Generic programming for indexed datatypes

Abstract

An indexed datatype is a type that uses a parameter as a type-level tag; a typical example is the type of vectors, which are indexed over a type-level natural number encoding their length. Since the introduction of generalised algebraic datatypes, indexed datatypes have become commonplace in Haskell. Values of indexed datatypes are often more involved than values of plain datatypes, and programmers would benefit from having generic programs on indexed datatypes. However, no generic programming library adequately supports them, leaving programmers with the tedious task of writing repetitive code.We show how to encode indexed datatypes in a generic programming library with type families and type-level representations in Haskell. Our approach can also be used in similar libraries, and is fully backwards-compatible. We show not only how to encode indexed datatypes generically, but also how to instantiate generic functions on indexed datatypes. Furthermore, all generic representations and instances are generated automatically, making life easier for users.

Generic Programming in OCaml

“…The open design of the library enables the user to define his own views. In addition to the low level view, we have included the sum-of-products view underlying the LIGD library [8] and Instant-Generics [7,27], the spine view underlying the SYB library [18] and the list-of-constructors view underlying RepLib [38].…”

A pattern for almost homomorphic functions

“…These same techniques convey the majority of the reusability of our hcompos function; our extensions just enable its heterogeneity. We believe that our extensions can also be applied to more expressive variants of instant-generics, including generic-deriving [12] and indexed data types (a subset of GADTs) [11].…”

“…In particular, nested recursion [1] and GADTs are crucial to encoding many interesting properties, such as well-scoped and/or well-typed term representations. While some uses of these features can be forced into the yoko representation types, current research, like that of Magalhães and Jeuring [11], is investigating more natural representations. One derivative of instant-generics that is better suited for these features is generic-deriving [12], which was recently integrated with GHC.…”

Functional modelling of musical harmony

“…We plan to see if the extensions to instant-generics reported by Magalhães and Jeuring (2011) allow us to continue using generic programming for our model.…”