Many modern programming languages support basic generic programming, sufficient to implement type-safe polymorphic containers. Some languages have moved beyond this basic support to a broader, more powerful interpretation of generic programming, and their extensions have proven valuable in practice. This paper reports on a comprehensive comparison of generics in six programming languages: C , Standard ML, Haskell, Eiffel, Java (with its proposed generics extension), and Generic C#. By implementing a substantial example in each of these languages, we identify eight language features that support this broader view of generic programming. We find these features are necessary to avoid awkward designs, poor maintainability, unnecessary run-time checks, and painfully verbose code. As languages increasingly support generics, it is important that language designers understand the features necessary to provide powerful generics and that their absence causes serious difficulties for programmers.

Generic Haskell is an extension of Haskell that supports the construction of generic programs. During the development of several applications, such as an XML editor and compressor, we encountered a number of limitations with the existing (Classic) Generic Haskell language, as implemented by the current Generic Haskell compiler. Specifically,

We show how to write generic programs and proofs in MartinL of type theory. To this end we consider several extensions of MartinL of's logical framework for dependent types. Each extension has a universes of codes (signatures) for inductively defined sets with generic formation, introduction, elimination, and equality rules. These extensions are modeled on Dybjer and Setzer's finitely axiomatized theories of inductive-recursive definitions, which also have a universe of codes for sets, and generic formation, introduction, elimination, and equality rules.

We give two nite axiomatizations of indexed inductive-recursive de nitions in intuitionistic type theory. They extend our previous nite axiomatizations of inductive-recursive de nitions of sets to indexed families of sets and encompass virtually all de nitions of sets which have been used in intuitionistic type theory. The more restricted of the two axiomatization arises naturally by considering indexed inductive-recursive de nitions as initial algebras in slice categories, whereas the other admits a more general and convenient form of an introduction rule.

Software testing is a labor-intensive and hence expensive, yet heavily used technique to control quality. In this paper we introduce Gast, a fully automatic test-tool. Properties from first order logic can be expressed in the system, Gast automatically generates appropriate test-data, evaluates the property for these values, and analyzes the test-results. In this way it becomes easier and cheaper to test software components. The distinguishing property of our system is that the test-data are generated in a systematic and generic way using generic programming techniques. This implies that there is no need for the user to indicate how data should be generated. Moreover, duplicated tests are avoided and for finite domains Gast is able to proof a property by testing it for all possible values. As an important side-e#ect, it also encourages stating formal properties of the software.

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.

Abstract. A generic function is defined by induction on the structure of types. The structure of a data type can be defined in several ways. For example, in PolyP a pattern functor gives the structure of a data type viewed as a fixed point, and in Generic Haskell a structural representation type gives an isomorphic type view of a data type in terms of sums of products. Depending on this generic view on the structure of data types, some generic functions are easier, more difficult, or even impossible to define. Furthermore, the efficiency of some generic functions can be improved by choosing a different view. This paper introduces generic views on data types and shows why they are useful. Furthermore, it shows how generic views have been added to Generic Haskell, an extension of the functional programming language Haskell that supports the construction of generic functions. The separation between inductive definitions on type structure and generic views allows us to combine many approaches to generic programming in a single framework. 1

Massive amounts of useful data are stored and processed in ad hoc formats for which common tools like parsers, printers, query engines and format converters are not readily available. In this paper, we explain the design and implementation of PADS/ML, a new language and system that facilitates the generation of data processing tools for ad hoc formats. The PADS/ML design includes features such as dependent, polymorphic and recursive datatypes, which allow programmers to describe the syntax and semantics of ad hoc data in a concise, easy-to-read notation. The PADS/ML implementation compiles these descriptions into ML structures and functors that include types for parsed data, functions for parsing and printing, and auxiliary support for user-specified, format-dependent and format-independent tool generation.

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.

Abstract. Generic programming allows you to write a function once, and use it many times at different types. Traditionally, generic functions are defined by induction on the structure of types. “Scrap your boilerplate” (SYB) is a radically different approach that dispatches on the structure of values. In previous work, we have shown how to reconcile both approaches using the concept of generic views: many generic functions can be based either on the classical sum-of-products view or on the view that underlies SYB, the so-called ‘spine ’ view. One distinct advantage of the spine view is its generality: it is applicable to a large class of data types, including generalised algebraic data types. Its main weakness roots in the value-orientation: one can only define generic functions that consume data (show) but not ones that produce data (read). Furthermore, functions that abstract over type constructors (map, reduce) are out of reach. In this paper, we show how to overcome both limitations. The main technical contributions are the ‘type spine ’ view and the ‘lifted spine ’ view. 1