I designed the Earl Grey language (http://breuleux.github.io/earl-grey/repl/ http://breuleux.github.io/earl-grey/repl/) on pretty much exactly the same principl

I designed the Earl Grey language (http://breuleux.github.io/earl-grey/repl/ http://breuleux.github.io/earl-grey/repl/) on pretty much exactly the same principle, it's pretty interesting to see someone else had the same idea. Operator precedence grammars are surprisingly powerful and pretty simple to write (you can write a working parser in ~100 lines of Python or JavaScript, including support for multifix). I did simplify the AST further than XL and added a few invariants. I have 3 leafs (literal, symbol, void) and 3 inner (send, multi, data). The inners roughly work like this: f x (send f x) [x] x [x, y, ...] (multi x y ...) {x, y, ...} (data x y ...) a + b (send + (data a b)) + a (send + (data (void) a)) a + (send + (data a (void))) [] serve as grouping brackets and are therefore purposefully erased from the parse tree if they only contain one expression. Prefix/postfix operators are interpreted as infix operators that have a blank operand on either side. Infix operators are themselves reduced to send/data, so "a + b" is equivalent to "[+]{a, b}". I find that a bit more robust and easier to manipulate generically.