Towards a categorical foundation for generic programming

2009

These lecture notes introduce libraries for datatype-generic programming in Haskell. We introduce three characteristic generic programming libraries: lightweight implementation of generics and dynamics, extensible and modular generics for the masses, and scrap your boilerplate. We show how to use them to use and write generic programs. In the case studies for the different libraries we introduce generic components of a medium-sized application which assists a student in solving mathematical exercises.

2000

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.

2005

The more expressive a type system, the more type information has to be provided in a program. Having to provide a type is sometimes a pain, but lacking expressivity is often even worse. There is a continuous struggle between expressivity and (type-) verbosity. However, even very expressive type systems allow type inference for parts of a program. Generic Haskell is an extension of Haskell that supports defining generic functions. Generic Haskell assumes that the type of a generic function is explicitly specified.

2006

Abstract A generic function is a function that is defined on the structure of data types: with a single definition, we obtain a function that works for many data types. In contrast, an ad-hoc polymorphic function requires a separate implementation for each data type. Previous work by Hinze on lightweight generic programming has introduced techniques that allow the definition of generic functions directly in Haskell.

2012

In Haskell, there is a clear distinction between values, types, and kinds. Values are built with constructors, such as True, which we colour in blue; we do not colour numerals, characters, or strings: Just 3, (Right 'p' Left "abc"). Datatypes, type synonyms, type variables, indexed families, and type classes are coloured in orange: Bool, Show α ⇒ Show [ α ], type family PF α. Kinds and kind variables are coloured in green: , → , Constraint. For simplicity we do not colour the arrow operator, as it can appear at different levels. Agda code The distinction between values and types is less clear in Agda. Our convention is to use blue for constructors (e.g. refl), orange for identifiers of type Set (e.g. _≡_), and green for identifiers of type Set 1 or (for simplicity) higher (e.g. Set). 2.2.3 Isomorphisms We have mentioned that some types are equivalent to others without formally defining this equivalence. When we say two types are equivalent we mean that they are isomorphic. The concept of isomorphism can be succinctly summarised as an Agda record type:

The more expressive a type system, the more type infor- mation has to be provided in a program. Having to provide a type is sometimes a pain, but lacking expressivity is often even worse. There is a continuous struggle between expressivity and (type-)verbosity. How- ever, even very expressive type systems allow type inference for parts of a program. Generic Haskell is an extension of Haskell that supports defin- ing generic functions. Generic Haskell assumes that the type of a generic function is explicitly specified. This is often no problem, but sometimes it is rather painful to have to specify a type - in particular for generic functions with many dependencies - and sometimes the specified type can be generalized. In this paper, we identify three type inference prob- lems specific to generic functions, and present (partial) solutions to each of them.

2003

Abstract Generic Haskell is an extension of Haskell that supports the construction of generic programs. During the development of several applications, such as an XML editor and compressor, we encountered a number of limitations with the existing (Classic) Generic Haskell language, as implemented by the current Generic Haskell compiler.

Generic Programming, 2003

ACM SIGPLAN …, 2009

Datatype-generic programming is defining functions that depend on the structure, or "shape", of datatypes. It has been around for more than 10 years, and a lot of progress has been made, in particular in the lazy functional programming language Haskell. There are more than 10 proposals for generic programming libraries or language extensions for Haskell. To compare and characterize the many generic programming libraries in a typed functional language, we introduce a set of criteria and develop a generic programming benchmark: a set of characteristic examples testing various facets of datatype-generic programming. We have implemented the benchmark for nine existing Haskell generic programming libraries and present the evaluation of the libraries. The comparison is useful for reaching a common standard for generic programming, but also for a programmer who has to choose a particular approach for datatype-generic programming.

Recently, generic programming becomes of a major interest in several programming paradigms. A recurrent idea to achieve genericity is to specify algorithms on their convenient data structure, and to allow these specifications to be instantiated onto a large number of neighboring data structures. Polytypic programming, shapely types and generic attribute grammars are generic programming methods related to this approach. A framework for generic programming is proposed to embed these methods. It consists in tools for automatic generation of morphisms between data structures, and for program composition. Thanks to this compositional approach, the complete specialization of generic programs could be advantageously delegated to a general and powerful mechanism of "symbolic composition", which performs deforestation and partial evaluation. 1 Introduction In several programming paradigms, generic programming is being emerging. Although this concept is not new, genericity currently...