Somewhat stale, but a recent post on the official Yahoo! Blog points out that there are over 30 search shortcuts you can use on the site. I don't know how or if they combine well with advanced search, but that's a mini-programming language.
Ob. geek. Clearly it's not Turing complete and probably not formally develped but therein lies a challenge for an enterprising domain specific language builder. Develop a tiny, accessible, extensible language for expressing search queries. Majority of language power has to available from one-liners of less than 40 characters or so.