# [Haskell-cafe] Odd behavior with Num instance for lists (was: f^n for functional iteration)

Bob Ippolito bob at redivi.com
Fri Dec 13 17:24:56 UTC 2013

```On Fri, Dec 13, 2013 at 8:57 AM, Mark Fredrickson <
mark.m.fredrickson at gmail.com> wrote:

> On Fri, Dec 13, 2013 at 8:59 AM, Antonio Nikishaev <me at lelf.lu> wrote:
>
>>
>>
>
> The previous exchange prompted me to whip up a Num instance for lists:
>
>     instance Num a => Num [a] where
>         negate = fmap negate
>         (+) = zipWith (+)
>         (*) = zipWith (+)
>         fromInteger x = [fromInteger x]
>         abs = fmap abs
>         signum = fmap signum
>
> It mostly behaves how one would expect:
>
>     let a = [1,2,3]
>     ghci> let b = [4,5,6,7]
>     ghci> a + b
>     [5,7,9]
>     ghci> 1 + a
>     [2]
>
> I was wondering whey `1 + a` succeeds. At first I thought it could be the
> `fromInteger` definition, but this explanation were true, I should be able
> to add integers and doubles freely, which I can't:
>
>     ghci> fromInteger (1::Integer) + (1.0::Double)
>     2.0
>     ghci> (1::Integer) + (1.0::Double)
>
>     <interactive>:30:17:
>     Couldn't match expected type `Integer' with actual type `Double'
>     In the second argument of `(+)', namely `(1.0 :: Double)'
>     ...
>
> Thanks for enlightening me.
>

`1 + a` works for the same reason `1 + (1.0::Double)` works: type
inference. `1 + a` in this instance is equivalent to `(1 :: Num [Integer])
+ a` which should compile down to something equivalent to `fromInteger 1 +
a`.

-bob
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