typesetting/csp/csp.rkt

#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)