A few days ago I wrote about adding a factorial operator to my assembler, and I noted that I knew not of any other languages that had such a feature. So imagine my surprise as I'm reading about XL (via Lobsters) and the second example is factorial! Not only that, but that was an example of extending the language itself! The last time I was this excited about software was reading about Synthesis OS, a JIT-based operating system where you could create your own system calls.
How it handles precedence is interesting. In my assembler, I have left or right associativity as an explicit field, whereas in XL, it's encoded in the precedence level itself—even if its left, odd if its right. I'm not sure how I feel about that. On the one hand it feels nice and it's one less field to carry around; on the other, being explicit as I did makes it clear if something is left or right. But on the gripping hand, it sounds like matching precedence on a left and right operator could lead to problems, so I still may have an explicitness problem.
But I digress.
It's a very simple language with only one keyword “is” and a user-definable precedence table. The parser generates a parse tree of only eight types, four leaf nodes (integer, real, text, name (or symbol)) and four non-leaf nodes (prefix, infix, postfix and block). And from there, you get XL.
This is something I definitely want to look into.