```
twice :: (a -> a) -> a -> a
twice f = (\x -> f (f x))
```

`twice twice` applies the function 4 times:

```
twice twice f
= twice (\y -> f (f y))
= (\x -> (\y -> f (f y)) ((\y -> f (f y)) x))
= (\x -> (\y -> f (f y)) (f (f x)))
= (\x -> f (f (f (f x))))
```

`twice twice twice` and `twice (twice twice)` each apply the function 16 times.

## One response to “Exercise 9.7”

More concisely:

twice f = f . f