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A polytypic value is one that is defined by induction on the structure of types. In Haskell the type structure is described by the so-called kind system, which distinguishes between manifest types like the type of integers and functions on types like the list type constructor. Previous approaches to polytypic programming were restricted in that they only allowed to parameterize values by types of one fixed kind. In this paper we show how to define values that are indexed by types of arbitrary kinds. It appears that these polytypic values possess types that are indexed by kinds. We present several examples that demonstrate that the additional exibility is useful in practice. One paradigmatic example is the mapping function, which describes the functorial action on arrows. A single polytypic definition yields mapping functions for datatypes of arbitrary kinds including first- and higher-order functors. Polytypic values enjoy polytypic properties. Using kind-indexed logical relations we prove...

Abstract. Refactoring is the process of improving the design of existing programs without changing their functionality. These notes cover refactoring in functional languages, using Haskell as the medium, and introducing the HaRe tool for refactoring in Haskell. 1

Abstract. Generic Haskell is an extension of Haskell that supports the construction of generic programs. These lecture notes describe the basic constructs of Generic Haskell and highlight the underlying theory. Generic programming aims at making programming more effective by making it more general. Generic programs often embody non-traditional kinds of polymorphism. Generic Haskell is an extension of Haskell [38] that supports the construction of generic programs. Generic Haskell adds to Haskell the notion of structural polymorphism, the ability to define a function (or a type) by induction on the structure of types. Such a function is generic in the sense that it works not only for a specific type but for a whole class of types. Typical examples include equality, parsing and pretty printing, serialising, ordering, hashing, and so on. The lecture notes on Generic Haskell are organized into two parts. This first part motivates the need for genericity, describes the basic constructs of Generic Haskell, puts Generic Haskell into perspective, and highlights the underlying theory. The second part entitled “Generic Haskell: applications ” delves deeper into the language discussing three non-trivial applications of Generic Haskell: generic dictionaries, compressing XML documents, and a generic version of the zipper data type. The first part is organized as follows. Section 1 provides some background discussing type systems in general and the type system of Haskell in particular. Furthermore, it motivates the basic constructs of Generic Haskell. Section 2 takes a closer look at generic definitions and shows how to define some popular generic functions. Section 3 highlights the theory underlying Generic Haskell and discusses its implementation. Section 4 concludes. 1

A tension in language design has been between simple semantics on the one hand, and rich possibilities for side-effects, exception handling and so on on the other. The introduction of monads has made a large step towards reconciling these alternatives. First proposed by Moggi as a way of structuring semantic descriptions, they were adopted by Wadler to structure Haskell programs, and now offer a general technique for delimiting the scope of effects, thus reconciling referential transparency and imperative operations within one programming language. Monads have been used to solve long-standing problems such as adding pointers and assignment, inter-language working, and exception handling to Haskell, without compromising its purely functional semantics. The course will introduce monads, effects and related notions, and exemplify their applications in programming (Haskell) and in compilation (MLj). The course will present typed metalanguages for monads and related categorica...

First-order languages based on rewrite rules share many features with functional languages. But one difference is that matching and rewriting can be made much more expressive and powerful by incorporating some built-in equational theories. To provide reasonable programming environments, compilation techniques for such languages based on rewriting have to be designed. This is the topic addressed in this paper. The proposed techniques are independent from the rewriting language and may be useful to build a compiler for any system using rewriting modulo associative and commutative (AC) theories. An algorithm for many-to-one AC matching is presented, that works efficiently for a restricted class of patterns. Other patterns are transformed to fit into this class. A refined data structure, namely compact bipartite graph, allows encoding all matching problems relative to a set of rewrite rules. A few optimisations concerning the construction of the substitution and of the reduced term are described. We also address the problem of non-determinism related to AC rewriting and show how to handle it through the concept of strategies. We explain how an analysis of the determinism can be performed at compile time and we illustrate the benefits of this analysis for the performance of the compiled evaluation process. Then we briefly introduce the ELAN system and its compiler, in order to give some experimental results and comparisons with other languages or rewrite engines.

We present # CIL , a typed #-calculus which serves as the foundation for a typed intermediate language for optimizing compilers for higher-order polymorphic programming languages. The key innovation of # CIL is a novel formulation of intersection and union types and flow labels on both terms and types. These flow types can encode polyvariant control and data flow information within a polymorphically typed program representation. Flow types can guide a compiler in generating customized data representations in a strongly typed setting. Since # CIL enjoys confluence, standardization, and subject reduction properties, it is a valuable tool for reasoning about programs and program transformations.

While interactive multimedia animation is a very compelling medium, few people are able to express themselves in it. There are too many low-level details that have to do not with the desired content—e.g., shapes, appearance and behavior—but rather how to get a computer to present the content. For instance, behaviors like motion and growth are generally gradual, continuous phenomena. Moreover, many such behaviors go on simultaneously. Computers, on the other hand, cannot directly accommodate either of these basic properties, because they do their work in discrete steps rather than continuously, and they only do one thing at a time. Graphics programmers have to spend much of their effort bridging the gap between what an animation is and how to present it on a computer. We propose that this situation can be improved by a change of language, and present Fran, synthesized by complementing an existing declarative host language, Haskell, with an embedded domain-specific vocabulary for modeled animation. As demonstrated in a collection of examples, the resulting animation descriptions are not only relatively easy to write, but also highly composable.

We present a typed intermediate language # CIL for optimizing compilers for function-oriented and polymorphically typed programming languages (e.g., ML). The language # CIL is a typed lambda calculus with product, sum, intersection, and union types as well as function types annotated with flow labels. A novel formulation of intersection and union types supports encoding flow information in the typed program representation. This flow information can direct optimization.

This paper introduces a new approach to optimising array algorithms in functional languages. We are specifically aiming at an efficient implementation of irregular array algorithms that are hard to implement in conventional array languages such as Fortran. We optimise the storage layout of arrays containing complex data structures and reduce the running time of functions operating on these arrays by meansofequationalprogramtransformations. Inparticular, this paper discusses a novel form of combinator loop fusion, whichbyremovingintermediatestructuresoptimisestheuse of the memory hierarchy. We identify a combinator named loopP that provides a general scheme for iterating over an array and that in conjunction with an array constructor replicateP is sufficient to express a wide range of array algorithms. On this basis, we define equational transformation rules that combine traversals of loopP and replicateP as well as sequences of applications of loopP into a single loopP traversal. Our approach naturally generalises to a parallel implementation and includes facilities for optimising load balancing and communication. A prototype implementation based on the rewrite rule pragma of the Glasgow Haskell Compiler is significantly faster than standard Haskell arrays and approaches the speed of hand coded C for simple examples. 1.