Departmental Papers (CIS)

Date of this Version


Document Type

Conference Paper


Stephanie Weirich and Chris Casinghino. Arity-generic type-generic programming. In ACM SIGPLAN Workshop on Programming Languages Meets Program Verification (PLPV), pages 15-26, January 2010

© ACM, 2010. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in {ACM SIGPLAN Workshop on Programming Languages Meets Program Verification (2010)} Email


Some programs are doubly-generic. For example, map is datatypegeneric in that many different data structures support a mapping operation. A generic programming language like Generic Haskell can use a single definition to generate map for each type. However, map is also arity-generic because it belongs to a family of related operations that differ in the number of arguments. For lists, this family includes repeat, map, zipWith, zipWith3, zipWith4, etc. With dependent types or clever programming, one can unify all of these functions together in a single definition. However, no one has explored the combination of these two forms of genericity. These two axes are not orthogonal because the idea of arity appears in Generic Haskell: datatype-generic versions of repeat, map and zipWith have different arities of kind-indexed types. In this paper, we define arity-generic datatype-generic programs by building a framework for Generic Haskell-style generic programming in the dependently-typed programming language Agda 2.



Date Posted: 23 July 2012