[Haskell-cafe] Re: Exception handling in numeric computations

[Luke Palmer]

On Tue, Mar 24, 2009 at 3:28 PM, Luke Palmer <lrpalmer at gmail.com> wrote:

> On Tue, Mar 24, 2009 at 3:14 PM, Xiao-Yong Jin <xj2106 at columbia.edu>wrote:
>
>> Jake McArthur <jake at pikewerks.com> writes:
>>
>> > Xiao-Yong Jin wrote:
>> > | The problem is that there will be many functions using such
>> > | a function to invert a matrix, making this inversion
>> > | function return Either/Maybe or packing it in a monad is
>> > | just a big headache.
>> >
>> > I disagree. If you try to take the inverse of a noninvertable matrix,
>> > this is an *error* in your code. Catching an error you created in pure
>> > code and patching it with chewing gum it is just a hack. A monadic
>> > approach (I'm putting Either/Maybe under the same umbrella for brevity)
>> > is the only solution that makes any sense to me, and I don't think it's
>> > ugly as you are making it out to be.
>> >
>>
>> Then, why is 'div' not of type 'a -> a -> ArithExceptionMonad a' ?
>> Why does it throws this /ugly/ /error/ when it is applied to
>> 0?  Why is it not using some beautiful
>> 'ArithExceptinoMonad'?  Is 'Control.Exception' just pure
>> /ugly/ and doesn't make any sense?
>
>
> It's a proof obligation, like using unsafePerformIO.  It is "okay" to use
> unsafePerformIO when it exhibits purely functional semantics, but it's
> possible to use it incorrectly, and there is no ImpureSemanticsException.
> If you are being rigorous, you simply have to prove that the denominator
> will not be zero, rather than relying on it to be caught at runtime.  You
> can move the check to runtime easily:
>
> safeDiv x 0 = Nothing
> safeDiv x y = Just (x `div` y)
>
> Going the other way, from a runtime check to an obligation, is impossible.
>

(well, except for div x y = fromJust (safeDiv x y).. but the runtime check
is still there in terms of operation)
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