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I wrote some prolog for a PL class recently and had to debug some cases of nontermination caused by the depth-first-search unification algorithm. I was wondering why prolog (or some other logic programming language) couldn't use breadth-first search instead, to avoid those cases, but couldn't find answers online - could someone who knows prolog better here have an answer?

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Other search algorithms can take up lots of memory to store progress they've made down different paths. Having only one active state also lets you map unification down to efficient low level cpu operations. If you have multiple states, you either have to copy lots of data when you fork the state or you use a persistent data structure but can't use side effects, so everything is a bit slower.

It's a tradeoff though. I work on miniKanren, which is a logic programming language with a complete search that doesn't hit the nontermination issues you mention. The complete search lets us do some pretty cool stuff with program synthesis (though we're not about to put any programmers out of business just yet): https://www.youtube.com/watch?v=er_lLvkklsk

Note that you can implement iterative deepening depth first search on top of prolog if you want a complete search there. Iterative deepening takes a little more time but avoids the memory problems with breath-first. SWI has tools built in to help there: http://www.swi-prolog.org/pldoc/doc_for?object=call_with_dep... And I believe Ciao implements its iterative deepening library with a meta-interpreter: https://ciao-lang.org/docs/ciao/id_doc.html#0

BFS space complexity is order exponential.

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