Re: [Axiom-math] What is the "+/" operator?

[Ralf Hemmecke]

On 05/24/2007 01:23 AM, Gabriel Dos Reis wrote:
> Ralf Hemmecke <address@hidden> writes:
>
> | On 05/23/2007 06:50 PM, Bill Page wrote:
> | > Quoting Martin Rubey <address@hidden>:
> | >
> | >> ... Igor Khavkine writes:
> | >>
> | >>> Can someone explain this syntax? Looking at the Axiom .spad files,
> | >>> I see that it has general usage +/[...some list construction...].
> | >>
> | >> It is old syntax for reduce and should go away.
> | 
> | I very much agree. The reason is that one should give an initial value
> | otherwise you might be surprised.
>
> I don't see why there should be a surprise.
>
> Reduction through "/" is a functional on monoid operations, so one
> should expect to give a unit element.

Sure. So whoever (which means a program) deals with "/" should first 
check whether the second argument is a List over a monoid and that the 
first argument is exactly *the* corresponding binary operation of that 
particular monoid.

If I look at it that way, then "/" should be a unary operation since 
what one currently writes as its first argument in

  (+)/[1,2,3]

is redundant information. The monoid is specified by the argument of 
List. (The problem arises if a set has two (or more) monoid structures 
implemented, like Integer.)

Or are you saying that you have a domain (like Integer) and the first 
argument then selects the monoid structure? What if I give a binary 
function as the first argument which doesn't make the underlying set 
into a monoid? That error cannot even be caught at runtime.

I am talking here about the compiler. If you have different plans with 
the interpreter, I don't care at the moment, but for the compiler I see 
no point why this form of "/" should be build into the (SPAD) language.

> reduce on the other hand would want an initial value, or a value to
> return when the list of operand is empty.

At least we agree on this.

Ralf