Num instance for functions

Some people have argued, that Num instances of (->) would be nice in order to add functions nicely, say for

f, g :: Num a => b -> a

you would define

(f+g) x = f x + g x

With an according definition of fromInteger

fromInteger = const

numeric literals would also denote constant functions. This allows

f+2  ==  \x -> f x + 2

.

Even nicer, the mathematically established notation of omitting the multiplication dot

2(x+y) :: Integer

will now be parsed by a Haskell compiler to the most obvious meaning

2 :: Integer

! :-)

Note

This article is in category Proposals in order to show people that this idea was already proposed, but that one should think twice implementing it. There should be a category Counterproposals.

See also

• The applicative-numbers package, which generates numeric class instances for arbitrary applicative functors (including functions).
• http://www.haskell.org/pipermail/haskell-cafe/2006-November/019374.html
• http://www.haskell.org/pipermail/haskell-cafe/2006-October/019105.html
• http://www.haskell.org/pipermail/haskell-cafe/2001-February/001531.html