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@ -2,16 +2,27 @@
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(require racket/generator graph)
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(provide (all-defined-out))
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(define-syntax when-debug
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(let ()
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(define debug #f)
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(if debug
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(make-rename-transformer #'begin)
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(λ (stx) (syntax-case stx ()
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[(_ . rest) #'(void)])))))
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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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(loop (cdr argss) (cons arg acc))))))))
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(struct $csp ([vars #:mutable]
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[constraints #:mutable]) #:transparent)
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(struct $csp (vars
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constraints
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[assignments #:auto]
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[checks #:auto]) #:mutable #:transparent
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#:auto-value 0)
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(define csp? $csp?)
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(define vars $csp-vars)
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(define constraints $csp-constraints)
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@ -25,7 +36,7 @@
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(raise-argument-error '$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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(apply ($constraint-proc constraint) args))))
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(define (make-constraint [names null] [proc values])
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($constraint names proc))
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@ -80,11 +91,11 @@
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((csp? procedure? (listof (listof name?))) ((or/c #false name?)) . ->* . void?)
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(set-$csp-constraints! csp (append (constraints csp)
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(for/list ([names (in-list namess)])
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(for ([name (in-list names)])
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(check-name-in-csp! 'add-constraints! csp name))
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(make-constraint names (if proc-name
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(procedure-rename proc proc-name)
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proc))))))
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(for ([name (in-list names)])
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(check-name-in-csp! 'add-constraints! csp name))
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(make-constraint names (if proc-name
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(procedure-rename proc proc-name)
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proc))))))
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(define/contract (add-pairwise-constraint! csp proc var-names [proc-name #false])
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((csp? procedure? (listof name?)) (name?) . ->* . void?)
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@ -118,7 +129,7 @@
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(check-name-in-csp! 'csp-var csp name)
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(for/first ([var (in-vars csp)]
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#:when (eq? name (var-name var)))
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var))
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var))
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(define/contract ($csp-vals csp name)
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(csp? name? . -> . (listof any/c))
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@ -131,7 +142,7 @@
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(csp? name? . -> . any/c)
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(for/or ([var (in-vars csp)]
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#:when (assigned-var? var))
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(eq? name (var-name var))))
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(eq? name (var-name var))))
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(define (reduce-function-arity proc pattern)
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(unless (match (procedure-arity proc)
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@ -162,27 +173,30 @@
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(ormap assigned-name? ($constraint-names constraint)))
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(make-csp (vars csp)
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(for/list ([constraint (in-constraints csp)])
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(cond
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[(and (if minimum-arity (<= minimum-arity (constraint-arity constraint)) #true)
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(partially-assigned? constraint))
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(match-define ($constraint cnames proc) constraint)
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($constraint (filter-not assigned-name? cnames)
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;; pattern is mix of values and boxed symbols (indicating variables to persist)
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;; use boxes here as cheap way to distinguish id symbols from value symbols
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(let ([reduce-arity-pattern (for/list ([cname (in-list cnames)])
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(if (assigned-name? cname)
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(first ($csp-vals csp cname))
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(box cname)))])
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(reduce-function-arity proc reduce-arity-pattern)))]
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[else constraint])))))
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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 boxed symbols (indicating variables to persist)
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;; use boxes here as cheap way to distinguish id symbols from value symbols
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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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(first ($csp-vals csp cname))
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(box cname)))])
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(reduce-function-arity proc reduce-arity-pattern)))]
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[else constraint])))))
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(define nassns 0)
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(define (reset-assns!) (set! nassns 0))
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(define/contract (assign-val csp name val)
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(csp? name? any/c . -> . csp?)
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(when-debug (set! nassns (add1 nassns)))
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(make-csp
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(for/list ([var (vars csp)])
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(if (eq? name (var-name var))
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($avar name (list val))
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var))
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(if (eq? name (var-name var))
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($avar name (list val))
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var))
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(constraints csp)))
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(define/contract (unassigned-vars csp)
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@ -214,7 +228,7 @@
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(csp? $var? . -> . exact-nonnegative-integer?)
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(for/sum ([constraint (in-constraints csp)]
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#:when (memq (var-name var) ($constraint-names constraint)))
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1))
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1))
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(define/contract (blended-variable-selector csp)
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(csp? . -> . (or/c #false (and/c $var? (not/c assigned-var?))))
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@ -256,8 +270,8 @@
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[cnames (in-value ($constraint-names constraint))]
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#:when (and (= (length names) (length cnames))
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(for/and ([name (in-list names)])
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(memq name cnames))))
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constraint))
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(memq name cnames))))
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constraint))
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(define (binary-constraint? constraint)
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(= 2 (constraint-arity constraint)))
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@ -265,6 +279,9 @@
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(define (constraint-relates? constraint name)
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(memq name ($constraint-names constraint)))
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(define nfchecks 0)
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(define (reset-nfcs!) (set! nfchecks 0))
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(define/contract (forward-check csp aname)
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(csp? name? . -> . csp?)
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(define aval (first ($csp-vals csp aname)))
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@ -280,20 +297,21 @@
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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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(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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($cvar-past var)
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null)))])]))
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(define checked-vars (map check-var (vars csp)))
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(when-debug (set! nfchecks (+ (length checked-vars) nchecks)))
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;; conflict-set will be empty if there are no empty domains
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(define conflict-set (for*/list ([var (in-list checked-vars)]
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#:when (empty? ($var-domain var))
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[name (in-list ($cvar-past var))])
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name))
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name))
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;; for conflict-directed backjumping it's essential to forward-check ALL vars
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;; (even after an empty domain is generated) and combine their conflicts
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;; so we can discover the *most recent past var* that could be the culprit.
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@ -310,13 +328,13 @@
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(constraint-relates? constraint aname)
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(let ([other-name (first (remq aname ($constraint-names constraint)))])
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(singleton-var? (csp-var csp other-name)))))
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constraint))
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constraint))
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(make-csp checked-vars nonsingleton-constraints))
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(define/contract (constraint-checkable? c names)
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($constraint? (listof name?) . -> . any/c)
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(for/and ([cname (in-list ($constraint-names c))])
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(memq cname names)))
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(memq cname names)))
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(define/contract (constraint-arity constraint)
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($constraint? . -> . exact-nonnegative-integer?)
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@ -325,6 +343,8 @@
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(define (singleton-var? var)
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(= 1 (length ($var-domain var))))
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(define nchecks 0)
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(define (reset-nchecks!) (set! nchecks 0))
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(define/contract (check-constraints csp)
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(csp? . -> . csp?)
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;; this time, we're not limited to assigned variables
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@ -332,12 +352,13 @@
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;; we also want to use "singleton" vars (that is, vars that have been reduced to a single domain value by forward checking)
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(define singleton-varnames (for/list ([var (in-vars csp)]
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#:when (singleton-var? var))
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(var-name var)))
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(var-name var)))
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(define-values (checkable-constraints other-constraints)
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(partition (λ (c) (constraint-checkable? c singleton-varnames)) (constraints csp)))
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(for ([constraint (in-list (sort checkable-constraints < #:key constraint-arity))]
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(for ([(constraint idx) (in-indexed (sort checkable-constraints < #:key constraint-arity))]
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#:unless (constraint csp))
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(backtrack!))
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(when-debug (set! nchecks (+ (add1 idx) nchecks)))
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(backtrack!))
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;; discard checked constraints, since they have no further reason to live
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(make-csp (vars csp) other-constraints))
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@ -346,15 +367,15 @@
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;; todo: why does this function slow down searches?
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(make-csp
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(for/list ([var (in-vars csp)])
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(match-define ($var name vals) var)
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(define procs (for*/list ([constraint (in-constraints csp)]
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[cnames (in-value ($constraint-names constraint))]
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#:when (and (= 1 (length cnames)) (eq? name (car cnames))))
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($constraint-proc constraint)))
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($var name
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(for*/fold ([vals vals])
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([proc (in-list procs)])
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(filter proc vals))))
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(match-define ($var name vals) var)
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(define procs (for*/list ([constraint (in-constraints csp)]
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[cnames (in-value ($constraint-names constraint))]
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#:when (and (= 1 (length cnames)) (eq? name (car cnames))))
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($constraint-proc constraint)))
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($var name
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(for*/fold ([vals vals])
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([proc (in-list procs)])
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(filter proc vals))))
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(constraints csp)))
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(define/contract (backtracking-solver
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@ -388,23 +409,27 @@
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;; todo: min-conflicts solver
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(define/contract ($csp-assocs csp)
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(define/contract (csp->assocs csp)
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(csp? . -> . (listof (cons/c name? any/c)))
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(for/list ([var (in-vars csp)])
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(match var
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[($var name domain) (cons name (first domain))])))
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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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#: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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(when-debug
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(reset-assns!)
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(reset-nfcs!)
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(reset-nchecks!))
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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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(finish-proc 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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#: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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