You could write an EA that writes code in a dynamic language like IronPython with the goal of creating code that a) executes without crashing and b) analyzes the stock market and intelligently buys and sells stock.
That's a very simplistic take on what would be necessary, but it's possible. You would need a host that provides a lot of methods for the IronPython code (technical indicators, etc) and a database of ticks.
It would also be smart to not just generate any old random code, lest you format your own hard-drive. You need a sandbox, and you need to limit the namespaces that are accessable, and you would need to provide a time limit to avoid infinite loops. You could also provide symantic guidelines that allow it to choose appropriate approved keywords instead of just stringing random letters together -- this would greatly speed up evolution.
So, I was involved with a project that did everything but the EA. We had a satellite dish that got real-time stock ticks from the NASDAQ, a service for trading that had an API, and a primitive decision making "brain" that made decisions as the ticks came in.
Sadly, one of the partners flipped out, quit his job, forked the project (got his own dish, etc), and started trading with logic that wasn't ready. He lost a bunch of money. It turns out that for some people this type of project is only a step away from common gambling. But anyway, the project kind of fizzled out after that. Evolving the logic part is the missing link though. And I know there are people out there doing this type of thing.