```Robert Klemme wrote:
> Michael Ulm wrote:
>
>>Robert Klemme wrote:
>>
>>>Ralph "PJPizza" Siegler wrote:
>>>
>>>
>>>>On Sat, May 21, 2005 at 01:30:13AM +0900, James Britt wrote:
>>>>
>>>>
>>>>>Eric Mahurin wrote:
>>>>>
>>>>>
>>>>>>I've never quite understood why most languages inherently
>>>>>>support returning only a single value
>>>>>
>>>>>
>>>>>Conceptual elegance?
>>>>>
>>>>>Seems cleaner to say that every expression returns an object,
>>>>>though that the object may be a container for other objects,
>>>>>rather than assert that expressions may return an unknown number
>>>>>of objects
>>>>>
>>>>>
>>>>>James
>>>>>
>>>>
>>>>I also think it may be from the original mathematical idea of a
>>>>"function', which only has 1 output value for a given set of inputs,
>>>
>>>
>>>Mathematical functions are in no way limited to yielding a single
>>>output value.
>>>
>>
>><pedant_mode>
>>But they are. A (mathematical) function  f: M -> N  from a set M to a
>>set N is usually defined as a subset of  M x N  such that for each
>>element  m in M  there exists exactly one element  n in N  such that
>>the pair (m, n) is in the subset; one then writes  f(m) = n.
>></pedant_mode>
>
>
> So what?  M can be A x B x C and N can be D x E - or whatever.
>
>
>>>>With multiple return values, more in the mindset of a "relation",
>>>>an n to m mapping
>>>
>>>
>>>That's what a mathematical function is basically.  Don't let sin,
>>>cos, max, min etc. fool you on this one. :-)
>>
>>Maybe you are thinking of vector valued functions, where the return
>>value is a vector? In that case, one still has only one return value
>>(the vector) which in turn contains other elements. This is very
>>similar to returning an array in ruby.
>
>
> With your reasoning there is also just a single input value for math
> functions.  So either functions have a single input and a single output
> value, or multiple at both ends.  But claiming that there can be multiple
> input values but only a single output value is at least a bit dishonest
> IMHO.
>

Indeed, strictly speaking, a mathematical function can only have one
input value. Mathematically, the notation f(x, y) is just a shorthand
for f([x, y]). If Kernigan and Richie had paid more attention at
math class we would have declarations like

(float, float) transform (float, float)

in C, and the world would be a better place for it :-)

Michael

--
Michael Ulm
R&D Team
ISIS Information Systems Austria
tel: +43 2236 27551-219, fax: +43 2236 21081
e-mail: michael.ulm / isis-papyrus.com