# Num instance for functions

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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 `Num`

bers, 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

- 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