Generic programming is about making programs more adaptable by making them more general. Generic programs often embody non-traditional kinds of polymorphism; ordinary programs are obtained from them by suitably instantiating their parameters. In contrast to normal programs, the parameters of a generic program are often quite rich in structure; for example, they may be other programs, types or type constructors, classes, concepts, or even programming paradigms.

The aim of our work is to be able to do fully formal, machine-verified proofs over Generic Haskell-style polytypic programs. In order to achieve this goal, we embed polytypic programming in the proof assistant Coq and provide an infrastructure for polytypic proofs. Polytypic functions are reified within Coq as a datatype and they can then be specialized by applying a dependently typed term specialization function. Polytypic functions are thus first-class citizens and can be passed as arguments or returned as results. Likewise, we reify polytypic proofs as a datatype and provide a lemma that a polytypic proof can be specialized to any datatype in the universe. The correspondence between polytypic functions and their polytypic proofs is very clear: programmers need to give proofs for, and only for, the same cases that they need to give instances for when they define the polytypic function itself. Finally, we discuss how to write (co)recursive functions and do (co)recursive proofs in a similar way that recursion is handled in Generic Haskell.

Earlier studies have introduced a list of high-level evaluation criteria to assess how well a language supports generic programming. Languages that meet all criteria include Haskell because of its type classes and C++ with the concept feature. We refine these criteria into a taxonomy that captures commonalities and differences between type classes in Haskell and concepts in C++ and discuss which differences are incidental and which ones are due to other language features. The taxonomy allows for an improved understanding of language support for generic programming, and the comparison is useful for the ongoing discussions among language designers and users of both languages.

Datatype-generic programming (DGP) involves parametrization of programs by the shape of data, in the form of type constructors such as ‘list of’. Most approaches to DGP are developed in pure functional programming languages such as Haskell. We argue that the functional object-oriented language Scala is in many ways a better choice. Not only does Scala provide equivalents of all the necessary functional programming features (such as parametric polymorphism, higher-order functions, higher-kinded type operations, and type- and constructor-classes), but it also provides the most useful features of object-oriented languages (such as subtyping, overriding, traditional single inheritance, and multiple inheritance in the form of traits). Common Haskell techniques for DGP can be conveniently replicated in Scala, whereas the extra expressivity provides some important additional benefits in terms of extensibility and reuse. We illustrate this by comparing two simple approaches in Haskell, pointing out their limitations and showing how equivalent approaches in Scala address some of these limitations. Finally, we present three case studies on how to implement in Scala real DGP approaches from the literature: Hinze's ‘Generics for the Masses’, Lämmel and Peyton Jones's ‘Scrap your Boilerplate with Class’, and Gibbons's ‘Origami Programming’.

The worker/wrapper transformation is a general technique for improving the performance of recursive programs by changing their types. The previous formalisation (A. Gill & G. Hutton, J. Funct. Program., vol. 19, 2009, pp. 227–251) was based upon a simple fixed-point semantics of recursion. In this paper, we develop a more structured approach, based upon initial-algebra semantics. In particular, we show how the worker/wrapper transformation can be applied to programs defined using the structured pattern of recursion captured by fold operators, and illustrate our new technique with a number of examples.

Term-rewriting systems can be expressed as generic programs parameterised over the shape of the terms being rewritten. Previous implementations of generic rewriting libraries require users to either adapt the datatypes that are used to describe these terms or to specify rewrite rules as functions. These are fundamental limitations: the former implies a lot of work for the user, while the latter makes it hard if not impossible to document, test, and analyze rewrite rules. In this article, we demonstrate how to overcome these limitations by making essential use of type-indexed datatypes. Our approach is lightweight in that it is entirely expressible in Haskell with GADTs and type families and can be readily packaged for use with contemporary Haskell distributions.