Barliman: trying the halting problem backwards, blindfolded - William Byrd, Greg Rosenblatt

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): [VIDEO] 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: [LINK] And I believe Ciao implements its iterative deepening library with a meta-interpreter: [LINK]

For anyone who finds this topic interesting, you might be interested in the following resources: [LINK] The second edition of `The Reasoned Schemer` (MIT Press, 2018): [LINK] The Clojure/conj 2016 talk Greg Rosenblatt and I gave on Barliman: [VIDEO] `A Unified Approach to Solving Seven Programming Problems (Functional Pearl)`, William E. Byrd, Michael Ballantyne, Gregory Rosenblatt, Matthew Might (ICFP 2017) (Open Access): [LINK] and the related talk: [LINK] and Nada Amin's interactive version of the paper: [LINK] Cheers, --Will

You might enjoy this amazing talk. I've linked to a part when the next 20 seconds of explanation turns the amazing up to 11. [VIDEO]

Have you checked out any of the minikanren logic programming environments people have implemented in scheme? The Reasoned Schemer is an accessible introduction to that space if you’re not put off by the socratic-themed dialogue. & the Barliman demo is still pretty exciting even after LLM codegen. [VIDEO]