Abstract
A generic function is defined by induction on the structure of types. The structure of a data type can be defined in several ways. For example, in PolyP a pattern functor gives the structure of a data type viewed as a fixed point, and in Generic Haskell a structural representation type gives an isomorphic type view of a data type in terms of sums of products. Depending on this generic view on the structure of data types, some generic functions are easier, more difficult, or even impossible to define. Furthermore, the efficiency of some generic functions can be improved by choosing a different view. This paper introduces generic views on data types and shows why they are useful. Furthermore, it shows how generic views have been added to Generic Haskell, an extension of the functional programming language Haskell that supports the construction of generic functions. The separation between inductive definitions on type structure and generic views allows us to combine many approaches to generic programming in a single framework.
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References
Jansson, P., Jeuring, J.: PolyP — a polytypic programming language extension. In: Conference Record of POPL 1997: The 24th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 470–482. ACM Press, New York (1997)
Hinze, R.: Polytypic values possess polykinded types. Science of Computer Programming 43(2-3), 129–159 (2002)
Lämmel, R., Jones, S.P.: Scrap your boilerplate: a practical approach to generic programming. ACM SIGPLAN Notices 38(3), 26–37 (2003); Proceedings ACM SIGPLAN Workshop on Types in Language Design and Implementation (TLDI 2003)
Jay, C.B.: Distinguishing data structures and functions: the constructor calculus and functorial types. In: Abramsky, S. (ed.) TLCA 2001. LNCS, vol. 2044, pp. 217–239. Springer, Heidelberg (2001)
Hoogendijk, P., de Moor, O.: Container types categorically. Journal of Functional Programming 10(2), 191–225 (2000)
Meijer, E., Fokkinga, M., Paterson, R.: Functional programming with bananas, lenses, envelopes, and barbed wire. In: Hughes, J. (ed.) FPCA 1991. LNCS, vol. 523, pp. 124–144. Springer, Heidelberg (1991)
Jansson, P., Jeuring, J.: A framework for polytypic programming on terms, with an application to rewriting. In: Jeuring, J. (ed.) Workshop on Generic Programming 2000, Ponte de Lima, Portugal, July 2000, pp. 33–45 (2000) Utrecht Technical Report UU-CS-2000-19
Löh, A., Jeuring, J., Clarke, D., Hinze, R., Rodriguez, A., de Wit, J.: The Generic Haskell user’s guide, version 1.42 (Coral). Technical Report UU-CS-2005-004, Institute of Information and Computing Sciences, Utrecht University (2005)
Löh, A.: Exploring Generic Haskell. PhD thesis, Utrecht University (September 2004)
Lämmel, R., Peyton Jones, S.: Scrap more boilerplate: reflection, zips, and generalised casts. In: Proceedings of the ACM SIGPLAN International Conference on Functional Programming, ICFP 2004, pp. 244–255. ACM Press, New York (2004)
Hinze, R., Jeuring, J.: Generic Haskell: applications. In: Backhouse, R., Gibbons, J. (eds.) Generic Programming. LNCS, vol. 2793, pp. 57–97. Springer, Heidelberg (2003)
Wadler, P.: Views: a way for pattern matching to cohabit with data abstraction. In: Conference Record of POPL 1987: The 14th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (1987)
Hinze, R., Jeuring, J.: Generic haskell: Practice and theory. In: Backhouse, R., Gibbons, J. (eds.) Generic Programming. LNCS, vol. 2793, pp. 1–56. Springer, Heidelberg (2003)
Malcolm, G.: Data structures and program transformation. Science of Computer Programming 14, 255–279 (1990)
Schrage, M.: Proxima, a presentation-oriented editor for structured documents. PhD thesis, Utrecht University (October 2004)
Reynolds, J.C.: Definitional interpreters for higher-order programming languages. In: ACM 1972: Proceedings of the ACM annual conference, pp. 717–740. ACM Press, New York (1972)
Hinze, R., Löh, A., Oliveira, B.C.d.S.: “Scrap Your Boilerplate” Reloaded. In: Hagiya, M., Wadler, P. (eds.) FLOPS 2006. LNCS, vol. 3945, pp. 13–29. Springer, Heidelberg (2006)
Holdermans, S., Jeuring, J., Löh, A., Rodriguez, A.: Generic views on data types. Technical Report UU-CS-2006-020, Department of Information and Computing Sciences, Utrecht University (2006)
Holdermans, S.: Generic views. Master’s thesis, Institute of Information and Computing Sciences, Utrecht University (2005)
Burton, F.W., Cameron, R.D.: Pattern matching with abstract data types. Journal of Functional Programming 3(2), 117–190 (1993)
Okasaki, C.: Views for Standard ML. In: SIGPLAN Workshop on ML, pp. 14–23 (1998)
Burton, F.W., Meijer, E., Sansom, P., Thompson, S., Wadler, P.: Views: an extension to Haskell pattern matching (1996), Available from: http://www.haskell.org/development/views.html
Abiteboul, S.: On views and XML. In: Proceedings of the 18th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pp. 1–9. ACM Press, New York (1999)
Ohori, A., Tajima, K.: A polymorphic calculus for views and object sharing. In: Proceedings of the 13th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pp. 255–266 (1994)
Souza dos Santos, C., Abiteboul, S., Delobel, C.: Virtual schemas and bases. In: Jarke, M., Bubenko, J., Jeffery, K. (eds.) EDBT 1994. LNCS, vol. 779, pp. 81–94. Springer, Heidelberg (1994)
Altenkirch, T., McBride, C.: Generic programming within dependently typed programming. In: Gibbons, J., Jeuring, J. (eds.) Generic Programming: IFIP TC2/WG2.1 Working Conference on Generic Programming, Number 115 in International Federation for Information Processing, Dagstuhl, Germany, July 11-12, 2002, pp. 1–20. Kluwer Academic Publishers, Dordrecht (2003)
Benke, M., Dybjer, P., Jansson, P.: Universes for generic programs and proofs in dependent type theory. Nordic Journal of Computing 10(4), 265–289 (2003)
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Holdermans, S., Jeuring, J., Löh, A., Rodriguez, A. (2006). Generic Views on Data Types. In: Uustalu, T. (eds) Mathematics of Program Construction. MPC 2006. Lecture Notes in Computer Science, vol 4014. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11783596_14
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DOI: https://doi.org/10.1007/11783596_14
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