Previous implementations of generic rewriting libraries have a number of limitations: they require the user to either adapt the datatype on which rewriting is applied, or the rewriting rules are specified as functions, which makes it hard or impossible to document, test, and analyse them. We describe a library that demonstrates how to overcome these limitations by defining rules in terms of datatypes, and show how to use a type-indexed datatype to automatically extend a datatype for syntax trees with a case for metavariables. We then show how rewrite rules can be implemented without any knowledge of how the datatype is extended with metavariables. We use Haskell, extended with associated type synonyms, to implement both type-indexed datatypes and generic functions. We analyse the performance of our library and compare it with other approaches to generic rewriting.
Previous implementations of generic rewriting libraries have a number of limitations: they require the user to either adapt the datatype on which rewriting is applied, or the rewriting rules are specified as functions, which makes it hard or impossible to document, test, and analyse them. We describe a library that demonstrates how to overcome these limitations by defining rules in terms of datatypes, and show how to use a type-indexed datatype to automatically extend a datatype for syntax trees with a case for metavariables. We then show how rewrite rules can be implemented without any knowledge of how the datatype is extended with metavariables. We use Haskell, extended with associated type synonyms, to implement both type-indexed datatypes and generic functions. We analyse the performance of our library and compare it with other approaches to generic rewriting.
Many datatype-generic functions need access to the recursive positions in the structure of the datatype, and therefore adopt a fixed point view on datatypes. Examples include variants of fold that traverse the data following the recursive structure, or the Zipper data structure that enables navigation along the recursive positions. However, Hindley-Milner-inspired type systems with algebraic datatypes make it difficult to express fixed points for anything but regular datatypes. Many real-life examples such as abstract syntax trees are in fact systems of mutually recursive datatypes and therefore excluded. Using Haskell's GADTs and type families, we describe a technique that allows a fixed-point view for systems of mutually recursive datatypes. We demonstrate that our approach is widely applicable by giving several examples of generic functions for this view, most prominently the Zipper.
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