[Haskell-cafe] noob question

[Ryan Ingram]

You can also do something like this (assuming -fglasgow-exts or
LANGUAGE Rank2Types):

f :: forall b. Fractional b => (forall a. Num a => a) -> b
f x = (1/x)^x

This says that the argument to f has to be able to be instantiated at
any numeric type, such as the result of a call to "fromInteger".  Now,
the compiler is free to instantiate the first x at Double and the
second at Integer.  Here's what it looks like in GHCi:

GHCi, version 6.8.2: http://www.haskell.org/ghc/  :? for help
Loading package base ... linking ... done.
Prelude> :set -XRank2Types -XPatternSignatures
Prelude> let f (x :: forall a. Num a => a) = (1 / x)^x
Prelude> :t f
f :: (Fractional t) => (forall a. (Num a) => a) -> t
Prelude> f 3
3.7037037037037035e-2

Higher rank types don't have inference, so you need to annotate your
function for them to work.

  -- ryan

On 2/25/08, Ben <thefunkslists at gmail.com> wrote:
>
>
> On Feb 25, 2008, at 4:11 PM, Philippa Cowderoy wrote:
> On Mon, 25 Feb 2008, Ben wrote:
>
> <interactive>:1:8:
>   Ambiguous type variable `t' in the constraints:
>     `Fractional t' arising from a use of `/' at <interactive>:1:8-10
>     `Integral t' arising from a use of `^' at <interactive>:1:7-15
>   Probable fix: add a type signature that fixes these type variable(s)
>
>
> / doesn't do integer division, so from there it concludes that you're
> working with a Fractional type - Haskell never coerces behind your back,
> so not only the result of / but also its parameters are Fractional.
>
> ^ only works for Integral types. You might consider that a little
> arbitrary, but hey - it's mostly like that because it's much easier to
> raise something to an integer power.
>
> There's no default it can pick that's both Fractional and Integral, so it
> doesn't know what type the expression should have and it's asking you to
> tell it ("add a type signature that fixes these type variable(s)"). In
> practice you won't be able to unless you've got a broken number type
> handy, but that's the way things go.
>
> Ok, that makes sense.  There's no num k that's both Fractional and Integral,
> where as in the case where I had the number literals, those were two
> different instances. What's the usual way of working around this?  Something
> like
>
> (\k -> (1/ fromInteger k) ^ k) 3
>
> ?
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