Map (higher-order function): Difference between revisions

Revision as of 18:01, 15 June 2020

Revision as of 12:36, 22 June 2020

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* <code>(map f . map g) list</code> and

* <code>map (f . g) list</code>

lead to the same result; that is, <math>\operatorname{map}(f) \circ \operatorname{map}(g) = \operatorname{map}(f \circ g)</math>.{{citation needed|date=October 2016}} However, the second form is more efficient to compute than the first form, because each <code>map</code> requires rebuilding an entire list from scratch. Therefore, compilers will attempt to transform the first form into the second; this type of optimization is known as ''map fusion'' and is the [[functional programming|functional]] analog of [[loop fusion]].<ref>[http://www.randomhacks.net/articles/2007/02/10/map-fusion-and-haskell-performance "Map fusion: Making Haskell 225% faster"]</ref>

Map functions can be and often are defined in terms of a [[Fold (higher-order function)|fold]] such as <code>foldr</code>, which means one can do a ''map-fold fusion'': <code>foldr f z . map g</code> is equivalent to <code>foldr (f . g) z</code>.