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A robust software component fulfills a contract: it expects data satisfying a certain property and promises to return data satisfying another property. The object-oriented community uses the design-by-contract approach extensively. Proposals for language extensions that add contracts to higher-order functional programming have appeared recently. In this paper we propose an embedded domain-specific language for typed, higher-order and first-class contracts, which is both more expressive than previous proposals, and allows for a more informative blame assignment. We take some first steps towards an algebra of contracts, and we show how to define a generic contract combinator for arbitrary algebraic data types. The contract language is implemented as a library in Haskell using the concept of generalised algebraic data types.

We introduce 2-3 finger trees, a functional representation of persistent sequences supporting access to the ends in amortized constant time, and concatenation and splitting in time logarithmic in the size of the smaller piece. Representations achieving these bounds have appeared previously, but 2-3 finger trees are much simpler, as are the operations on them. Further, by defining the split operation in a general form, we obtain a general purpose data structure that can serve as a sequence, priority queue, search tree, priority search queue and more.

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.

This paper describes a new approach to generic functional programming, which allows us to define functions generically for all datatypes expressible in Haskell. A generic function is one that is defined by induction on the structure of types. Typical examples include pretty printers, parsers, and comparison functions.The advanced type system of Haskell presents a real challenge: datatypes may be parameterized not only by types but also by type constructors, type definitions may involve mutual recursion, and recursive calls of type constructors can be arbitrarily nested. We show thatdespite this complexity-a generic function is uniquely defined by giving cases for primitive types and type constructors (such as disjoint unions and Cartesian products). Given this information a generic function can be specialized to arbitrary Haskell datatypes.The key idea of the approach is to model types by terms of the simply typed X-calculus augmented by a family of recursion operators. While conceptually simple, our approach places high demands on the type system: it requires polymorphic recursion, rank-n types, and a strong form of type constructor polymorphism.Finally, we point out connections to Haskell's class system and show that our approach generalizes type classes in some respects.

A generic function is a function that can be instantiated on many data types to obtain data type specific functionality. Examples of generic functions are the functions that can be derived in Haskell, such as show , read , and '=='. The recent years have seen a number of proposals that support the definition of generic functions. Some of the proposals define new languages, some define extensions to existing languages. As a common characteristic none of the proposals can be made to work within Haskell 98: they all require something extra, either a more sophisticated type system or an additional language construct. The purpose of this pearl is to show that one can, in fact, program generically within Haskell 98 obviating to some extent the need for fancy type systems or separate tools. Haskell's type classes are at the heart of this approach: they ensure that generic functions can be defined succinctly and, in particular, that they can be used painlessly.

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