By allowing the programmer to write code that can generate code at run-time, meta-programming offers a powerful approach to program construction. For instance, meta-programming can often be employed to enhance program efficiency and facilitate the construction of generic programs. However, meta-programming, especially in an untyped setting, is notoriously error-prone. In this paper, we aim at making meta-programming less error-prone by providing a type system to facilitate the construction of correct meta-programs. We first introduce some code constructors for constructing typeful code representation in which program variables are represented in terms of deBruijn indexes, and then formally demonstrate how such typeful code representation can be used to support meta-programming. With our approach, a particular interesting feature is that code becomes first-class values, which can be inspected as well as executed at run-time. The main contribution of the paper lies in the recognition and then the formalization of a novel approach to typed meta-programming that is practical, general and flexible.

Engineering high-performance parallel programs is hard: not only must a correct, efficient and inherently-parallel algorithm be developed, but the computations must be effectively and efficiently coordinated across multiple processors. It has long been recognised that ideas and approaches drawn from functional programming may be particularly applicable to parallel and distributed computing (e.g. Wegner 1971). There are several reasons for this suitability. Concurrent stateless computations are much easier to coordinate, high-level coordination abstractions reduce programming effort, and declarative notations are amenable to reasoning, i.e. to optimising transformations, derivation and performance analysis.

Concepts and techniques from modern programming languages have much to offer to the security of computer systems. This special issue is devoted to research on those concepts and techniques. Over 60 active researchers working in this area were invited to contribute. In particular, a number of the participants of the Dagstuhl Seminar on Language-Based Security were encouraged to submit. Submitted articles were reviewed by 3–4 referees. As a result of the reviewing process, five articles were selected for inclusion in the special issue.

A compiler structured as a small number of monolithic passes is difficult to understand and difficult to maintain. The steep learning curve is daunting, and even experienced developers find that modifying existing passes is difficult and often introduces subtle and tenacious bugs. These problems are especially frustrating when the developer is a student in a compiler class. An attractive alternative is to structure a compiler as a collection of many fine-grained passes, each of which performs a single task. This structure aligns the implementation of a compiler with its logical organization, simplifying development, testing, and debugging. This paper describes the methodology and tools comprising a framework for constructing such compilers.

This pearl explains Church numerals, twice. The first explanation links Church numerals to Peano numerals via the well-known encoding of data types in the polymorphic λ-calculus. This view suggests that Church numerals are folds in disguise. The second explanation, which is more elaborate, but also more insightful, derives Church numerals from first principles, that is, from an algebraic specification of addition and multiplication. Additionally, we illustrate the use of the parametricity theorem by proving exponentiation as reverse application correct.

This is a tutorial on using type-indexed embedding/projection pairs when writing interpreters in statically-typed functional languages. The method allows (higher-order) values in the interpreting language to be embedded in the interpreted language and values from the interpreted language may be projected back into the interpreting one. This is particularly useful when adding command-line interfaces or scripting languages to applications written in functional languages. We first describe the basic idea and show how it may be extended to languages with recursive types and applied to elementary meta-programming. We then show how the method combines with Filinski's continuation-based monadic reflection operations to define an [lsquor]extensional[rsquor] version of the call-by-value monadic translation and hence to allow values to be mapped bidirectionally between the levels of an interpreter for a functional language parameterized by an arbitrary monad. Finally, we show how SML functions may be embedded into, and projected from, an interpreter for an asynchronous $\pi$-calculus via an ‘extensional’ variant of a standard translation from $\lambda$ into $\pi$.

The functional programming language Haskell and its type system are used to define and analyse the nature of some problems and tools in machine learning and data mining. Data types and type-classes for statistical models are developed that allow models to be manipulated in a precise, type-safe and flexible way. The statistical models considered include probability distributions, mixture models, function-models, time-series, and classification- and function-model-trees. The aim is to improve ways of designing and programming with models, not only of applying them.

This pearl gives a discount proof of the folklore theorem that every strongly $\beta$-normalizing $\lambda$-term is typable with an intersection type. (We consider typings that do not use the empty intersection $\omega$ which can type any term.) The proof uses the perpetual reduction strategy which finds a longest path. This is a simplification over existing proofs that consider any longest reduction path. The choice of reduction strategy avoids the need for weakening or strengthening of type derivations. The proof becomes a bargain because it works for more intersection type systems, while being simpler than existing proofs.

Classical application domains of parallel computing are dominated by processing large arrays of numerical data. Whereas most functional languages focus on lists and trees rather than on arrays, SAC is tailor-made in design and in implementation for efficient high-level array processing. Advanced compiler optimizations yield performance levels that are often competitive with low-level imperative implementations. Based on SAC, we develop compilation techniques and runtime system support for the compiler-directed parallel execution of high-level functional array processing code on shared memory architectures. Competitive sequential performance gives us the opportunity to exploit the conceptual advantages of the functional paradigm for achieving real performance gains with respect to existing imperative implementations, not only in comparison with uniprocessor runtimes. While the design of SAC facilitates parallelization, the particular challenge of high sequential performance is that realization of satisfying speedups through parallelization becomes substantially more difficult. We present an initial compilation scheme and multi-threaded execution model, which we step-wise refine to reduce organizational overhead and to improve parallel performance. We close with a detailed analysis of the impact of certain design decisions on runtime performance, based on a series of experiments.

Haskell is a functional programming language whose evaluation is lazy by default. However, Haskell also provides pattern matching facilities which add a modicum of eagerness to its otherwise lazy default evaluation. This mixed or “non-strict” semantics can be quite difficult to reason with. This paper introduces a programming logic, P-logic, which neatly formalizes the mixed evaluation in Haskell pattern-matching as a logic, thereby simplifying the task of specifying and verifying Haskell programs. In p-logic, aspects of demand are reflected or represented within both the predicate language and its model theory, allowing for expressive and comprehensible program verification.

Access control mechanisms are often used with the intent of enforcing confidentiality and integrity policies, but few rigorous connections have been made between information flow and runtime access control. The Java virtual machine and the .NET runtime system provide a dynamic access control mechanism in which permissions are granted to program units and a runtime mechanism checks permissions of code in the calling chain. We investigate a design pattern by which this mechanism can be used to achieve confidentiality and integrity goals: a single interface serves callers of more than one security level and dynamic access control prevents release of high information to low callers. Programs fitting this pattern would be rejected by previous flow analyses. We give a static analysis that admits them, using permission-dependent security types. The analysis is given for a class-based object-oriented language with features including inheritance, dynamic binding, dynamically allocated mutable objects, type casts and recursive types. The analysis is shown to ensure a noninterference property formalizing confidentiality and integrity.

We consider a propositional spatial logic for finite trees. The logic includes $\A \Par \B$ (tree composition), $\A \,{\Guarantee}\, \B$ (the implication induced by composition), and $\Zero$ (the unit of composition). We show that the satisfaction and validity problems are equivalent, and decidable. The crux of the argument is devising a finite enumeration of trees to consider when deciding whether a spatial implication is satisfied. We introduce a sequent calculus for the logic, and show it to be sound and complete with respect to an interpretation in terms of satisfaction. Finally, we describe a complete proof procedure for the sequent calculus. We envisage applications in the area of logic-based type systems for semistructured data. We describe a small programming language based on this idea.

In this paper, we present some experience of using the concurrent functional language Erlang to implement a distributed video-on-demand server. For performance reasons, the server is deployed in a cheap cluster made from off-the-shelf components. The demanding system requirements, in addition to the complex and ever-changing domain, suggested a highly flexible and scalable architecture as well as a quite sophisticated control software. Functional programming played a key role in the development, allowing us to identify functional abstractions throughout the system. Using these building blocks, large configurations can be defined using functional and process composition, reducing the effort spent on adapting the system to the frequent changes in requirements. The server evolved from a prototype that was the result of a project supported by a regional cable company, and it is currently being used to provide services for real-world users. Despite our initial concerns, efficiency has not been a major issue.

Staging is a programming technique for dividing the computation in order to exploit the early availability of some arguments. In the early stages the program uses the available arguments to generate, at run time, the code for the late stages. A type system for staging should ensure that only well-typed expressions are generated, and that only expressions with no free variables are permitted for evaluation. In this paper, we present a calculus for staged computation in which code from the late stages is composed by splicing smaller code fragments into a larger context, possibly incurring capture of free variables. The type system ensures safety by tracking the names of free variables for each code fragment. The type system is based on the necessity operator □ from constructive modal logic, which we index with a set of names C. Our type □CA classifies expressions of type A that belong to the late stage, and whose free names are in the set C.

We introduce a typed λ-calculus which allows the use of exceptions in the ML style. It is an extension of the system $AF_2$ of Krivine & Leivant (Krivine, 1990; Leivant, 1983). We show its main properties: confluence, strong normalization and weak subject reduction. The system satisfies the “the proof as program” paradigm as in $AF_2$. Moreover, the underlined logic of our system is intuitionistic logic.

Countdown is the name of a game in which one is given a list of source numbers and a target number, with the aim of building an arithmetic expression out of the source numbers to get as close to the target as possible. Starting with a relational specification we derive a number of functional programs for solving Countdown. These programs are obtained by exploiting the properties of the folds and unfolds of various data types, a style of programming Gibbons has aptly called origami programming. Countdown is attractive as a case study in origami programming both as an illustration of how different algorithms can emerge from a single specification, as well as the space and time trade-offs that have to be taken into account in comparing functional programs.

Stack inspection is a mechanism for programming secure applications in the presence of code from various protection domains. Run-time checks of the call stack allow a method to obtain information about the code that (directly or indirectly) invoked it in order to make access control decisions. This mechanism is part of the security architecture of Java and the .NET Common Language Runtime. A central problem with stack inspection is to determine to what extent the local checks inserted into the code are sufficient to guarantee that a global security property is enforced. A further problem is how such verification can be carried out in an incremental fashion. Incremental analysis is important for avoiding re-analysis of library code every time it is used, and permits the library developer to reason about the code without knowing its context of deployment. We propose a technique for inferring interfaces for stack-inspecting libraries in the form of secure calling context for methods. By a secure calling context we mean a pre-condition on the call stack sufficient for guaranteeing that execution of the method will not violate a given global property. The technique is a constraint-based static program analysis implemented via fixed point iteration over an abstract domain of linear temporal logic properties.

We present the Zen toolkit for morphological and phonological processing of natural languages. This toolkit is presented in literate programming style, in the Pidgin ML subset of the Objective Caml functional programming language. This toolkit is based on a systematic representation of finite state automata and transducers as decorated lexical trees. All operations on the state space data structures use the zipper technology, and a uniform sharing functor permits systematic maximum sharing as dags. A particular case of lexical maps is specially convenient for building invertible morphological operations such as inflected forms dictionaries, using a notion of differential word. As a particular application, we describe a general method for tagging a natural language text given as a phoneme stream by analysing possible euphonic liaisons between words belonging to a lexicon of inflected forms. The method uses the toolkit methodology by constructing a non-deterministic transducer, implementing rational rewrite rules, by mechanical decoration of a trie representation of the lexicon index. The algorithm is linear in the size of the lexicon. A coroutine interpreter is given, and its correctness and completeness are formally proved. An application to the segmentation of Sanskrit by sandhi analysis is demonstrated.

Algorithmic skeletons are abstractions from common patterns of parallel activity which offer a high degree of reusability for developers of parallel algorithms. Their close association with higher order functions (HOFs) makes functional languages, with their strong transformational properties, excellent vehicles for skeleton-based parallel program development. However, using HOFs in this way raises substantial problems of identification of useful HOFs within a given application and of resource allocation on target architectures. We present the design and implementation of a parallelising compiler for Standard ML which exploits parallelism in the familiar $map$ and $fold$ HOFs through skeletons for processor farms and processor trees, respectively. The compiler extracts parallelism automatically and is target architecture independant. HOF execution within a functional language can be nested in the sense that one HOF may be passed and evaluated during the execution of another HOF. We are able to exploit this by nesting our parallel skeletons in a processor topology which matches the structure of the Standard ML source. However, where HOF arguments result from partially applied functions, free variable bindings must be identified and communicated through the corresponding skeleton hierarchy to where those arguments are actually applied. We describe the analysis leading from input Standard ML through HOF instantiation and backend compilation to an executable parallel program. We also present an overview of the runtime system and the execution model. Finally, we give parallel performance figures for several example programs, of varying computational loads, on the Linux-based Beowulf, IBM SP/2, Fujitsu AP3000 and Sun StarCat 15000 MIMD parallel machines. These demonstrate good cross-platform consistency of parallel code behaviour.

Functional programming fits well with the use of descriptive markup in HTML and XML. There is also a good fit between S-expressions in Lisp and the XML data set. These similarities are exploited in LAML which is a software package for Scheme. LAML supports exact mirrors of the three variants of XHTML 1.0, SVG 1.0, and a number of more specialized XML languages. The mirrors are all synthesized from document type definitions (DTDs). Each element in a mirror is represented by a named function in Scheme. The mirror functions validate the XML document while it is generated. The validation is based on finite state automata automatically derived from the DTD.