Chapter 1. Generic Haskell: Practice and Theory

Abstract

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.

Datatype-Generic Programming

“…Section 2 builds on many discussions with colleagues in and around the Datatype-Generic Programming project at Oxford and Nottingham. My views on origami programming in Section 3 are based on ideas from the Algebra of Programming ('Squiggol') community, and especially the work of: Roland Backhouse and Grant Malcolm [92,7,6]; Richard Bird and Oege de Moor [9,10]; Maarten Fokkinga, Erik Meijer and Ross Paterson [32,101]; Johan Jeuring, Patrik Jansson, Ralf Hinze and Andres Löh [68,69,57,60,91]; and John Hughes [66]. The analogy between design patterns and higher-order datatype-generic programs discussed in Section 4 elaborates on arguments developed in a course presented while on sabbatical at the University of Canterbury in New Zealand in early 2005, and explored further at tutorials at ECOOP [39] and OOPSLA [40] later that year; the contribution of participants at those venues and at less formal presentations of the same ideas is gratefully acknowledged.…”

“…Typical examples of the latter are pretty printers and marshallers; these can be defined once and for all for lists, trees, and so on, in a typesafe way, but not in a way that guarantees any kind of uniformity in behaviour at the instances for different shapes. This approach to datatype genericity has been variously called polytypism [68], structural polymorphism [118] or typecase [131,26], and is the meaning given to 'generic programming' by the Generic Haskell [60,91] team. Whatever the name, functions are defined inductively by case analysis on the structure of datatypes; the different approaches differ slightly in the class of datatypes covered.…”

“…It is a bit tedious to have to provide a new instance of Bifunctor for each new datatype shape; one would of course prefer a single datatype-generic definition. This is the kind of feature for which Generic Haskell [60] is designed, and one can almost achieve the same effect in Haskell [17,58,26]. One might hope that these instance definitions would in fact be inferred, in the languages of tomorrow [97,62].…”

“…This definition could be derived automatically [62], or given polytypically once and for all, assuming some universal representation of datatypes such as sums and products [60] or regular functors [38]:…”

Prototyping Generic Programming in Template Haskell

“…Classic examples are small functions like maps and folds [8], but also more complex functions, like parsers and pretty printers [11] and tools for editing and compressing XML documents [5], can be dened generically. There exist a number of languages for writing generic functional programs [1,3,6,7,10,12,13], each of which has its strengths and weaknesses, and researchers in generic programming are still searching for The Right Way. Implementing a generic programming language is no small task, which makes it cumbersome to experiment with new designs.…”