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#lang debug racket
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(require racket/generator racket/control sugar/debug)
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(provide (all-defined-out))
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(struct $csp ([vars #:mutable]
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[constraints #:mutable]) #:transparent)
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(define (make-csp [vars null] [constraints null]) ($csp (for/list ([var (in-list vars)])
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(let loop ([var var])
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(match var
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[(list (? symbol? name) vals) (loop ($var name vals))]
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[($var name vals) ($varc name vals null)])))
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constraints))
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(define debug (make-parameter #false))
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(define-syntax-rule (in-cartesian x)
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(in-generator (let ([argss x])
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(let loop ([argss argss][acc empty])
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(if (null? argss)
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(yield (reverse acc))
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(for ([arg (in-list (car argss))])
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(loop (cdr argss) (cons arg acc))))))))
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(struct $var (name vals) #:transparent)
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(struct $varc $var (culprits) #: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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;; apply proc in many-to-many style
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(for/and ([args (in-cartesian (map (λ (cname) ($csp-vals csp cname)) ($constraint-names constraint)))])
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(apply ($constraint-proc constraint) args))))
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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 "one of these existing csp var names: ~v" names) name)))
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(define (nary-constraint? constraint n)
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(= n (constraint-arity 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-or-procedure [vals-or-procedure empty])
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(($csp? (or/c (listof $var-name?) procedure?)) ((or/c (listof any/c) procedure?)) . ->* . void?)
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(for/fold ([vars ($csp-vars csp)]
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#:result (set-$csp-vars! csp vars))
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([name (in-list (if (procedure? names-or-procedure)
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(names-or-procedure)
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names-or-procedure))])
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(when (memq name (map $var-name vars))
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(raise-argument-error 'add-vars! "var that doesn't already exist" name))
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(append vars (list ($varc name
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(if (procedure? vals-or-procedure)
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(vals-or-procedure)
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vals-or-procedure)
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null)))))
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(define/contract (add-var! csp name [vals-or-procedure empty])
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(($csp? $var-name?) ((or/c (listof any/c) procedure?)) . ->* . void?)
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(add-vars! csp (list name) vals-or-procedure))
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(define/contract (add-constraints! csp proc namess [proc-name #false])
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(($csp? procedure? (listof (listof $var-name?))) ((or/c #false $var-name?)) . ->* . void?)
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(set-$csp-constraints! csp (append ($csp-constraints csp)
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(for/list ([names (in-list namess)])
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(for ([name (in-list names)])
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(check-name-in-csp! 'add-constraints! csp name))
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($constraint names (if proc-name
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(procedure-rename proc proc-name)
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proc))))))
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(define/contract (add-pairwise-constraint! csp proc var-names [proc-name #false])
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(($csp? procedure? (listof $var-name?)) ($var-name?) . ->* . void?)
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(add-constraints! csp proc (combinations var-names 2) proc-name))
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(define/contract (add-constraint! csp proc var-names [proc-name #false])
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(($csp? procedure? (listof $var-name?)) ($var-name?) . ->* . void?)
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(add-constraints! csp proc (list var-names) proc-name))
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(define/contract (no-solutions? csp)
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($csp? . -> . boolean?)
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(zero? (state-count csp)))
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(struct inconsistency-signal (csp) #:transparent)
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(define use-reduce-arity? (make-parameter #t))
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(define use-mac? (make-parameter #t))
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(define use-remove-constraints? (make-parameter #t))
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(define use-validate-assignments? (make-parameter #t))
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(define/contract (apply-unary-constraint csp constraint #:culprit [culprit #f])
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(($csp? unary-constraint?) (#:culprit (or/c #f $var-name?)) . ->* . $csp?)
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(define (update-csp-vars name vals)
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(for/list ([var (in-list ($csp-vars csp))])
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(define new-culprits (if (and culprit (< (length vals) (length ($var-vals var))))
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(remove-duplicates (cons culprit ($varc-culprits var)) eq?)
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($varc-culprits var)))
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(if (eq? ($var-name var) name)
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($varc name vals new-culprits)
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var)))
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(match-define ($constraint (list name) proc) constraint)
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(match (if (promise? proc)
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(force proc)
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(filter proc ($csp-vals csp name)))
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[(list) (raise (inconsistency-signal csp))]
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[(list assigned-val) ((if (use-validate-assignments?) make-nodes-consistent values)
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((if (use-remove-constraints?) remove-assigned-constraints values)
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((if (use-reduce-arity?) reduce-constraint-arity values)
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((if (use-validate-assignments?) validate-assignments values)
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(let ([csp ($csp
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(update-csp-vars name (list assigned-val))
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($csp-constraints csp))])
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(if (use-mac?)
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(make-arcs-consistent csp #:mac name)
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csp))))))]
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[(list new-vals ...) ($csp (update-csp-vars name new-vals)
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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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(if (use-remove-constraints?)
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(remove constraint ($csp-constraints csp))
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($csp-constraints 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 ($csp-var csp name)
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($csp? $var-name? . -> . $var?)
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(check-name-in-csp! '$csp-var 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))
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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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($var-vals ($csp-var csp name)))
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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 ($constraint names constraint-proc)) arc)
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(match-define (list other-name) (remove name names))
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(define proc (if (eq? name (first names)) ; name is on left
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constraint-proc ; so val stays on left
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(λ (val other-val) (constraint-proc other-val val)))) ; otherwise reverse arg order
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(define (satisfies-arc? val)
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(for/or ([other-val (in-list ($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 "~a-arc-to-~a" (object-name proc) other-name))))
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#:culprit 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 $arc?))
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(for/list ([arc (in-list arcs)]
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#:when (and
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(memq name ($constraint-names ($arc-constraint arc)))
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(not (eq? name ($arc-name 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 $var-name (assigned-vars csp)))))
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(define/contract (remove-assigned-constraints csp [arity #false])
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(($csp?) ((or/c #false exact-nonnegative-integer?)) . ->* . $csp?)
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($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 (and (if arity (= arity (constraint-arity constraint)) #true)
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(constraint-assigned? csp constraint)))
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constraint)))
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(define/contract (make-arcs-consistent csp #:mac [mac-name #f])
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(($csp?) (#:mac (or/c $var-name? #f)) . ->* . $csp?)
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;; csp is arc-consistent if every pair of variables (x y)
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;; has values in their domain that satisfy every binary constraint
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;; AC-3 as described by AIMA @ 265
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(define (mac-condition? arc)
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(and
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(constraint-contains-name? ($arc-constraint arc) mac-name)
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(memq ($arc-name arc) (map $var-name (unassigned-vars csp)))))
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(define starting-arcs
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(for/list ([arc (in-list (binary-constraints->arcs (filter binary-constraint? ($csp-constraints csp))))]
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#:when ((if mac-name mac-condition? values) arc))
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arc))
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(for/fold ([csp csp]
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[arcs starting-arcs]
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#:result csp)
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([i (in-naturals)]
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#:break (empty? arcs))
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(match-define (cons ($arc name proc) other-arcs) arcs)
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(define reduced-csp (reduce-domains-by-arc csp ($arc name proc)))
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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 (starting-arcs . terminating-at . name) other-arcs))))))
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(define/contract (var-assigned? var)
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($var? . -> . boolean?)
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(= 1 (remaining-values var)))
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(define/contract (solution-complete? csp)
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($csp? . -> . 'lean?)
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(and (andmap var-assigned? ($csp-vars csp)) (empty? ($csp-constraints 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 $var?))
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(match-define-values (assigned unassigned) (assigned-helper csp))
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assigned)
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(define/contract (constraint-arity constraint)
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($constraint? . -> . exact-nonnegative-integer?)
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(length ($constraint-names constraint)))
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(define/contract (var-degree csp var)
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($csp? $var? . -> . exact-nonnegative-integer?)
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(for/sum ([constraint (in-list ($csp-constraints csp))]
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#:when (constraint-contains-name? constraint ($var-name var)))
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1))
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(define use-mrv? (make-parameter #t))
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(define/contract (select-unassigned-var csp)
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($csp? . -> . (or/c #f $var?))
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(match (unassigned-vars csp)
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[(list) #f]
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[(list uvars ...)
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(cond
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[(use-mrv?)
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;; minimum remaining values (MRV) rule
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(define mrv-arg (argmin remaining-values uvars))
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(match (filter (λ (var) (= (remaining-values mrv-arg) (remaining-values var))) uvars)
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[(list winning-uvar) winning-uvar]
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[(list mrv-uvars ...)
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;; use degree as tiebreaker for mrv
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(define max-degree-arg (argmax (λ (var) (var-degree csp var)) mrv-uvars))
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;; use random tiebreaker for degree
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(first (shuffle (filter (λ (var) (= (var-degree csp max-degree-arg) (var-degree csp var))) mrv-uvars)))])]
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[else (first uvars)])]))
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(define/contract (order-domain-values vals)
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((listof any/c) . -> . (listof any/c))
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;; todo: least constraining value sort
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vals)
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(define/contract (constraint-contains-name? constraint name)
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($constraint? $var-name? . -> . boolean?)
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(and (memq name ($constraint-names constraint)) #true))
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(define/contract (validate-assignments csp)
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($csp? . -> . $csp?)
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(define assigned-constraints (filter (λ (c) (constraint-assigned? csp c)) ($csp-constraints csp)))
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(for ([constraint (in-list (sort assigned-constraints < #:key constraint-arity))]
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#:unless (constraint csp))
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(raise (inconsistency-signal csp)))
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csp)
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(define/contract (assign-val csp name val)
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($csp? $var-name? any/c . -> . $csp?)
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(check-name-in-csp! 'assign-val csp name)
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(define assignment-constraint ($constraint (list name) (delay (list val))))
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(apply-unary-constraint csp assignment-constraint))
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(define/contract (assign-val! csp name val)
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($csp? $var-name? any/c . -> . void?)
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(check-name-in-csp! 'assign-val! csp name)
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(define new-csp (assign-val csp name val))
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(set-$csp-vars! csp ($csp-vars new-csp))
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(set-$csp-constraints! csp ($csp-constraints new-csp)))
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(define (reduce-arity proc pattern)
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(unless (match (procedure-arity proc)
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[(arity-at-least val) (<= val (length pattern))]
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[(? number? val) (= val (length pattern))])
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(raise-argument-error 'reduce-arity (format "list of length ~a, same as procedure arity" (procedure-arity proc)) pattern))
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(define reduced-arity-name (string->symbol (format "reduced-arity-~a" (object-name proc))))
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(define-values (id-names vals) (partition symbol? pattern))
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(define new-arity (length id-names))
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(procedure-rename
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(λ xs
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(unless (= (length xs) new-arity)
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(apply raise-arity-error reduced-arity-name new-arity xs))
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(apply proc (for/fold ([acc empty]
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[xs xs]
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[vals vals]
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#:result (reverse acc))
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([pat-item (in-list pattern)])
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(if (symbol? pat-item)
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(values (cons (car xs) acc) (cdr xs) vals)
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(values (cons (car vals) acc) xs (cdr vals))))))
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reduced-arity-name))
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(define/contract (assigned-name? csp name)
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($csp? $var-name? . -> . boolean?)
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(and (memq name (map $var-name (assigned-vars csp))) #true))
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(define/contract (reduce-constraint-arity csp [minimum-arity #false])
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(($csp?) ((or/c #false exact-nonnegative-integer?)) . ->* . $csp?)
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(let ([assigned-name? (curry assigned-name? csp)])
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(define (partially-assigned? constraint)
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(ormap assigned-name? ($constraint-names constraint)))
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($csp ($csp-vars csp)
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(for/list ([constraint (in-list ($csp-constraints csp))])
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(cond
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[(and (if minimum-arity (<= minimum-arity (constraint-arity constraint)) #true)
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(partially-assigned? constraint))
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(match-define ($constraint cnames proc) constraint)
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($constraint (filter-not assigned-name? cnames)
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;; pattern is mix of values and symbols (indicating variables to persist)
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(let ([reduce-arity-pattern (for/list ([cname (in-list cnames)])
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(if (assigned-name? cname)
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($csp-ref csp cname)
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cname))])
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(reduce-arity proc reduce-arity-pattern)))]
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[else constraint])))))
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(define/contract (conflict-set csp name)
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($csp? $var-name? . -> . (listof $var-name?))
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;; earlier assigned variables that participate in constraints with name
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(define assigned-names (reverse (map $var-name (assigned-vars csp))))
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(define earlier-assigned-names (memq name assigned-names))
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(for*/list ([constraint (in-list ($csp-constraints csp))]
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[cnames (in-value ($constraint-names constraint))]
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#:when (and (andmap (λ (cname) (memq cname earlier-assigned-names)) cnames)
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(constraint-contains-name? constraint name))
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[cname (in-list cnames)]
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#:unless (eq? cname name))
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cname))
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(define use-cdj? (make-parameter #f))
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(define/contract (select-k sig name krecs)
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(inconsistency-signal? $var-name? (listof (cons/c $var-name? continuation?)) . -> . continuation?)
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;; select the most recent (ie topmost) k that is in the signal
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;; todo: repair backjumping
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(cond
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[(use-cdj?)
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(define assigned-names (map car krecs)) ; already in reverse chron order
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(define csp (inconsistency-signal-csp sig))
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(define backjump-dest
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(let loop ([name name][cset (conflict-set csp name)])
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(define next-name (for/first ([previously-assigned-name (in-list (memq name assigned-names))]
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#:when (memq previously-assigned-name cset))
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previously-assigned-name))
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(define next-cset (conflict-set csp next-name))
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(if (empty? next-cset)
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next-name
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(loop next-name (remq next-name (remove-duplicates (append next-cset cset) eq?))))))
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(cdr (assq backjump-dest krecs))]
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[else (cdr (first krecs))]))
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(define/contract (backtrack-solution-generator csp)
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($csp? . -> . generator?)
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;; as described by AIMA @ 271
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(generator () (let backtrack ([csp (make-arcs-consistent (make-nodes-consistent csp))]
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[backjump-krecs null])
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(match (select-unassigned-var csp)
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[#f (yield ($csp (for/list ([v (in-list ($csp-vars csp))])
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(match v
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[($varc name vals _) ($var name vals)]
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[(? $var? v) v]))
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($csp-constraints csp)))]
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[($var name vals)
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(call/prompt
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(thunk
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(for ([val (in-list (order-domain-values vals))])
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(let/cc backjump-k
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(let ([backjump-krecs (cons (cons name backjump-k) backjump-krecs)])
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(with-handlers ([inconsistency-signal?
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(λ (sig)
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(define backjump-k (select-k sig name backjump-krecs))
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(backjump-k))])
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(backtrack (assign-val csp name val) backjump-krecs)))))))]))))
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(define/contract (solve* csp [finish-proc values][solution-limit +inf.0])
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(($csp?) (procedure? integer?) . ->* . (non-empty-listof any/c))
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(define solutions
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(for/list ([solution (in-producer (backtrack-solution-generator 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-signal csp)))
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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) (first ($csp-vals csp name)))
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(define/contract (alldiff . xs)
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(() #:rest (listof any/c) . ->* . boolean?)
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(= (length (remove-duplicates xs)) (length xs)))
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(define/contract (alldiff= x y)
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(any/c any/c . -> . boolean?)
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(not (= x y)))
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(define/contract (remaining-values var)
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|
($var? . -> . exact-nonnegative-integer?)
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|
(length ($var-vals var)))
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|
|
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|
(define/contract (state-count csp)
|
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|
($csp? . -> . exact-nonnegative-integer?)
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(for/product ([var (in-list ($csp-vars csp))])
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|
(remaining-values var))) |