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Algebraic Specialization of Generic Functions for Recursive Types

ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE 2011年第5期229卷 57-74页

作者： Cunha, Alcino Pacheco, Hugo Univ Minho Dep Informat Ctr Ciencias Tecnol Computac Campus Gualta P-4710057 Braga Portugal

Defining functions over large, possibly recursive, data structures usually involves a lot of boilerplate. This code simply traverses non-interesting parts of the data, and rapidly becomes a maintainability problem. Many generic programming libraries have been proposed to address this issue. Most of them allow the user to specify the behavior just for the interesting bits of the structure, and provide traversal combinators to "scrap the boilerplate". The expressive power of these libraries usually comes at the cost of efficiency, since runtime checks are used to detect where to apply the type-specific behavior. In previous work we have developed an effective rewrite system for specialization and optimization of generic programs. In this paper we extend it to also cover recursive data types. The key idea is to specialize traversal combinators using well-known recursion patterns, such as folds or paramorphisms. These are ruled by a rich set of algebraic laws that enable aggressive optimizations. We present a type-safe encoding of this rewrite system in Haskell, based on recent language extensions such as type-indexed type families.

关键词： Generic programming recursion patterns Rewrite systems Specialization Type families

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Generic Point-free Lenses

Generic Point-free Lenses

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10th International Conference on Mathematics of Program Construction

作者： Pacheco, Hugo Cunha, Alcino Univ Minho DI CCTC Braga Portugal

ISBN: (纸本)9783642133206

Lenses are one the most popular approaches to define bidirectional transformations between data models. A bidirectional transformation with view-update, denoted a lens, encompasses the definition of a forward transformation projecting concrete models into abstract views, together with a backward transformation instructing how to translate an abstract view to an update over concrete models. In this paper we show that most of the standard point-free combinators can be lifted to lenses with suitable backward semantics, allowing us to use the point-free style to define powerful bidirectional transformations by composition. We also demonstrate how to define generic lenses over arbitrary inductive data types by lifting standard recursion patterns, like folds or unfolds. To exemplify the power of this approach, we "lensify" some standard functions over naturals and lists, which are tricky to define directly "by-hand" using explicit recursion.

关键词： point-free bidirectional transformations lenses recursion patterns inductive types

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