Pure Functional Language Research Articles

Modularity in Meta-Languages

A meta-language for semantics has a high degree of modularity<br />when descriptions of individual language constructs can be formulated independently using it, and do not require reformulation when new constructs are added to the described language. The quest for modularity in semantic meta-languages has been going on for more than two decades. Here, most of the main meta-languages for operational, denotational, and hybrid styles of semantics are compared regarding their modularity. A simple bench-mark is used: describing the semantics of a pure functional language, then extending the described language with references, exceptions, and concurrency constructs. For each style of semantics, at least one of the considered meta-languages appears to provide a high degree of modularity.

On the performance of pure and impure parallel functional programs

This paper reports on the memory performance of parallel scientific algorithms, written in both pure and impure functional styles. The Id programming language is used, since it allows both pure and impure parallel functional programs to be expressed. The non-strict storage model of Id is introduced. The study focuses on two algorithms: the Dongarra Sorensen Eignensolver and the NAS FT three dimensional heat equation solver, based on FFTs. This study verifies the claim that functional languages allow a composition of programs from modules, exploiting the inter- and intra-module parallelism without the need for rewrinting these modules. But it also shows that memory use of pure functional programs can be excessive, and theat impure functional programs can be as memory-efficient as imperative implementations.

When is a functional program not a functional program?

In an impure functional language, there are programs whose behaviour is completely functional (in that they behave extensionally on inputs), but the functions they compute cannot be written in the purely functional fragment of the language. That is, the class of programs with functional behaviour is more expressive than the usual class of pure functional programs. In this paper we introduce this extended class of "functional" programs by means of examples in Standard ML, and explore what they might have to offer to programmers and language implementors.After reviewing some theoretical background, we present some examples of functions of the above kind, and discuss how they may be implemented. We then consider two possible programming applications for these functions: the implementation of a search algorithm, and an algorithm for exact real-number integration. We discuss the advantages and limitations of this style of programming relative to other approaches. We also consider the increased scope for compiler optimizations that these functions would offer.

Monadic Encapsulation of Effects: a Revised Approach

Launchbury and Peyton-Jones came up with an ingenious idea for embedding regions of imperative programming in a pure functional language like Haskell. The key idea was based on a simple modification of Hindley-Milner's type system. Our first contribution is to propose a more natural encapsulation construct exploiting higher-order kinds, which achieves the same encapsulation effect, but avoids the “bogus” type parameter of the original proposal. The second contribution is a stronger type safety result, namely encapsulation of strict state in higher-order lambda-calculus. We formalise the intended implementation as a very simple big-step operational semantics on untyped terms, which captures interesting implementation details not captured by the reduction semantics proposed previously.

Design of an Actor language for implicit parallel programming

Software tools that support implicit parallel programming hold the key to reducing the complexity of parallel programming and realizing more ubiquitous parallel computation. This paper addresses the topic of implicit concurrent object-oriented programming. It presents a new language, SYMPAL, which unlike most existing COOP languages that provide explicit constructs for concurrency control, is based on a unification of object orientation and pure functional programming with the goals of supporting implicit programming and high efficiency in massively concurrent object-oriented programming. Extensive experience with SYMPAL applications on a parallel machine indicates that it achieves these goals.

A practical language and toolkit for high-integrity tools

This paper shows how a safe interface to heap storage, based on garbage collection as provided in implementations of pure functional languages, can be combined with imperative languages. It also shows how expressive notation from functional languages, such as algebraic data types and equational definition of functions with pattern matching, can be adopted. The paper argues that the resulting combination is appropriate for the construction of high-integrity tools, based on an assessment against the same criteria as have been used for assessing the suitability of imperative languages for producing high-integrity software.

Specialization of lazy functional logic programs

Partial evaluation is a method for program specialization based on fold/unfold transformations [8, 25]. Partial evaluation of pure functional programs uses mainly static values of given data to specialize the program [15, 44]. In logic programming, the so-called static/dynamic distinction is hardly present, whereas considerations of determinacy and choice points are far more important for control [12]. We discuss these issues in the context of a (lazy) functional logic language. We formalize a two-phase specialization method for a non-strict, first order, integrated language which makes use of lazy narrowing to specialize the program w.r. t. a goal. The basic algorithm (first phase) is formalized as an instance of the framework for the partial evaluation of functional logic programs of [2, 3], using lazy narrowing. However, the results inherited by [2, 3] mainly regard the termination of the PE method, while the (strong) soundness and completeness results must be restated for the lazy strategy. A post-processing renaming scheme (second phase) is necessary which we describe and illustrate on the well-known matching example. This phase is essential also for other non-lazy narrowing strategies, like innermost narrowing, and our method can be easily extended to these strategies. We show that our method preserves the lazy narrowing semantics and that the inclusion of simplification steps in narrowing derivations can improve control during specialization.

State in Haskell

Some algorithms make critical internal use of updatable state, even though their external specification is purely functional. Based on earlier work on monads, we present a way of securely encapsulating stateful computations that manipulate multiple, named, mutable objects, in the context of a non-strict, purely-functional language. The security of the encapsulation is assured by the type system, using parametricity. The same framework is also used to handle input/output operations (state changes on the external world) and calls to C.

Special Issue on State-of-the-art applications of pure functional programming languages

Special Issue on State-of-the-art applications of pure functional programming languages

A polymorphic library for constructive solid geometry

AbstractSolid modelling using constructive solid geometry (CSG) includes many examples of stylised divide-and-conquer algorithms. We identify the sources of these recurrent patterns and describe a Geometric Evaluation Library (GEL) which captures them as higher-order functions. This library then becomes the basis of developing CSG applications quickly and concisely. GEL is currently implemented as a set of separately compiled modules in the pure functional language Hope+. We evaluate our work in terms of performance and general applicability. We also assess the benefits of the functional paradigm in this domain and the merits of programming with a set of higher-order functions.

A CORRECTNESS PROOF OF PARALLEL SCAN

The parallel scan algorithm plays an important role in parallel programming, but previous explanations of it generally rely on informal methods that fail to establish its correctness. Equational reasoning in a pure functional language provides a formal vehicle for stating the parallel scan algorithm and proving that a parallel architecture executes it correctly. The two key ideas in the proof are (1) a collection of lemmas that show how folds and scans can be decomposed into smaller problems, supporting a divide-and-conquer strategy, and (2) a formal specification of the abstract parallel architecture in the same language used to specify the problem, making it possible to reason formally about how the architecture executes the algorithm.

Experiments with destructive updates in a lazy functional language

The aggregate update problem has received considerable attention since pure functional programming languages were recognised as an interesting research topic. There is extensive literature in this area, which proposes a wide variety of solutions. We have tried to apply some of the proposed solutions to our own applications to see how these solutions work in practice. We have been able to use destructive updates but are not convinced that this could have been achieved without application specific knowledge. In particular, no form of update analysis has been reported that is applicable to non-flat domains in polymorphic languages with higher order functions. It is our belief that a refinement of the monolithic approach towards constructing arrays may be a good alternative to using the incremental approach with destructive updates.

Lazy functional state threads

Some algorithms make critical internal use of updatable state, even though their external specification is purely functional. Based on earlier work on monads, we present a way of securely encapsulating stateful computations that manipulate multiple, named, mutable objects, in the context of a non-strict, purely-functional language. The security of the encapsulation is assured by the type system, using parametricity. Intriguingly, this parametricity requires the provision of a (single) constant with a rank-2 polymorphic type.

Using memorization to achieve polynomial complexity of purely functional executable specifications of non-deterministic top-down parsers

Norvig [1991] has shown that a process with properties that are similar to those of Earley's algorithm can be generated by a simple top-down backtracking parser when augmented by memoization. Unfortunately, Norvig's approach cannot be implemented directly in pure functional programming languages such as Miranda, Haskell, LML, etc, owing to the fact that such languages do not provide any form of mutable object. This restriction is a necessary condition for referential transparency, a property of programs that simplifies reasoning about them and which is widely regarded as one of the main advantages of the pure functional programming style. In this note, we show how Norvig's approach can be adapted and used to achieve polynomial complexity of non-deterministic top-down backtracking parsers that are implemented as executable specifications in pure functional programming languages. The technique that we present uses a slight variation of an approach to implementing memoization in pure functional languages that is described in Field and Harrison [1988].

Special Issue on State-of-Theart Applications of Pure Functional Programming languages

Special Issue on State-of-Theart Applications of Pure Functional Programming languages

A concurrent copying garbage collector for languages that distinguish (im)mutable data

This paper describes the design and implementation of a concurrent compacting garbage collector for languages that distinguish mutable data from immutable data ( e.g. , ML) as well for languages that manipulate only immutable data ( e.g. , pure functional languages such as Haskell). The collector runs on shared-memory parallel computers and requires minimal mutator/collector synchronization. No special hardware or operating system support is required. Our concurrent collector derives from sequential semi-space copying collectors. The collector requires that a heap object includes forwarding pointer in addition to its data fields. An access to an immutable object can be satisfied either by the original or the forwarded copy of the object. A mutable object is always accessed through the forwarded copy, if one exists. Measurements of this collector in a Standard ML compiler on a shared-memory computer indicate that it eliminates perceptible garbage-collection pauses by reclaiming storage in parallel with the computation proper. All observed pause times are less than 20 milliseconds. We describe extensions for the concurrent collection of multiple mutator threads and refinements to our design that can improve its efficiency.

Comprehending monads

Category theorists invented monads in the 1960's to express concisely certain aspects of universal algebra. Functional programmers invented list comprehensions in the 1970's to express concisely certain programs involving lists. This paper shows how list comprehensions may be generalised to an arbitrary monad, and how the resulting programming feature can express concisely in a pure functional language some programs that manipulate state, handle exceptions, parse text, or invoke continuations. A new solution to the old problem of destructive array update is also presented. No knowledge of category theory is assumed.

A domain-theoretic approach to functional and logic programming

AbstractThe integration of functional and logic programming languages has been a topic of great interest in the last decade. Many proposals have been made, yet none is completely satisfactory especially in the context of higher order functions and lazy evaluation. This paper addresses these shortcomings via a new approach: domain theory as a common basis for functional and logic programming. Our integrated language remains essentially within the functional paradigm. The logic programming capability is provided by set abstraction (via Zermelo-Frankel set notation), using the Herbrand universe as a set abstraction generator, but for efficiency reasons our proposed evaluation procedure treats this generator's enumeration parameter as a logical variable. The language is defined in terms of (computable) domain-theoretic constructions and primitives, using the lower (or angelic) powerdomain to model the set abstraction facility. The result is a simple, elegant and purely declarative language that successfully combines the most important features of both pure functional programming and pure Horn logic programming. Referential transparency with respect to the underlying mathematical model is maintained throughout. An implicitly correct operational semantics is obtained by direct execution of the denotational semantic definition, modified suitably to permit logical variables whenever the Herbrand universe is being generated within a set abstraction. Completeness of the operational semantics requires a form of parallel evaluation, rather than the more familiar left-most rule.

Implementation of a “Lisp comprehension” macro

This paper describes a set of Lisp macros that enable the use of "list comprehensions" which are a very powerful notation that provides a very compact expression of common list operations see [2] for a full discussion. List comprehensions have been introduced by David Turner in KRC, where they were called ZF-expressions [7]. They have since been introduced in several other pure functional languages like SASL [8], Miranda 1 [5] and Haskell [3].

Turtle walk through functional language

In this paper implementation and usage of a turtle graphics in (pure) functional programming language - LispKit Lisp is described. With all basic graphics functions available, implementation of a turtle graphics is enabled. Since turtle graphics is second most common way of using graphics, this implementation is a significant improvement of LispKit Lisp abilities. All necessary functions of a turtle graphics are implemented in LispKit Lisp, and they simply should be appended to any program which uses them.