Difference between revisions of "Num instance for functions"

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(BASIC blog post)
(Refurbish very patchy article to contain the essentials)
 
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Some people have argued, that <hask>Num</hask> instances of <hask>(->)</hask> would be nice in order
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It is possible to write a <hask>Num</hask> instance for functions in Haskell:
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to add functions nicely, say for
  
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<haskell>f, g :: Num a => b -> a</haskell>
  
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you would define
  
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<haskell>(f+g) x = f x + g x</haskell>
  
   
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<haskell>
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With an according definition of <hask>fromInteger</hask>
  
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instance Num b => Num (a -> b) where
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<haskell>fromInteger = const</haskell>
  
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negate = fmap negate
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numeric literals would also denote constant functions. This allows
  
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<haskell>f+2 == \x -> f x + 2</haskell>.
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(+) = liftA2 (+)
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(*) = liftA2 (*)
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fromInteger = pure . fromInteger
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abs = fmap abs
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signum = fmap signum
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</haskell>
   
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This allows writing expressions of the form
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Even nicer, the mathematically established notation of omitting the
  
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multiplication dot
  
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<haskell>2(x+y) :: Integer</haskell>
  
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will now be parsed by a Haskell compiler to the most obvious meaning
  
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<haskell>2 :: Integer</haskell>
  
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! :-)
  
   
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<haskell>
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== Note ==
  
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> (sin^2 + cos^2) 123.4
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1.0
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</haskell>
   
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where functions can be added like <hask>Num</hask>bers, leaving their arguments open for later.
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This article is in category Proposals in order to show people that this idea was already proposed,
  
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but that one should think twice implementing it.
  
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There should be a category Counterproposals.
  
   
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The usefulness of this instance is debatable, and it is not currently part of [[Language and library specification|the language report]] or defined in any popular library.
   
 
== See also ==
  
== See also ==
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[[Category:Humor]]
  
[[Category:Humor]]
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[[Category:Proposals]]
  
 
[[Category:FAQ]]
  
[[Category:FAQ]]
 
[[Category:Style]]
  
[[Category:Style]]

Latest revision as of 01:24, 28 December 2014

It is possible to write a Num instance for functions in Haskell: 

instance Num b => Num (a -> b) where
      negate      = fmap negate
      (+)         = liftA2 (+)
      (*)         = liftA2 (*)
      fromInteger = pure . fromInteger
      abs         = fmap abs
      signum      = fmap signum

This allows writing expressions of the form 

> (sin^2 + cos^2) 123.4
1.0

where functions can be added like Numbers, leaving their arguments open for later.

The usefulness of this instance is debatable, and it is not currently part of the language report or defined in any popular library.

See also
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