Abstract. The last decade has seen a number of approaches to datatype-generic programming: PolyP, Functorial ML, ‘Scrap Your Boilerplate’, Generic Haskell, ‘Generics for the Masses’, etc. The approaches vary in sophistication and target audience: some propose full-blown programming languages, some suggest libraries, some can be seen as categorical programming methods. In these lecture notes we compare the various approaches to datatype-generic programming in Haskell. We introduce each approach by means of example, and we evaluate it along different dimensions (expressivity, ease of use, etc). 1

Abstract. Strategic programming is generic programming with the use of strategies. A strategy is a generic data-processing action which can traverse into heterogeneous data structures while mixing uniform and type-specific behaviour. With strategic programming, one gains full control over the application of basic actions, most notably full traversal control. Using a combinator style, traversal schemes can be defined, and actual traversals are obtained by passing the problem-specific ingredients as parameters to suitable schemes. The prime application domain for strategic programming is program transformation and analysis. In this paper, we provide a language-independent definition that generalises over existing incarnations of this idiom in term rewriting, functional programming, and object-oriented programming.

This paper presents a preprocessor which generates code from type de nitions. The preprocessor uses rules to describe the pattern of the produced code. In this way, instances may be derived for type classes. Utility functions for manipulating types, especially records, can also be produced. The set of rules is easily extendible; by adding derivation rules for new type classes, instance derivation is possible for classes de ned outside the prelude. 1

The expressive power of functional programming can be improved by identifying and exploiting the characteristics that distinguish data types from function types. Data types support generic functions for equality, mapping, folding, etc. that do not apply to functions. Such generic functions require case analysis, or pattern-matching, where the branches may have incompatible types, e.g. products or sums. This is handled in the constructor calculus where specialisation of program extensions is governed by constructors for data types. Typing of generic functions employs polymorphism over functors in a functorial type system. The expressive power is greatly increased by allowing the functors to be polymorphic in the number of arguments they take, i.e. in their arities. The resulting system can define and type the fundamental examples above. Some basic properties are established, namely subject reduction, the Church-Rosser property, and the existence of a practical type inference algorithm.

Parallel primitives (skeletons) intend to encourage programmers to build a parallel program from ready-made components for which efficient implementations are known to exist, making the parallelization process easier. However, programmers often suffer from the difficulty to choose a combination of proper parallel primitives so as to construct efficient parallel programs. To overcome this difficulty, we shall propose a new transformation, called diffusion, which can efficiently decompose a recursive definition into several functions such that each function can be described by some parallel primitive. This allows programmers to describe algorithms in a more natural recursive form. We demonstrate our idea with several interesting examples. Our diffusion transformation should be significant not only in development of new parallel algorithms, but also in construction of parallelizing compilers.

Type-directed programming is an important and widely used paradigm in the design of software. With this form of programming, a program may analyze type information to determine its behavior. By analyzing the structure of data, many operations, such as serialization, cloning, structural equality, and iterators, may be defined once, for all types of data. The benefit of type-directed programming is that as software evolves, operations need not be updated---they will automatically adapt to new data forms. Otherwise, each of these operations must be individually redefined for each type of data, forcing programmers to revisit the same program logic many times during a program's lifetime.

The study of inductive and coinductive types (like finite lists and streams, respectively) is usually conducted within the framework of category theory, which to all intents and purposes is a theory of sets and functions between sets. Allegory theory, an extension of category theory due to Freyd, is better suited to modelling relations between sets as opposed to functions between sets. The question thus arises of how to extend the standard categorical results on the existence of final objects in categories (for example, coalgebras and products) to their existence in allegories. The motivation is to streamline current work on generic programming, in which the use of a relational theory rather than a functional theory has proved to be desirable. In this paper, we define the notion of a relational final dialgebra and prove, for an important class of dialgebras, that a relational final dialgebra exists in an allegory if and only if a final dialgebra exists in the underlying category of map...

Abstract Many functions have to be written over and over again for different datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on different datatypes. Examples of such functions are pretty printers, pattern matchers, equality functions, unifiers, rewriting functions, etc. Such functions are called polytypic functions. A polytypic function is a function that is defined by induction on the structure of user-defined datatypes. This thesis introduces polytypic functions, shows how to construct and reason about polytypic functions and describes the implementation of the polytypic programming system PolyP. PolyP extends a functional language (a subset of Haskell) with a construct for writing polytypic functions. The extended language type checks definitions of polytypic functions, and infers the types of all other expressions. Programs in the extended language are translated to Haskell.

This paper examines the use of type-safe linguistic reflection in Haskell, a functional language. Several uses are identified: providing an extensible system of instance derivation; extending derivation beyond type classes and providing a method for polytypic programming. A preprocessor for Haskell is presented that performs compile-time reflection upon type declarations in source code. 1 Introduction This paper examines the use of type-safe linguistic reflection in Haskell, a functional language. Several uses are identified: providing an extensible system of instance derivation; extending derivation beyond type classes and providing a method for polytypic programming. A preprocessor for Haskell is presented that performs compile-time reflection upon type declarations in source code. The rest of the paper is structured as follows. Section 2 examines the existing derivation mechanism of Haskell. The concepts of linguistic reflection are described in Section 3. Section 4 introduc...

: Generic control operators, such as fold, have been introduced in functional programming to increase the power and applicability of data-structure-based transformations. This is achieved by making the structure of the data more explicit in program specifications. We argue that this very important property is one of the original concepts of attribute grammars. In this paper, we present the similarities between the fold formalism and attribute grammars. In particular, we show the equivalence of their respective deforestation methods. Given these results and the fundamental role of deforestation in the concept of structuredirected genericity, first devised for attribute grammars with descriptional composition, we show how the fold operator with its fusion method allow us to transport this concept in the area of functional programming. Key-words: Attribute grammars, static analysis, functional programming, structuredirected programming, program transformation, deforestation, genericity....