# Num instance for functions

From HaskellWiki

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
- http://augustss.blogspot.com/2009/02/regression-they-say-that-as-you-get.html