A Formal Comparison of Approaches to Datatype-Generic Programming
Datatype-generic programming increases program abstraction and reuse by making functions operate uniformly across different types. Many approaches to generic programming have been proposed over the years, most of them for Haskell, but recently also for dependently typed languages such as Agda. Diffe...
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| Published in: | Electronic proceedings in theoretical computer science Vol. 76; no. Proc. MSFP 2012; pp. 50 - 67 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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11.02.2012
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| ISSN: | 2075-2180, 2075-2180 |
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| Abstract | Datatype-generic programming increases program abstraction and reuse by making functions operate uniformly across different types. Many approaches to generic programming have been proposed over the years, most of them for Haskell, but recently also for dependently typed languages such as Agda. Different approaches vary in expressiveness, ease of use, and implementation techniques. Some work has been done in comparing the different approaches informally. However, to our knowledge there have been no attempts to formally prove relations between different approaches. We thus present a formal comparison of generic programming libraries. We show how to formalise different approaches in Agda, including a coinductive representation, and then establish theorems that relate the approaches to each other. We provide constructive proofs of inclusion of one approach in another that can be used to convert between approaches, helping to reduce code duplication across different libraries. Our formalisation also helps in providing a clear picture of the potential of each approach, especially in relating different generic views and their expressiveness. |
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| AbstractList | Datatype-generic programming increases program abstraction and reuse by making functions operate uniformly across different types. Many approaches to generic programming have been proposed over the years, most of them for Haskell, but recently also for dependently typed languages such as Agda. Different approaches vary in expressiveness, ease of use, and implementation techniques. Some work has been done in comparing the different approaches informally. However, to our knowledge there have been no attempts to formally prove relations between different approaches. We thus present a formal comparison of generic programming libraries. We show how to formalise different approaches in Agda, including a coinductive representation, and then establish theorems that relate the approaches to each other. We provide constructive proofs of inclusion of one approach in another that can be used to convert between approaches, helping to reduce code duplication across different libraries. Our formalisation also helps in providing a clear picture of the potential of each approach, especially in relating different generic views and their expressiveness. |
| Author | Magalhães, José Pedro Löh, Andres |
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| Cites_doi | 10.4204/EPTCS.43.2 10.1007/978-3-540-76786-2_2 10.1145/2103786.2103795 10.1145/581690.581698 10.1145/263699.263763 10.1007/978-3-642-04652-0_5 10.1145/1863543.1863547 10.1007/11737414_3 10.1145/1706356.1706366 10.1017/S0956796803000315 10.1007/978-3-642-13321-3_8 10.1145/1596550.1596585 10.1017/S0956796811000098 10.1017/S0956796810000158 10.1007/11783596_14 10.1145/1411318.1411321 10.1017/S0956796810000183 10.1145/2036918.2036920 10.1017/S0956796809007345 10.1007/3540543961_7 10.1145/1707790.1707799 10.1007/BFb0054285 10.1145/1411286.1411301 10.1017/S0956796806006022 10.1007/978-3-540-76786-2_1 10.1016/j.scico.2007.10.006 10.1145/1863523.1863529 |
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| References | Ralf Hinze (HinzeJeuringLoh:2007) 2007; 4719 José Pedro Magalhães (jpm:ogie:10) 2010 Ralf Hinze (GP3D) 2009; 74 Ulf Norell (norell2009dependently) 2009; 5832 José Pedro Magalhães (jpm:gdmh:10) 2010 Stefan Holdermans (GenericViews) 2006; 4014 Jeremy Gibbons (Gibbons2007:Datatype) 2007; 4719 Patrik Jansson (polyp) 1997 Stephanie Weirich (arity) 2010 Andreas Abel (MiniAgda) 2010 Nils Anders Danielsson (subtyping) 2010; 6120 Ralf Hinze (GM) 2006; 16 (haskellbook) 2003 Alexey Rodriguez Yakushev (multirec) 2009 Wendy Verbruggen (formalGH) 2010; 20 Dimitrios Vytiniotis (OutsideIn) 2011; 21 Thomas van Noort (1411321) 2008 James Chapman (levitation) 2010 Brent A. Yorgey (jpm:ghp:12) 2012 Andres Löh (jpm:gpif:11) 2011 Erik Meijer (bananas) 1991; 523 Thomas van Noort (jpm:ladgr:10) 2010; 20 Andres Löh (exploringGH) 2004 Shin-Cheng Mu (AoPA) 2009; 19 Ralf Hinze (SYBreloaded) 2006; 3945 Richard Bird (nested) 1998; 1422 Alexey Rodriguez Yakushev (UUCS2008010) 2008 James Cheney (LIGD) 2002 |
| References_xml | – volume-title: Proceedings Workshop on Partiality and Recursion in Interactive Theorem Provers year: 2010 ident: MiniAgda article-title: MiniAgda: Integrating Sized and Dependent Types doi: 10.4204/EPTCS.43.2 – volume: 4719 start-page: 72 volume-title: Datatype-Generic Programming year: 2007 ident: HinzeJeuringLoh:2007 article-title: Comparing Approches to Generic Programming in Haskell doi: 10.1007/978-3-540-76786-2_2 – start-page: 53 volume-title: Proceedings of the ACM SIGPLAN Workshop on Types in Language Design and Implementation year: 2012 ident: jpm:ghp:12 article-title: Giving Haskell a Promotion doi: 10.1145/2103786.2103795 – volume-title: Exploring Generic Haskell year: 2004 ident: exploringGH – start-page: 90 volume-title: Proceedings of the ACM SIGPLAN Workshop on Haskell year: 2002 ident: LIGD article-title: A lightweight implementation of generics and dynamics doi: 10.1145/581690.581698 – start-page: 470 volume-title: Proceedings of the ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages year: 1997 ident: polyp article-title: PolyP—a polytypic programming language extension doi: 10.1145/263699.263763 – volume: 5832 start-page: 230 volume-title: Advanced Functional Programming, 6th International School, AFP 2008, Revised Lectures year: 2009 ident: norell2009dependently article-title: Dependently typed programming in Agda doi: 10.1007/978-3-642-04652-0_5 – start-page: 3 volume-title: Proceedings of the ACM SIGPLAN International Conference on Functional Programming year: 2010 ident: levitation article-title: The gentle art of levitation doi: 10.1145/1863543.1863547 – volume: 3945 start-page: 13 volume-title: Functional and Logic Programming year: 2006 ident: SYBreloaded article-title: ``Scrap Your Boilerplate'' Reloaded doi: 10.1007/11737414_3 – start-page: 33 volume-title: Proceedings of the ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation year: 2010 ident: jpm:ogie:10 article-title: Optimizing Generics Is Easy! doi: 10.1145/1706356.1706366 – volume-title: Haskell 98, Language and Libraries. The Revised Report year: 2003 ident: haskellbook doi: 10.1017/S0956796803000315 – volume: 6120 start-page: 100 volume-title: Mathematics of Program Construction year: 2010 ident: subtyping article-title: Subtyping, Declaratively doi: 10.1007/978-3-642-13321-3_8 – start-page: 233 volume-title: Proceedings of the ACM SIGPLAN International Conference on Functional Programming year: 2009 ident: multirec article-title: Generic programming with fixed points for mutually recursive datatypes doi: 10.1145/1596550.1596585 – volume: 21 start-page: 333 year: 2011 ident: OutsideIn article-title: OutsideIn(X)—Modular type inference with local assumptions publication-title: Journal of Functional Programming doi: 10.1017/S0956796811000098 – volume: 20 start-page: 213 year: 2010 ident: formalGH article-title: Formal polytypic programs and proofs publication-title: Journal of Functional Programming doi: 10.1017/S0956796810000158 – volume: 4014 start-page: 209 volume-title: Mathematics of Program Construction year: 2006 ident: GenericViews article-title: Generic Views on Data Types doi: 10.1007/11783596_14 – start-page: 13 volume-title: Proceedings of the ACM SIGPLAN Workshop on Generic Programming year: 2008 ident: 1411321 article-title: A lightweight approach to datatype-generic rewriting doi: 10.1145/1411318.1411321 – volume: 20 start-page: 375 year: 2010 ident: jpm:ladgr:10 article-title: A lightweight approach to datatype-generic rewriting publication-title: Journal of Functional Programming doi: 10.1017/S0956796810000183 – start-page: 1 volume-title: Proceedings of the ACM SIGPLAN Workshop on Generic Programming year: 2011 ident: jpm:gpif:11 article-title: Generic programming with indexed functors doi: 10.1145/2036918.2036920 – volume: 19 start-page: 545 year: 2009 ident: AoPA article-title: Algebra of programming in Agda: Dependent types for relational program derivation publication-title: Journal of Functional Programming doi: 10.1017/S0956796809007345 – volume: 523 start-page: 124 volume-title: Functional Programming Languages and Computer Architecture year: 1991 ident: bananas article-title: Functional programming with bananas, lenses, envelopes and barbed wire doi: 10.1007/3540543961_7 – start-page: 15 volume-title: Proceedings of the ACM SIGPLAN Workshop on Programming Languages meets Program Verification year: 2010 ident: arity article-title: Arity-generic datatype-generic programming doi: 10.1145/1707790.1707799 – volume: 1422 start-page: 52 volume-title: Mathematics of Program Construction year: 1998 ident: nested article-title: Nested datatypes doi: 10.1007/BFb0054285 – start-page: 111 volume-title: Proceedings of the ACM SIGPLAN Symposium on Haskell year: 2008 ident: UUCS2008010 article-title: Comparing libraries for generic programming in Haskell doi: 10.1145/1411286.1411301 – volume: 16 start-page: 451 year: 2006 ident: GM article-title: Generics for the Masses publication-title: Journal of Functional Programming doi: 10.1017/S0956796806006022 – volume: 4719 start-page: 1 volume-title: Spring School on Datatype-Generic Programming year: 2007 ident: Gibbons2007:Datatype article-title: Datatype-Generic Programming doi: 10.1007/978-3-540-76786-2_1 – volume: 74 start-page: 590 year: 2009 ident: GP3D article-title: Generic programming in 3D publication-title: Science of Computer Programming doi: 10.1016/j.scico.2007.10.006 – start-page: 37 volume-title: Proceedings of the ACM Symposium on Haskell year: 2010 ident: jpm:gdmh:10 article-title: A generic deriving mechanism for Haskell doi: 10.1145/1863523.1863529 |
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