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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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(struct $constraint (names proc) #:transparent)
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(struct $var (name domain) #:transparent)
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(define $var-name? symbol?)
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(struct $cvar $var (past) #:transparent)
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(struct $avar $var () #:transparent)
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(struct inconsistency-signal (csp) #:transparent)
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(struct $backtrack (names) #:transparent)
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(define current-select-variable (make-parameter #f))
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(define current-order-values (make-parameter #f))
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(define current-inference (make-parameter #f))
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(define current-solver (make-parameter #f))
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(define current-shuffle (make-parameter #t))
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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/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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($var-domain ($csp-var csp name)))
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(define order-domain-values values)
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(define/contract (assign-val csp name val)
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($csp? $var-name? any/c . -> . $csp?)
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($csp
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(for/list ([var ($csp-vars csp)])
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(if (eq? name ($var-name var))
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($avar name (list val))
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var))
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($csp-constraints csp)))
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(define (unassigned-vars csp)
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(for/list ([var (in-list ($csp-vars csp))]
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#:unless ($avar? var))
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var))
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(define/contract (first-unassigned-variable csp)
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($csp? . -> . (or/c #false (and/c $var? (not/c $avar?))))
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(match (unassigned-vars csp)
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[(? empty?) #false]
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[xs (first xs)]))
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(define/contract (argmin-random-tie proc xs)
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(procedure? (non-empty-listof any/c) . -> . any/c)
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(define ordered-xs (sort xs < #:key proc))
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(first ((if (current-shuffle) shuffle values)
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(takef ordered-xs (λ (x) (= (proc (car ordered-xs)) (proc x)))))))
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(define/contract (minimum-remaining-values csp)
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($csp? . -> . (or/c #false (and/c $var? (not/c $avar?))))
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(struct $mrv-rec (var num) #:transparent)
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(match (unassigned-vars csp)
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[(? empty?) #false]
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[xs (argmin-random-tie (λ (var) (length ($var-domain var))) xs)]))
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(define first-domain-value values)
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(define (no-inference csp name) csp)
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(define/contract (relating constraints names)
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((listof $constraint?) (listof $var-name?) . -> . (listof $constraint?))
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(for*/list ([constraint (in-list constraints)]
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[cnames (in-value ($constraint-names constraint))]
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#:when (for/and ([name (in-list names)])
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(memq name cnames)))
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constraint))
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(define/contract (forward-check csp aname)
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($csp? $var-name? . -> . $csp?)
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(define aval (first ($csp-vals csp aname)))
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(define (check-var var)
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(match var
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;; don't check against assigned vars, or the reference var
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;; (which is probably assigned but maybe not)
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[(? (λ (x) (or ($avar? x) (eq? ($var-name x) aname)))) var]
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[($var name vals)
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(match (($csp-constraints csp) . relating . (list aname name))
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[(? empty?) var]
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[constraints
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(define new-vals
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(for/list ([val (in-list vals)]
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#:when (for/and ([constraint (in-list constraints)])
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(let ([proc ($constraint-proc constraint)])
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(if (eq? name (first ($constraint-names constraint)))
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(proc val aval)
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(proc aval val)))))
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val))
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($cvar name new-vals (cons aname (if ($cvar? var)
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($cvar-past var)
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null)))])]))
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(define checked-vars (map check-var ($csp-vars csp)))
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;; conflict-set will be empty if there are no empty domains
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(define conflict-set (for*/list ([var (in-list checked-vars)]
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#:when (empty? ($var-domain var))
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[name (in-list ($cvar-past var))])
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name))
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;; for conflict-directed backjumping it's essential to forward-check ALL vars
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;; (even after an empty domain is generated) and combine their conflicts
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;; so we can discover the *most recent past var* that could be the culprit.
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;; If we just bail out at the first conflict, we may backjump too far based on its history
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;; (and thereby miss parts of the search tree)
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(when (pair? conflict-set)
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(raise ($backtrack conflict-set)))
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($csp checked-vars ($csp-constraints csp)))
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(define/contract (backtracking-solver
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csp
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#:select-variable [select-unassigned-variable
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(or (current-select-variable) first-unassigned-variable)]
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#:order-values [order-domain-values (or (current-order-values) first-domain-value)]
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#:inference [inference (or (current-inference) no-inference)])
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(($csp?) (#:select-variable procedure? #:order-values procedure? #:inference procedure?) . ->* . generator?)
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(generator ()
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(let loop ([csp csp])
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(match (select-unassigned-variable csp)
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[#false (yield csp)]
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[($var name domain)
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(define (wants-backtrack? exn)
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(and ($backtrack? exn) (memq name ($backtrack-names exn))))
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(for/fold ([conflicts null]
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#:result (void))
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([val (in-list (order-domain-values domain))])
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(with-handlers ([wants-backtrack?
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(λ (bt) (append conflicts (remq name ($backtrack-names bt))))])
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(define csp-with-assignment (assign-val csp name val))
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(loop (inference csp-with-assignment name)))
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conflicts)]))))
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(define/contract (solution-consistent? solution)
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($csp? . -> . boolean?)
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(for/and ([c (in-list ($csp-constraints solution))])
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(apply ($constraint-proc c) (for*/list ([name (in-list ($constraint-names c))]
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[var (in-list ($csp-vars solution))]
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#:when (eq? name ($var-name var)))
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(first ($var-domain var))))))
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(define/contract ($csp-assocs csp)
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($csp? . -> . (listof (cons/c $var-name? any/c)))
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(for/list ([var (in-list ($csp-vars csp))])
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(match var
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[($var name domain) (cons name (first domain))])))
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(define/contract (solve* csp
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#:finish-proc [finish-proc $csp-assocs]
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#:solver [solver (or (current-solver) backtracking-solver)]
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#:count [max-solutions +inf.0])
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(($csp?) (#:finish-proc procedure? #:solver procedure? #:count integer?) . ->* . (listof any/c))
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(for/list ([solution (in-producer (solver csp) (void))]
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[idx (in-range max-solutions)])
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(unless (solution-consistent? solution)
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(raise (list 'wtf solution)))
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(finish-proc solution)))
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(define/contract (solve csp
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#:finish-proc [finish-proc $csp-assocs]
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#:solver [solver (or (current-solver) backtracking-solver)])
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(($csp?) (#:finish-proc procedure? #:solver procedure?) . ->* . (or/c #false any/c))
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(match (solve* csp #:finish-proc finish-proc #:solver solver #:count 1)
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[(list solution) solution]
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[else #false]))
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(define (<> a b) (not (= a b)))
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(define (neq? a b) (not (eq? a b)))
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