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Generic Programming with Adjunctions

  • Ralf Hinze
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7470)

Abstract

Adjunctions are among the most important constructions in mathematics. These lecture notes show they are also highly relevant to datatype-generic programming. First, every fundamental datatype—sums, products, function types, recursive types—arises out of an adjunction. The defining properties of an adjunction give rise to well-known laws of the algebra of programming. Second, adjunctions are instrumental in unifying and generalising recursion schemes. We discuss a multitude of basic adjunctions and show that they are directly relevant to programming and to reasoning about programs.

Keywords

Natural Transformation Category Theory Universal Property Recursive Call Left Adjoint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ralf Hinze
    • 1
  1. 1.Department of Computer ScienceUniversity of OxfordOxfordEngland

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