A lightweight approach to datatype-generic rewriting

Abstract

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.

Generic programming with indexed functors

“…The regular library of Van Noort et al (2008) considers functors defining single datatypes without parameters. This corresponds to instantiating the input index to ⊥ + (no parameters, one recursive slot) and the output index to , and allowing fixed points only on the outside, of type ⊥ + → ⊥ .…”

“…In fact, many earlier approaches such as regular (van Noort et al 2008), PolyP (Jansson and Jeuring 1997), and Multirec (Rodriguez Yakushev et al 2009) can be readily derived from our approach by parameter instantiation. Unlike Chapman et al (2010), however, we do not strive to devise a minimal, self-encoding universe, but instead prefer a representation which maps naturally to the usual way of defining a datatype.…”

Generic programming for indexed datatypes

“…In this paper we use a lightweight generic programming library using type-level representations with type families in a style similar to that first described by Chakravarty et al (2009) and used by Van Noort et al (2010) which we call instant-generics (the same name as its Hackage package).…”

Canonical Forms in Interactive Exercise Assistants

“…The results are promising, and are expected to be used in mathematics courses in Dutch high schools next year. Further investigation is needed to understand how views can be incorporated in our generalized rewriting framework, in which we use generic programming techniques [12]. More information about our tools can be found on http:// ideas.cs.uu.nl/.…”