[Mulgara-dev] Re: Bug list and versions

[Andrae Muys]

On 14/11/2006, at 9:51 AM, Life is hard, and then you die wrote:
>> On 11/13/06, Life is hard, and then you die <ronald at innovation.ch>  
>> wrote:
> The real thing is more complicated and has multiple terms being OR'd
> together. Each OR term has a different set of AND'd terms, concluding
> with a <mulgara:is> clause. I.e. EXPRESSION_A is really something like
>
>   (constr_1a and constr_1b and constr_1c and $t <mulgara:is> '0') or
>   (constr_2a and constr_2b and $t <mulgara:is> '1') or
>   (constr_3a and constr_3b and constr_3c and constr_3d and $t  
> <mulgara:is> '2') or
>   ...
>
> $t occurs only in the <mulgara:is> clause, nowhere else. The purpose
> of that <mulgara:is> clause is to know which of the OR terms matched
> (and there may be multiple of them).
>
> Now, in the above example, the second clause is a degenerate form that
> was being generated in certain corner cases (I'm dealing with this
> case specially now).

And the problem isn't the $t in any case.  In the degenerate case you  
sent us, it's the $b being present in only one of the arguments to  
the disjunction that is triggering the bug.

> you get one line for every matching $b, just as expected. So it's just
> in the context of an OR that things don't work. I understood OR to be
> a set-theoretic union, so it shouldn't matter if I do one query with
> 3 OR terms, or 3 queries each with only one of the OR terms.

OR is not strictly speaking a set-theoretic union, but a disjunction.

So given the following tuples:

A  $a  $b      B   $a   $b
     1   5           2    6
                     2    7

the actual semantics are not tabular, but logical:

A = { {a->1, b->5} }               implies (a==1) ^ (b==5) -> #t
B = { {a->2, b->6}, {a->2, b->7} } implies ((a==2) ^ (b==6)) v  
((a==2) ^ (b==7)) -> #t

and consequently

A or B |- ((a==1) ^ (b==5)) v ((a==2) ^ (b==6)) v ((a==2) ^ (b==7)) - 
 > #t

which in sets-of-bindingsets notation is
   { {a->1, b->5}, {a->2, b->6}, {a->2, b->7} }
and in tabular format is:

A or B  $a  $b
          1   5
          2   6
          2   7

Given

C = { {a->2, c->8} }

A or C |- ((a==1) ^ (b==5) v ((a==2) ^ (c==8))
       ie. { {a->1, b->5}, {a->2, c->8} }
which in tabular format is:

A or C  $a  $b  $c
          1   5   -
          2   -   8

So you are right, disjunction is isomorphic with set-theoretic union,  
and indeed when the propositions represented by the various tuples  
are or'ed the result is the set-theoretic union of their variable  
bindings; but the interface to that result is via a tabular form.   
Consequently we have these "binding-doesn't-exist"/"don't  
care"/"variable unbound" (whatever you want to call it) values  
turning up in the mapping from the logical proposition to the table.   
These values are not NULL's, rather they are DONTCARE's - they  
literally indicate that the truth value of that term in the sum-of- 
products form is independent of that variable.


> The problem is that this won't work well if there are 10 terms....

Nope it won't.  So it's probably important that we get this bug  
fixed :).  Just be aware that avoiding UNBOUND's is good practice  
(even if not always possible).

Andrae

-- 
Andrae Muys
andrae at netymon.com
Principal Mulgara Consultant
Netymon Pty Ltd