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Re: reduce metaoperator on an empty list

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From:
Sam Vilain
Date:
May 19, 2005 20:09
Subject:
Re: reduce metaoperator on an empty list
Message ID:
428D54D4.7090204@vilain.net
Stuart Cook wrote:
> In Haskell, there is a distinction between foldl and foldl1 (similar
> remarks apply to foldr/foldr1[1]):
> The former (foldl) requires you to give an explicit 'left unit'[2],
> which is implicitly added to the left of the list being reduced. This
> means that folding an empty list will just give you the unit.
> i.e.
> foldl (+) 0 [a,b,c] = ((0+a)+b)+c
> foldl (+) 0 [] = 0
> The latter (foldl1) doesn't use a unit value, but this means that you
> can't fold empty lists.
> i.e.
> foldl1 (+) [a,b,c] = (a+b)+c
> foldl1 (+) [] = ***error***

sure.  Maybe the identity values could be supplied by making the reduce operator
for them a curried version of reduce, where reduce requires a list with at least
one element (or DIES :))

eg, something similar to; (sorry for the psuedo-perl6, corrections welcome :))

   sub prefix:<[+]> (*@args) ::= &reduce.assuming(func => &infix:<+>, first => 0);
   sub prefix:<[*]> (*@args) ::= &reduce.assuming(func => &infix:<*>, first => 1);

This would mean that unless the operator specifically defines a curried reduce
version of itself, then the [] version of it on an empty list will be a hard run-time
error.

Then again, maybe an identity trait is more elegant and covers the varied ways
that multiple operators combine inside reduce..

 > You /could/ try to do something 'sensible' and return 0 or undef, but
 > this seems likely to result in more confusion.

Personally I think returning an undef for this kind of situation would be as wrong
as returning undef for 0/0.

Sam.

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