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==Optimizations==
The mathematical basis of maps allow for a number of [[Optimization (computer science)|optimization]]s. If one has <code>map f . map g</code> ('.' is [[function composition (computer science)|function composition]]) then it is the same as the simpler <code>map (f . g) xs</code>; that is,
<math>\left( \text{map}\,f \right) \circ \left( \text{map}\,g \right) = \text{map}\,\left( f \circ g \right)</math>. This particular optimization eliminates an expensive second map by fusing it with the first map; thus it is a "map fusion"<ref>[http://www.randomhacks.net/articles/2007/02/10/map-fusion-and-haskell-performance "Map fusion: Making Haskell 225% faster"]</ref>.
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