zlacker

Depth-first backtracking is trivial to implement, and it's trivial to blend into the language. Breadth-first backtracking is much harder to implement, and I'm not sure that it's trivial to build into a language (though this may be a lack of imagination).

Icon had both, but depth-first backtracking was the default and trivial to use, while breadth-first backtracking required using "co-expressions" (co-routines), though at least Icon had a trivial syntax for causing procedure argument expressions to be made into co-expressions. But Icon's approach does not make breadth-first backtracking be a first-class language feature like depth-first backtracking, and this is where my imagination gets stuck. To be fair, I've not truly thought much about this problem.