fresh implementation

csp/csp.rkt

@@ -0,0 +1,161 @@
+#lang debug racket
+
+(struct $csp ([vars #:mutable]
+              [constraints #:mutable]) #:transparent)
+
+(struct $var (name vals) #:transparent)
+(define $var-name? symbol?)
+(struct $constraint (names proc) #:transparent)
+
+(define/contract (check-name-in-csp! caller csp name)
+  (symbol? $csp? $var-name? . -> . void?)
+  (define names (map $var-name ($csp-vars csp)))
+  (unless (memq name names)
+    (raise-argument-error caller (format "csp variable name: ~v" names) name)))
+
+(define/contract (nary-constraint? constraint num)
+  ($constraint? exact-nonnegative-integer? . -> . boolean?)
+  (= num (length ($constraint-names constraint))))
+
+(define/contract (unary-constraint? constraint)
+  ($constraint? . -> . boolean?)
+  (nary-constraint? constraint 1))
+
+(define/contract (binary-constraint? constraint)
+  ($constraint? . -> . boolean?)
+  (nary-constraint? constraint 2))
+
+(define/contract (add-var! csp name [vals empty])
+  (($csp? $var-name?) ((listof any/c)) . ->* . void?)
+  (when (memq name (map $var-name ($csp-vars csp)))
+    (raise-argument-error 'add-var! "var that doesn't exist" name))
+  (set-$csp-vars! csp (cons ($var name vals) ($csp-vars csp))))
+
+(define/contract (add-constraint! csp proc var-names)
+  ($csp? procedure? (listof $var-name?) . -> . void?)
+  (for ([name (in-list var-names)])
+       (check-name-in-csp! 'add-constraint! csp name))
+  (set-$csp-constraints! csp (cons ($constraint var-names proc) ($csp-constraints csp))))
+
+(define/contract (apply-unary-constraint csp constraint)
+  ($csp? unary-constraint? . -> . $csp?)
+  (match-define ($constraint (list constraint-name) proc) constraint)
+  (check-has-solutions!
+   ($csp (for/list ([var (in-list ($csp-vars csp))])
+                   (match-define ($var name vals) var)
+                   (if (eq? name constraint-name)
+                       ($var name (filter proc vals))
+                       var))
+         ;; once the constraint is applied, it can go away
+         (remove constraint ($csp-constraints csp)))))
+
+(define/contract (no-solutions? csp)
+  ($csp? . -> . boolean?)
+  (for/or ([var (in-list ($csp-vars csp))])
+          (empty? ($var-vals var))))
+
+(define/contract (check-has-solutions! csp)
+  ($csp? . -> . $csp?)
+  (when (no-solutions? csp) (raise 'no-solutions))
+  csp)
+
+(define/contract (make-node-consistent csp)
+  ($csp? . -> . $csp?)
+  (for/fold ([csp csp])
+            ([constraint (in-list ($csp-constraints csp))]
+             #:when (unary-constraint? constraint))
+    (apply-unary-constraint csp constraint)))
+
+(define/contract ($csp-vals csp name)
+  ($csp? $var-name? . -> . (listof any/c))
+  (check-name-in-csp! '$csp-vals csp name)
+  (for/first ([var (in-list ($csp-vars csp))]
+              #:when (eq? name ($var-name var)))
+             ($var-vals var)))
+
+(struct $arc (name constraint) #:transparent)
+
+(define/contract (revise csp arc)
+  ($csp? $arc? . -> . $csp?)
+  (match-define ($arc name ($constraint names constraint-proc)) arc)
+  (match-define (list other-name) (remove name names))
+  (define proc (if (eq? name (first names)) ; name is on left
+                   constraint-proc ; so val goes on left
+                   (λ (val other-val) (constraint-proc other-val val)))) ; otherwise reverse arg order
+  (define (satisfies-arc? val)
+    (for/or ([other-val (in-list ($csp-vals csp other-name))])
+            (proc val other-val)))
+  (apply-unary-constraint csp ($constraint (list name)
+                                           (procedure-rename
+                                            satisfies-arc?
+                                            (string->symbol (format "satisfies-arc-with-~a?" other-name))))))
+
+(define/contract (binary-constraints->arcs constraints)
+  ((listof binary-constraint?) . -> . (listof $arc?))
+  (for*/list ([constraint (in-list constraints)]
+              [name (in-list ($constraint-names constraint))])
+             ($arc name constraint)))
+
+(define/contract (terminating-at arcs name)
+  ((listof $arc?) $var-name? . -> . (listof $arc?))
+  ;; #true if name is in constraint name list and is not name of arc
+  (for/list ([arc (in-list arcs)]
+             #:when (and
+                     (not (eq? name ($arc-name arc)))
+                     (memq name ($constraint-names ($arc-constraint arc)))))
+            arc))
+
+(define/contract (ac-3 csp)
+  ($csp? . -> . $csp?)
+  ;; as described by AIMA @ 265
+  (define all-arcs (binary-constraints->arcs (filter binary-constraint? ($csp-constraints csp))))
+  (for/fold ([csp csp]
+             [arcs all-arcs]
+             #:result csp)
+            ([i (in-naturals)]
+             #:break (empty? arcs))
+    (match-define (cons arc other-arcs) arcs)
+    (match-define ($arc name _) arc)
+    (define revised-csp (revise csp arc))
+    (values revised-csp (if (= (length ($csp-vals csp name)) (length ($csp-vals revised-csp name)))
+                            ;; revision did not reduce the domain, so keep going
+                            other-arcs
+                            ;; revision reduced the domain, so supplement the list of arcs
+                            (remove-duplicates (append (all-arcs . terminating-at . name) other-arcs))))))
+
+(define/contract (make-arc-consistent csp)
+  ($csp? . -> . $csp?)
+  ;; csp is arc-consistent if every pair of variables (x y)
+  ;; has values in their domain that satisfy every binary constraint
+  (ac-3 csp))
+
+(define/contract (solve csp)
+  ($csp? . -> . any/c)
+  ;; todo: backtracking search
+  ($csp-vars (make-arc-consistent (make-node-consistent csp))))
+
+
+(define csp ($csp empty empty))
+
+(define digits (range 7))
+(add-var! csp 't digits)
+(add-var! csp 'w digits)
+(add-var! csp 'o '(2 6 7))
+
+(define (sum-three t w o) (= 3 (+ t w o)))
+(add-constraint! csp sum-three '(t w o))
+
+(define diff (compose1 not =))
+(add-constraint! csp diff '(t w))
+(add-constraint! csp diff '(w o))
+(add-constraint! csp diff '(t o))
+
+(add-constraint! csp < '(t w))
+
+(define three-or-less (curryr <= 3))
+(add-constraint! csp three-or-less '(t))
+(add-constraint! csp three-or-less '(w))
+(add-constraint! csp three-or-less '(o))
+
+csp
+(solve csp)