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#lang debug racket
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(require racket/generator)
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(provide (all-defined-out))
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(struct $csp ([vars #:mutable]
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[constraints #:mutable]) #:transparent)
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(define (make-csp) ($csp null null))
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(struct $var (name vals) #:transparent)
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(define $var-name? symbol?)
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(struct $constraint (names proc) #:transparent
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#:property prop:procedure
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(λ (constraint csp)
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(unless ($csp? csp)
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(raise-argument-error '$constraint-proc "$csp" csp))
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(match-define ($constraint names proc) constraint)
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(cond
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[(empty? names) (proc)]
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[else
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(match-define (cons name other-names) names)
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(for/and ([val (in-list ($csp-vals csp name))])
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;; todo: reconsider efficiency of currying every value
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(($constraint other-names (curry proc val)) csp))])))
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(define/contract (check-name-in-csp! caller csp name)
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(symbol? $csp? $var-name? . -> . void?)
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(define names (map $var-name ($csp-vars csp)))
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(unless (memq name names)
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(raise-argument-error caller (format "csp variable name: ~v" names) name)))
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(define (nary-constraint? constraint n)
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(= n (length ($constraint-names constraint))))
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(define/contract (unary-constraint? constraint)
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($constraint? . -> . boolean?)
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(nary-constraint? constraint 1))
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(define/contract (binary-constraint? constraint)
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($constraint? . -> . boolean?)
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(nary-constraint? constraint 2))
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(define/contract (add-vars! csp names [vals-or-procedure empty])
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(($csp? (listof $var-name?)) ((or/c (listof any/c) procedure?)) . ->* . void?)
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(for/fold ([vars ($csp-vars csp)]
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#:result (set-$csp-vars! csp vars))
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([name (in-list names)])
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(when (memq name (map $var-name vars))
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(raise-argument-error 'add-vars! "var that doesn't exist" name))
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(append vars
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(let ([vals (if (procedure? vals-or-procedure)
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(vals-or-procedure)
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vals-or-procedure)])
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(list ($var name vals))))))
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(define/contract (add-var! csp name [vals-or-procedure empty])
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(($csp? $var-name?) ((or/c (listof any/c) procedure?)) . ->* . void?)
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(add-vars! csp (list name) vals-or-procedure))
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(define/contract (add-constraint! csp proc var-names)
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($csp? procedure? (listof $var-name?) . -> . void?)
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(for ([name (in-list var-names)])
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(check-name-in-csp! 'add-constraint! csp name))
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(set-$csp-constraints! csp (append ($csp-constraints csp) (list ($constraint var-names proc)))))
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(define/contract (no-solutions? csp)
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($csp? . -> . boolean?)
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(for/or ([var (in-list ($csp-vars csp))])
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(empty? ($var-vals var))))
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(struct inconsistency-error () #:transparent)
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(define/contract (apply-unary-constraint csp constraint)
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($csp? unary-constraint? . -> . $csp?)
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(match-define ($constraint (list constraint-name) proc) constraint)
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(define new-csp ($csp (for/list ([var (in-list ($csp-vars csp))])
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(match-define ($var name vals) var)
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(if (eq? name constraint-name)
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;; special rule: use promise for a constant value
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;; to skip the filtering
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($var name (if (promise? proc)
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(force proc)
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(filter proc vals)))
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var))
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;; once the constraint is applied, it can go away
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;; ps this is not the same as an "assigned" constraint
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;; because the var may still have multiple values
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(remove constraint ($csp-constraints csp))))
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(when (no-solutions? new-csp) (raise (inconsistency-error)))
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new-csp)
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(define/contract (make-nodes-consistent csp)
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($csp? . -> . $csp?)
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(for/fold ([csp csp])
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([constraint (in-list ($csp-constraints csp))]
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#:when (unary-constraint? constraint))
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(apply-unary-constraint csp constraint)))
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(define/contract ($csp-vals csp name)
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($csp? $var-name? . -> . (listof any/c))
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(check-name-in-csp! '$csp-vals csp name)
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(for/first ([var (in-list ($csp-vars csp))]
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#:when (eq? name ($var-name var)))
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($var-vals var)))
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(struct $arc (name constraint) #:transparent)
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(define/contract (reduce-domains-by-arc csp arc)
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($csp? $arc? . -> . $csp?)
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(match-define ($arc name ($constraint names constraint-proc)) arc)
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(match-define (list other-name) (remove name names))
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(define proc (if (eq? name (first names)) ; name is on left
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constraint-proc ; so val goes on left
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(λ (val other-val) (constraint-proc other-val val)))) ; otherwise reverse arg order
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(define (satisfies-arc? val)
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(for/or ([other-val (in-list ($csp-vals csp other-name))])
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(proc val other-val)))
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(apply-unary-constraint csp ($constraint (list name)
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(procedure-rename
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satisfies-arc?
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(string->symbol (format "satisfies-arc-with-~a?" other-name))))))
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(define/contract (binary-constraints->arcs constraints)
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((listof binary-constraint?) . -> . (listof $arc?))
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(for*/list ([constraint (in-list constraints)]
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[name (in-list ($constraint-names constraint))])
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($arc name constraint)))
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(define/contract (terminating-at arcs name)
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((listof $arc?) $var-name? . -> . (listof $arc?))
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(for/list ([arc (in-list arcs)]
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#:when (eq? name (second ($constraint-names ($arc-constraint arc)))))
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arc))
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(define/contract (constraint-assigned? csp constraint)
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($csp? $constraint? . -> . any/c)
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(for/and ([name (in-list ($constraint-names constraint))])
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(memq name (map $var-name (assigned-vars csp)))))
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(define/contract (remove-assigned-constraints csp)
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($csp? . -> . $csp?)
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($csp
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($csp-vars csp)
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(for/list ([constraint (in-list ($csp-constraints csp))]
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#:unless (constraint-assigned? csp constraint))
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constraint)))
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(define/contract (ac-3 csp)
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($csp? . -> . $csp?)
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;; as described by AIMA @ 265
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(define all-arcs (binary-constraints->arcs (filter binary-constraint? ($csp-constraints csp))))
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(for/fold ([csp csp]
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[arcs all-arcs]
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#:result (remove-assigned-constraints csp))
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([i (in-naturals)]
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#:break (empty? arcs))
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(match-define (cons arc other-arcs) arcs)
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(match-define ($arc name _) arc)
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(define reduced-csp (reduce-domains-by-arc csp arc))
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(values reduced-csp (if (= (length ($csp-vals csp name)) (length ($csp-vals reduced-csp name)))
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;; revision did not reduce the domain, so keep going
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other-arcs
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;; revision reduced the domain, so supplement the list of arcs
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(remove-duplicates (append (all-arcs . terminating-at . name) other-arcs))))))
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(define/contract (make-arcs-consistent csp)
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($csp? . -> . $csp?)
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;; csp is arc-consistent if every pair of variables (x y)
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;; has values in their domain that satisfy every binary constraint
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(ac-3 csp))
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(define/contract (var-assigned? var)
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($var? . -> . boolean?)
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(= 1 (length ($var-vals var))))
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(define/contract (assignment-complete? csp)
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($csp? . -> . boolean?)
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(andmap var-assigned? ($csp-vars csp)))
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(define (assigned-helper csp) (partition var-assigned? ($csp-vars csp)))
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(define/contract (unassigned-vars csp)
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($csp? . -> . (listof $var?))
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(match-define-values (assigned unassigned) (assigned-helper csp))
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unassigned)
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(define/contract (assigned-vars csp)
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($csp? . -> . (listof $var?))
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(match-define-values (assigned unassigned) (assigned-helper csp))
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assigned)
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(define/contract (select-unassigned-var csp)
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($csp? . -> . $var?)
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(define uvars (unassigned-vars csp))
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(when (empty? uvars)
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(raise-argument-error 'select-unassigned-var "csp with unassigned vars" csp))
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;; minimum remaining values (MRV) rule
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(argmin (λ (var) (length ($var-vals var))) uvars))
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(define/contract (order-domain-values vals)
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((listof any/c) . -> . (listof any/c))
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;; todo: least constraining value sort
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vals)
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;; todo: inferences between assignments
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(define infer values)
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(define/contract (constraint-has-name? constraint name)
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($constraint? $var-name? . -> . boolean?)
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(and (memq name ($constraint-names constraint)) #true))
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(define/contract (assign-val csp name val)
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($csp? $var-name? any/c . -> . $csp?)
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(define csp-with-assignment (apply-unary-constraint csp ($constraint (list name) (delay (list val)))))
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(for/fold ([csp csp-with-assignment])
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([constraint (in-list ($csp-constraints csp))]
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#:when (and (constraint-has-name? constraint name)
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(constraint-assigned? csp constraint)))
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(unless (constraint csp) (raise (inconsistency-error)))
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(remove-assigned-constraints csp)))
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(define/contract (backtracking-solver csp)
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($csp? . -> . generator?)
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(generator ()
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(let backtrack ([csp (make-arcs-consistent (make-nodes-consistent csp))])
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(cond
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[(assignment-complete? csp) (yield csp)]
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[else ;; we have at least 1 unassigned var
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(match-define ($var name vals) (select-unassigned-var csp))
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(for ([val (in-list (order-domain-values vals))])
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(with-handlers ([inconsistency-error? void])
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(backtrack (infer (assign-val csp name val)))))]))))
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(define/contract (solve* csp [finish-proc values][solution-limit +inf.0])
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(($csp?) (procedure? integer?) . ->* . (listof any/c))
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(define solutions
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(for/list ([solution (in-producer (backtracking-solver csp) (void))]
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[idx (in-range solution-limit)])
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(finish-proc solution)))
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(unless (pair? solutions) (raise (inconsistency-error)))
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solutions)
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(define/contract (solve csp [finish-proc values])
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(($csp?) (procedure?) . ->* . any/c)
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(first (solve* csp finish-proc 1)))
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(define ($csp-ref csp name) (car ($csp-vals csp name)))
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(define/contract (alldiff . xs)
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(() #:rest (listof any/c) . ->* . boolean?)
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(= (length (remove-duplicates xs)) (length xs)))
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