A new approach to generic functional programming

Abstract

This paper describes a new approach to generic functional programming, which allows us to define functions generically for all datatypes expressible in Haskell. A generic function is one that is defined by induction on the structure of types. Typical examples include pretty printers, parsers, and comparison functions.The advanced type system of Haskell presents a real challenge: datatypes may be parameterized not only by types but also by type constructors, type definitions may involve mutual recursion, and recursive calls of type constructors can be arbitrarily nested. We show thatdespite this complexity-a generic function is uniquely defined by giving cases for primitive types and type constructors (such as disjoint unions and Cartesian products). Given this information a generic function can be specialized to arbitrary Haskell datatypes.The key idea of the approach is to model types by terms of the simply typed X-calculus augmented by a family of recursion operators. While conceptually simple, our approach places high demands on the type system: it requires polymorphic recursion, rank-n types, and a strong form of type constructor polymorphism.Finally, we point out connections to Haskell's class system and show that our approach generalizes type classes in some respects.

Trends in Functional Programming

“…For algebraic datatypes, we expect it should be straightforward to extend our theory using ideas from generic programming as in [8], while first-order functions could be handled by representing functions using tries as in the improved Lazy Smallcheck [15]. Another interesting area to explore is dependent type theory.…”

The HERMIT in the machine

“…This is a well-studied problem, and a variety of approaches have been proposed (Hinze 2000;Peyton Jones 2003, 2004;Löh 2004;Visser 2005;Rodriguez et al 2008;Yakushev et al 2009;Magalhães et al 2010). This section describes one such approach to the problem: the Kansas University Rewrite Engine (KURE), a Haskell-embedded domain-specific language for strategic rewriting.…”

Dependency-style generic haskell

“…The original work of Hinze enabled independent generic functions to be written in a natural recursive style [15], though such functions could only be written for fixed kinds such as or → . Hinze [16] then lifted this restriction.…”

“…This facilitates the automatic overloading of certain functions for datatypes which have the deriving clause specified. Hinze and Peyton Jones explore an extension, following Hinze's earlier ideas [15], which integrated generics with Haskell's type class system [20]. This system suffers from some limitations due to the interaction with the type class system.…”