Re: Relational metamethods and mixed types

[Geoff Leyland <geoff_leyland@...>]

Hi David,

Thanks for you thoughts!

On 24/03/2009, at 2:19 PM, David Manura wrote:

> On Mon, Mar 23, 2009 at 8:03 PM, Geoff Leyland wrote:
> > PiL says: "Unlike arithmetic metamethods, relational metamethods do  
> > not
> > support mixed types...".  Supporting mixed types would be very handy
> > for defining constraints in Linear Programs, where you could go:
> >  a_constraint = 2 * x1 + 3 * x2 + 4 * x3 <= 6
> > ...The pure Lua alternative I can think of is to offer easy  
> > constructors
> > for term lists:
> > a_constraint = 2 * x1 + 3 * x2 + 4 * x3 <= make_term_list(6)
>
> Even that won't work because, moreover, "these operators always result
> in false or true." [1]  Therefore, a_constraint always assumes the
> value true or false, not some expression object.

Thanks, I didn't read the docs far enough earlier, and that one just  
bit me as your mail arrived.  Oh well...

> Your approach is fairly similar to [2], which has some limitations as
> you have shown.

Thanks - that provides a reply to my earlier mail about Short  
Anonymous Functions - I figured it had to be a common approach.  I  
note you mention Todd Veldhuizen on the wiki page - I corresponded  
with him a bit back in the days when template expressions were new...

> Here's a few alternatives:
>
>  a_constraint = le(2 * x1 + 3 * x2 + 4 * x3, 6)
>  a_constraint = (2 * x1 + 3 * x2 + 4 * x3):le(6)
>  a_constraint = Constraint[[2 * x1 + 3 * x2 + 4 * x3 <= 6]]

I tend to like the second at the moment, though I couldn't say why.  I  
considered the third initially, and then went off it when I realised  
template expressions might get me there.  Your hints about only  
parsing lightly could be useful though.  I'm just not sure I have the  
time to develop more than one approach very far, so I'm gonna have to  
guess the right one at the start.

> I tend to like the last one since putting the expression into a string
> you parse yourself allows much flexibility, few gotchas, and a
> familiar syntax.  If you need to substitute Lua variables into those
> expressions, it's a bit more cumbersome, but you might use the
> approaches in [3,4] and take care about security concerns similar to
> SQL injection.

Yes, well, list comprehensions are on the list of things I'll have to  
tackle at some stage, so that's very helpful (I had found it before).   
I think I'll probably mostly be doing conditional sums over late-bound  
sets though, so once again, Template Expressions would be a really  
nice way of building them up

> Metalua[5], token filters, or patching Lua are other alternatives if
> you want a more seamless syntax.

I'd really like to do as much in as pure Lua as possible if I can (not  
counting bindings to an LP solver).  Pulp[1] and pyomo[2] manage quite  
nicely in Python, and Lua is so close...

Cheers,
Geoff

[1] http://code.google.com/p/pulp-or/
[2] http://www.optimization-online.org/DB_HTML/2008/09/2095.html