sudoku_compact.clj

gistfile1.clj

;; based on core.logic 0.8-alpha2 or core.logic master branch

(ns sudoku
  (:refer-clojure :exclude [==])
  (:use clojure.core.logic))

(defn get-square [rows x y]
  (for [x (range x (+ x 3))
        y (range y (+ y 3))]
    (get-in rows [x y])))

(defn init [vars hints]
  (if (seq vars)
    (let [hint (first hints)]
      (all
        (if-not (zero? hint)
          (== (first vars) hint)
          succeed)
        (init (next vars) (next hints))))
    succeed))

(defn sudokufd [hints]
  (let [vars (repeatedly 81 lvar) 
        rows (->> vars (partition 9) (map vec) (into []))
        cols (apply map vector rows)
        sqs  (for [x (range 0 9 3)
                   y (range 0 9 3)]
               (get-square rows x y))]
    (run 1 [q]
      (== q vars)
      (everyg #(infd % (domain 1 2 3 4 5 6 7 8 9)) vars)
      (init vars hints)
      (everyg distinctfd rows)
      (everyg distinctfd cols)
      (everyg distinctfd sqs))))

;; ====

(comment
  (sudokufd
    [0 0 3  0 2 0  6 0 0
     9 0 0  3 0 5  0 0 1
     0 0 1  8 0 6  4 0 0

     0 0 8  1 0 2  9 0 0
     7 0 0  0 0 0  0 0 8
     0 0 6  7 0 8  2 0 0

     0 0 2  6 0 9  5 0 0
     8 0 0  2 0 3  0 0 9
     0 0 5  0 1 0  3 0 0])
)

I am not trying to accomplish anything in particular, apart from simply trying to understand the small example you gave in one of your comments on the HN thread (which has proven to be surprinsingly harder than I assumed, perhaps due to the fact that my Prolog skills are farther than I thought, and/or that the CL doc is rather sparse for the moment). In particular, I wanted to understand how to reverse the goal (i.e. find the triples for which x + y != z). My first attempt was to use the "disequality" contraint, but since I could not make sense of its result:

(run* [q]
    (fresh [x y z]
        (infd x y z (interval 1 3))
        (+fd x y z)
        (!= q [x y z])))
;; => ((_.0 :- (!= _.0 [<lvar:x_4549> <lvar:y_4550> <lvar:z_4551>])))

my second attempt was the code I posted earlier (using "project"). I now understand that an interval is a special CL object that does not interoperate with normal Clojure arithmetic ops, and I guess it means I would have to write a function similar to "+fd", but unfortunately that's where it stops for me, as I simply cannot understand its source code for the moment.

@cjauvin

  (run* [q]
    (fresh [x y z n]
      (infd x y z n (interval 1 3))
      (+fd x y n)
      (!=fd z n)
      (== q [x y z])))

Is probably what you want.

It makes good sense.. many thanks! I guess I'll have no other choice than to go through The Reasoned Schemer, to go deeper.

Hey David, where did "infd" go? It's nowhere to be found in the master branch. thx!

@postspectacular - it's in clojure.core.logic.fd now. Here's an updated version that I've been using in my core.logic talks:

https://gist.github.com/orb/5884956

Dead link: http://dosync.posterous.com/friendlier-shorter. Posterous Spaces are no longer available. Has this been republished elsewhere?

https://web.archive.org/web/20130511050728/http://dosync.posterous.com/friendlier-shorter