Marshall
Posts:
1,928
Registered:
8/9/06
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Re: 0^0=1
Posted:
May 5, 2012 1:35 PM
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On Friday, May 4, 2012 8:43:55 PM UTC-7, Dan Christensen wrote:
> On May 4, 7:48 pm, Marshall <marshall.spi...@gmail.com> wrote:
> > On Friday, May 4, 2012 9:01:55 AM UTC-7, Gus Gassmann wrote:
> >
> > > Fact is, sums, products, minima, maxima and string concatenations can
> > > be defined consistently over empty lists, and one should do so in
> > > order to avoid unnecessary case distinctions.
> >
> > Yes; more generally, the n-ary form of any binary function with
> > an identity can (should!) be defined to be that identity in the
> > arity-0 case. For example:
> >
> > AND(true, false, true) = false;
> > AND(true, false) = false;
> > AND(true) = true;
> > AND() = true;
> >
> > All the same reasoning for empty products applies. This is
> > widely understood in the CS field.
> >
> > (Min and max have identities for quantities like 32-bit integer
> > but don't in the general case.)
> >
> > Gus's earlier example program was entirely canonical and
> > ordinary; Dan's suggestion to complicate it by adding
> > extra checking make for a worse program.
> >
>
> Under what conditions should a product function return a value of 1?
> How about only when the the numbers supplied to it multiply to give
> you 1.
Yes, exactly. Just like Gus's code does, and the LISP n-ary product
does, and the earlier mentioned fold function present in functional
languages.
Marshall
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