let x! = if x == 0 then 1 else x * (x - 1)! end in 5! end
Any operator can be prefix, infix or postfix depending on the relative priority with the operators next to them. For instance, in "1 ^ * 2" the engine interprets ^ as postfix because ^ has higher priority (it just gets null as its right hand side). In "1 * ^ 2", ^ is prefix. Unless specified otherwise operators are given maximal priority, which is why the factorial example works.
The engine just has specific provisions to allow operators in "prefix position" to have different priority than in infix position, otherwise prefix minus would fail to work as expected.
See line 266 for the syntax definition (the precedence entry for "->" on line 278 is also relevant) and line 409 for the implementation of pattern matching. I use a few auxiliary functions here: extractArgs just checks that an AST node has a certain form and extracts parts of it, and listify is a kind of normalization function that will give you a list of expressions or statements.
I think the code is relatively straightforward: we have a list of "pattern -> body" statements. For each entry we create a fresh environment for the variables declared by the pattern and we try to match the pattern with the value. For matching, if a pattern is a variable name we set that variable in the environment, if it's a number or string we check for equality, and if it's a list of subpatterns we check that we have a list of the correct length and we check the subpatterns recursively. If there's a match, we execute the corresponding body.
If that interests you, I wrote a compile-to-JS language called Earl Grey (http://breuleux.github.io/earl-grey/repl/) using a similar parser and it has rather sophisticated pattern matching. The implementation is quite a lot more than 450 lines, though :)
The engine just has specific provisions to allow operators in "prefix position" to have different priority than in infix position, otherwise prefix minus would fail to work as expected.