rediscovered by us, subsidiary case analyses on the results of intermediate computations, which commonly take place on the right-hand side of definitions by pattern matching, should rather be handled on the left. In simply-typed languages, this subsumes the trivial case of Boolean guards; in our setting it becomes yet more powerful. Thirdly, elementary pattern matching decompositions have a well-defined interface given by a dependent type; they correspond to the statement of an induction principle for the datatype. More general, user-definable decompositions may be defined which also have types of the same general form. Elementary pattern matching may therefore be recast in abstract form, with a semantics given by translation. Such abstract decompositions of data generalize Wadler's (1987) notion of ‘view’. The programmer wishing to introduce a new view of a type $\mathit{T}$, and exploit it directly in pattern matching, may do so via a standard programming idiom. The type theorist, looking through the Curry–Howard lens, may see this as proving a theorem, one which establishes the validity of a new induction principle for $\mathit{T}$. We develop enough syntax and semantics to account for this high-level style of programming in dependent type theory. We close with the development of a typechecker for the simply-typed lambda calculus, which furnishes a view of raw terms as either being well-typed, or containing an error. The implementation of this view is ipso facto a proof that typechecking is decidable.

We describe the FC++ library, a rich library supporting functional programming in C++. Prior approaches to encoding higher order functions in C++ have suffered with respect to polymorphic functions from either lack of expressiveness or high complexity. In contrast, FC++ offers full and concise support for higher-order polymorphic functions through a novel use of C++ type inference. The FC++ library has a number of useful features, including a generalized mechanism to implement currying in C++, a “lazy list” class which enables the creation of “infinite data structures”, a subtype polymorphism facility, and an extensive library of useful functions, including a large part of the Haskell Standard Prelude. The FC++ library has an efficient implementation. We show the results of a number of experiments which demonstrate the value of optimizations we have implemented. These optimizations have improved the run-time performance by about an order of magnitude for some benchmark programs that make heavy use of FC++ lazy lists. We also make an informal performance comparison with similar programs written in Haskell.