From the type of a polymorphic function we can derive a theorem that it satisfies. Every function of the same type satisfies the same theorem. This provides a free source of useful theorems, courtesy of Reynolds' abstraction theorem for the polymorphic lambda calculus.

We study Girard's Linear Logic from the point of view of giving a concrete computational interpretation of the logic, based on the Curry-Howard isomorphism. In the case of Intuitionistic Linear Logic, this leads to a refinement of the lambda calculus, giving finer control over order of evaluation and storage allocation, while maintaining the logical content of programs as proofs, and computation as cut-elimination.

This paper generalizes many-sorted algebra (hereafter, MSA) to order-sorted algebra (hereafter, OSA) by allowing a partial ordering relation on the set of sorts. This supports abstract data types with multiple inheritance (in roughly the sense of object-oriented programming), several forms of polymorphism and overloading, partial operations (as total on equationally defined subsorts), exception handling, and an operational semantics based on term rewriting. We give the basic algebraic constructions for OSA, including quotient, image, product and term algebra, and we prove their basic properties, including Quotient, Homomorphism, and Initiality Theorems. The paper's major mathematical results include a notion of OSA deduction, a Completeness Theorem for it, and an OSA Birkhoff Variety Theorem. We also develop conditional OSA, including Initiality, Completeness, and McKinsey-Malcev Quasivariety Theorems, and we reduce OSA to (conditional) MSA, which allows lifting many known MSA results to OSA. Retracts, which intuitively are left inverses to subsort inclusions, provide relatively inexpensive run-time error handling. We show that it is safe to add retracts to any OSA signature, in the sense that it gives rise to a conservative extension. A final section compares and contrasts many different approaches to OSA. This paper also includes several examples demonstrating the flexibility and applicability of OSA, including some standard benchmarks like STACK and LIST, as well as a much more substantial example, the number hierarchy from the naturals up to the quaternions.

Notions of program dependency arise in many settings: security, partial evaluation, program slicing, and call-tracking. We argue that there is a central notion of dependency common to these settings that can be captured within a single calculus, the Dependency Core Calculus (DCC), a small extension of Moggi's computational lambda calculus. To establish this thesis, we translate typed calculi for secure information flow, binding-time analysis, slicing, and call-tracking into DCC. The translations help clarify aspects of the source calculi. We also define a semantic model for DCC and use it to give simple proofs of noninterference results for each case.

The Spineless Tagless G-machine is an abstract machine designed to support nonstrict higher-order functional languages. This presentation of the machine falls into three parts. Firstly, we give a general discussion of the design issues involved in implementing non-strict functional languages. Next, we present the STG language, an austere but recognisably-functional language, which as well as a denotational meaning has a well-defined operational semantics. The STG language is the "abstract machine code" for the Spineless Tagless G-machine. Lastly, we discuss the mapping of the STG language onto stock hardware. The success of an abstract machine model depends largely on how efficient this mapping can be made, though this topic is often relegated to a short section. Instead, we give a detailed discussion of the design issues and the choices we have made. Our principal target is the C language, treating the C compiler as a portable assembler. Version 2.5 of this paper (minus appendix) appe...

Lists are often used as "glue" to connect separate parts of a program together. We propose an automatic technique for improving the efficiency of such programs, by removing many of these intermediate lists, based on a single, simple, local transformation. We have implemented the method in the Glasgow Haskell compiler.

Programming parallel machines is notoriously difficult. Factors contributing to this difficulty include the complexity of concurrency, the effect of resource allocation on performance and the current diversity of parallel machine models. The net result is that effective portability, which depends crucially on the predictability of performance, has been lost. Functional programming languages have been put forward as solutions to these problems, because of the availability of implicit parallelism. However, performance will be generally poor unless the issue of resource allocation is addressed explicitly, diminishing the advantage of using a functional language in the first place. We present a methodology which is a compromise between the extremes of explicit imperative programming and implicit functional programming. We use a repertoire of higher-order parallel forms, skeletons, as the basic building blocks for parallel implementations and provide program transformations wh...

We give an overview of the Glasgow Haskell compiler, focusing especially on way in which we have been able to exploit the rich theory of functional languages to give very practical improvements in the compiler. The compiler is portable, modular, generates good code, and is freely available. 1 Introduction Computer Science is both a scientific and an engineering discipline. As a scientific discipline, it seeks to establish generic principles and theories that can be used to explain or underpin a variety of particular applications. As an engineering discipline, it constructs substantial artefacts of software and hardware, sees where they fail and where they work, and develops new theory to underpin areas that are inadequately supported. (Milner [1991] eloquently argues for this dual approach in Computer Science. ) Functional programming is a research area that offers an unusually close interplay between these two aspects (Peyton Jones [1992b]). Theory often has immediate practical appl...

The code compiled from a non-strict functional program usually manipulates heap-allocated boxed numbers. Compilers for such languages often go to considerable trouble to optimise operations on boxed numbers into simpler operations on their unboxed forms. These optimisations are usually handled in an ad hoc manner in the code generator, because earlier phases of the compiler have no way to talk about unboxed values. We present a new approach, which makes unboxed values into (nearly) first-class citizens. The language, including its type system, is extended to handle unboxed values. The optimisation of boxing and unboxing operations can now be reinterpreted as a set of correctness-preserving program transformations. Indeed the particular transformations required are ones which a compiler would want to implement anyway. The compiler becomes both simpler and more modular. Two other benefits accrue. Firstly, the results of strictness analysis can be exploited within the same uniform transformational framework. Secondly, new algebraic data types with unboxed components can be declared. Values of these types can be manipulated much more efficiently than the corresponding boxed versions. Both a static and a dynamic semantics are given for the augmented language. The denotational dynamic semantics is notable for its use of unpointed domains.

The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of Wright Laboratory or the U. S. Government. Keywords: Data-parallel, parallel algorithms, supercomputers, nested parallelism, This report describes Nesl, a strongly-typed, applicative, data-parallel language. Nesl is intended to be used as a portable interface for programming a variety of parallel and vector computers, and as a basis for teaching parallel algorithms. Parallelism is supplied through a simple set of data-parallel constructs based on sequences, including a mechanism for applying any function over the elements of a sequence in parallel and a rich set of parallel functions that manipulate sequences. Nesl fully supports nested sequences and nested parallelism—the ability to take a parallel function and apply it over multiple instances in parallel. Nested parallelism is important for implementing algorithms with irregular nested loops (where the inner loop lengths depend on the outer iteration) and for divide-and-conquer algorithms. Nesl also provides a performance model for calculating the asymptotic performance of a program on