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Logic Programming is Underrated

09 March 2013

Mark Engelberg wrote a very interesting post titled Logic Programming is Overrated. I take issue with a quite a few points made in that post and I would like to address a couple of them here.

First off, yes, list comprehensions are an excellent concise, readable way to do search when the search is reasonably small and when you don't really care about performance. That said making any judgements about core.logic and its utility for solving problems based on blog post code written by someone having a bit of fun makes little sense in my opinion - imagine judging the utility of object oriented or functional programming this way.

What follows is an explanation of how I would approach the problem. The main insight here is the original problem is a finite domain problem in disguise - surprisingly similar to solving sudoku!

My solution solves the puzzle about five times faster on my machine than Mark's optimized list comprehension version without any change to the order of the rules.

Admittedly, Mark's version wins on the readability and concision fronts due to the moving between keywords and integers in my code. This could be avoided with support for CLP(Set) which is on the roadmap for core.logic and I sketch my ideal puzzle solution near the bottom of the post.

Here's my approach to the puzzle solution:

(defn puzzle []
  (let [vs (take 20 (repeatedly lvar))
        ps (->> (partition 4 vs)
             (map #(into {}
               (map vector [:name :cheese :mag :reserv] %)))
             (into []))]
    (run* [q]
      (== q ps)
      (everyg #(fd/in % (fd/interval 1 5)) vs)
      (everyg fd/distinct (apply map vector (map vals ps)))
        [(ruleo q :name :landon :reserv :730pm)
         (ruleo q :name :jason :cheese :mozzarella)]
        [(ruleo q :name :landon :cheese :mozzarella)
         (ruleo q :name :jason :reserv :730pm)]) ;; 1
      (ruleo q :cheese :blue :mag :fortune) ;; 2
      (neg-ruleo q :cheese :muenster :mag :vogue) ;; 3
      (peopleo q
        [[:mag :fortune] [:name :landon] [:reserv :5pm]
         [:cheese :mascarpone] [:mag :vogue]]) ;; 4
      (neg-ruleo q :reserv :5pm :mag :time) ;; 5
      (earliero q :mag :cosmopolitan :cheese :mascarpone) ;; 6
      (earliero q :cheese :blue :name :bailey) ;; 7
        [(ruleo q :reserv :7pm :mag :fortune)]
        [(ruleo q :reserv :730pm :mag :fortune)]) ;; 8
      (earliero q :mag :time :name :landon) ;; 9
      (neg-ruleo q :name :jamari :mag :fortune) ;; 10
      (ruleo q :reserv :5pm :cheese :mozzarella)))) ;; 11

This above solution takes about 84ms if we only ask for the first solution on my machine compared to about 430ms with a list comprehension. If we call doall instead of first on the result of invoking puzzle, it takes 270ms to determine there is only one solution. This is still faster than the list comprehension.

How can a solution like this with no goal reordering outperform a tuned list comprehension given the copious use of unification, constraints, membero and other costly high level stuff? I mention some great books below which give insights into the how and why.

In summary, do you need logic programming to solve logic puzzles? Absolutely not! Should you implement logic puzzles using core.logic? Most definitely! Importantly, you must try both approaches in order to understand the tradeoffs. What bothered me about Mark's post was the abundance of opinions with little evidence of core.logic experience.

You can see the entire solution for the puzzle here. Again I'm not completely satisfied with this, I look forward to something more like this, which in my humble opinion, is pretty sweet.

As to whether logic programming is useful for "real world" problems, I recommend picking up a Bratko's 4th edition of Prolog Programming for Artificial Intelligence and/or Concepts, Techniques, and Models of Computer Programming. Both are eye-opening as far as how broadly these approaches can be applied.

If you don't trust books talk to Martin Trojer who has used core.logic at the bank UBS or talk to ThreatGRID - they run core.logic on a 12 64-core blade cluster to do threat analysis on the fly (with the rules written by domain experts - I guess the DSL isn't too "complex" for them).

Mark's post had plenty of valid points like better integration with Clojure, tracing goal execution, integration with external solvers, we're working on it.