Why is there no PRODUCT aggregate function in SQL?

For MSSQL you can use this. It can be adopted for other platforms: it's just maths and aggregates on logarithms.

SELECT
    GrpID,
    CASE
       WHEN MinVal = 0 THEN 0
       WHEN Neg % 2 = 1 THEN -1 * EXP(ABSMult)
       ELSE EXP(ABSMult)
    END
FROM
    (
    SELECT
       GrpID, 
       --log of +ve row values
       SUM(LOG(ABS(NULLIF(Value, 0)))) AS ABSMult,
       --count of -ve values. Even = +ve result.
       SUM(SIGN(CASE WHEN Value < 0 THEN 1 ELSE 0 END)) AS Neg,
       --anything * zero = zero
       MIN(ABS(Value)) AS MinVal
    FROM
       Mytable
    GROUP BY
       GrpID
    ) foo

Taken from my answer here: SQL Server Query - groupwise multiplication

I don't know why there isn't one, but (take more care over negative numbers) you can use logs and exponents to do:-

select exp (sum (ln (table.price))) from table ...

You can perform a product aggregate function, but you have to do the maths yourself, like this...

SELECT
    Exp(Sum(IIf(Abs([Num])=0,0,Log(Abs([Num])))))*IIf(Min(Abs([Num]))=0,0,1)*(1-2*(Sum(IIf([Num]>=0,0,1)) Mod 2)) AS P
FROM
   Table1

Source: http://productfunctionsql.codeplex.com/

There is no PRODUCT set function in the SQL Standard. It would appear to be a worthy candidate, though (unlike, say, a CONCATENATE set function: it's not a good fit for SQL e.g. the resulting data type would involve multivalues and pose a problem as regards first normal form).

The SQL Standards aim to consolidate functionality across SQL products circa 1990 and to provide 'thought leadership' on future development. In short, they document what SQL does and what SQL should do. The absence of PRODUCT set function suggests that in 1990 no vendor though it worthy of inclusion and there has been no academic interest in introducing it into the Standard.

Of course, vendors always have sought to add their own functionality, these days usually as extentions to Standards rather than tangentally. I don't recall seeing a PRODUCT set function (or even demand for one) in any of the SQL products I've used.

In any case, the work around is fairly simple using log and exp scalar functions (and logic to handle negatives) with the SUM set function; see @gbn's answer for some sample code. I've never needed to do this in a business application, though.

In conclusion, my best guess is that there is no demand from SQL end users for a PRODUCT set function; further, that anyone with an academic interest would probably find the workaround acceptable (i.e. would not value the syntactic sugar a PRODUCT set function would provide).

Out of interest, there is indeed demand in SQL Server Land for new set functions but for those of the window function variety (and Standard SQL, too). For more details, including how to get involved in further driving demand, see Itzik Ben-Gan's blog.