Apply CSS styles to an element depending on its child elements

As far as I'm aware, styling a parent element based on the child element is not an available feature of CSS. You'll likely need scripting for this.

It'd be wonderful if you could do something like div[div.a] or div:containing[div.a] as you said, but this isn't possible.

You may want to consider looking at jQuery. Its selectors work very well with 'containing' types. You can select the div, based on its child contents and then apply a CSS class to the parent all in one line.

If you use jQuery, something along the lines of this would may work (untested but the theory is there):

$('div:has(div.a)').css('border', '1px solid red');

or

$('div:has(div.a)').addClass('redBorder');

combined with a CSS class:

.redBorder
{
    border: 1px solid red;
}

Here's the documentation for the jQuery "has" selector.

Basically, no. The following would be what you were after in theory:

div.a < div { border: solid 3px red; }

Unfortunately it doesn't exist.

There are a few write-ups along the lines of "why the hell not". A well fleshed out one by Shaun Inman is pretty good:

http://www.shauninman.com/archive/2008/05/05/css_qualified_selectors