A polytypic function is a function that can be instantiated on many data types to obtain data type specific functionality. Examples of polytypic functions are the functions that can be derived in Haskell, such as show , read , and ` '. More advanced examples are functions for digital searching, pattern matching, unification, rewriting, and structure editing. For each of these problems, we not only have to define polytypic functionality, but also a type-indexed data type: a data type that is constructed in a generic way from an argument data type. For example, in the case of digital searching we have to define a search tree type by induction on the structure of the type of search keys. This paper shows how to define type-indexed data types, discusses several examples of type-indexed data types, and shows how to specialize type-indexed data types. The approach has been implemented in Generic Haskell, a generic programming extension of the functional language Haskell.

Generic Haskell is an extension of Haskell that supports the construction of generic programs. These lecture notes discuss three advanced generic programming applications: generic dictionaries, compressing XML documents, and the zipper: a data structure used to represent a tree together with a subtree that is the focus of attention, where that focus may move left, right, up or down the tree. When describing and implementing these examples, we will encounter some advanced features of Generic Haskell, such as type-indexed data types, dependencies between and generic abstractions of generic functions, adjusting a generic function using a default case, and generic functions with a special case for a particular constructor.

Several generic programs for converting values from regular datatypes to some other format, together with their corresponding inverses, are constructed. Among the formats considered are shape plus contents, compact bit streams and pretty printed strings. The different data conversion programs are constructed using John Hughes' arrow combinators along with a proof that printing (from a regular datatype to another format) followed by parsing (from that format back to the regular datatype) is the identity. The printers and parsers are described in PolyP, a polytypic extension of the functional language Haskell.

A polytypic (or generic) program captures a common pattern of computation over dierent datatypes by abstracting over the structure of the datatype. Examples of algorithms that can be dened polytypically are equality tests, mapping functions and pretty printers. A commonly used technique to implement polytypic programming is specialization, where a specialized version of a polytypic function is generated for every datatype it is used at. In this paper we describe an alternative technique that allows polytypic functions to be dened using Haskell's class system (extended with multi-parameter type classes and functional dependencies). This technique brings the power of polytypic programming inside Haskell allowing us to dene a Haskell library of polytypic functions. It also increases our exibility, reducing the dependency on a polytypic language compiler.

Functional generic programming extends functional programming with the ability to parameterize functions on the structure of a datatype. This allows a programmer to implement certain algorithms once and for all, instead of re-implementing them for each datatype they apply to. Examples of such algorithms include simple traversals and pretty printing as well as more complex XML processing tools. The topic of this dissertation is the implementation of functional generic programming. More precisely we address two particular questions: how can we reduce the amount of work required to implement generic programming languages, and how can we embed generic programming in an existing functional language. To answer the rst question we show how meta-programming can be used to quickly prototype generic programming languages. In particular we describe prototype implementations of two generic programming languages: PolyP [15] and Generic Haskell [4]. The prototypes are extremely light-weight while still retaining most of the functionality of the original languages. One thing that is missing, though, is a way of adding type systems to the prototypes. In