QUickCheck is a tool which aids the Haskell programmer in formulating and testing properties of programs. Properties are described as Haskell functions, and can be automatically tested on random input, but it is also possible to define custom test data generators. We present a number of case studies, in which the tool was successfully used, and also point out some pitfalls to avoid. Random testing is especially suitable for functional programs because properties can be stated at a fine grain. When a function is built from separately tested components, then random testing suffices to obtain good coverage of the definition under test.

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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...

The recent years have seen a number of proposals for extending statically typed languages by dynamics or generics. Most proposals --- if not all --- require significant extensions to the underlying language. In this paper we show that this need not be the case. We propose a particularly lightweight extension that supports both dynamics and generics. Furthermore, the two features are smoothly integrated: dynamic values, for instance, can be passed to generic functions. Our proposal makes do with a standard Hindley-Milner type system augmented by existential types. Building upon these ideas we have implemented a small library that is readily usable both with Hugs and with the Glasgow Haskell compiler.

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.

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.

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Abstract. The paper “Scrap your boilerplate ” (SYB) introduces a combinator library for generic programming that offers generic traversals and queries. Classically, support for generic programming consists of two essential ingredients: a way to write (type-)overloaded functions, and independently, a way to access the structure of data types. SYB seems to lack the second. As a consequence, it is difficult to compare with other approaches such as PolyP or Generic Haskell. In this paper we reveal the structural view that SYB builds upon. This allows us to define the combinators as generic functions in the classical sense. We explain the SYB approach in this changed setting from ground up, and use the understanding gained to relate it to other generic programming approaches. Furthermore, we show that the SYB view is applicable to a very large class of data types, including generalized algebraic data types. 1

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.