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163 lines
6.7 KiB
Racket
163 lines
6.7 KiB
Racket
#lang debug racket
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(require racket/generator sugar graph rackunit math)
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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 vals) #:transparent)
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(define $var-name? symbol?)
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(struct $avar $var () #:transparent)
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(struct inconsistency-signal (csp) #:transparent)
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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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($var-vals ($csp-var csp name)))
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(define order-domain-values values)
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(define (assign-val csp name val)
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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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($csp-constraints csp)))
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(define current-select-variable (make-parameter #f))
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(define current-order-values (make-parameter #f))
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(define current-inference (make-parameter #f))
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(define (first-unassigned-variable csp)
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(for/first ([var ($csp-vars csp)]
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#:unless ($avar? var))
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var))
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(check-equal? (first-unassigned-variable ($csp (list ($var 'a (range 3)) ($var 'b (range 3))) null)) ($var 'a (range 3)))
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(check-equal? (first-unassigned-variable ($csp (list ($avar 'a (range 3)) ($var 'b (range 3))) null)) ($var 'b (range 3)))
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(check-false (first-unassigned-variable ($csp (list ($avar 'a (range 3)) ($avar 'b (range 3))) null)))
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(define first-domain-value values)
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(define (no-inference csp name) csp)
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(define (forward-check csp aname)
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(define aval (first ($csp-vals csp aname)))
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(define (filter-vals var)
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(match-define ($var name vals) var)
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(define new-vals
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(match (for*/list ([constraint (in-list ($csp-constraints csp))]
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[cnames (in-value ($constraint-names constraint))]
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#:when (and (memq aname cnames) (memq name cnames)))
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constraint)
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[(list) vals]
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[constraints
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(for*/list ([val (in-list vals)]
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[constraint (in-list constraints)]
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[cnames (in-value ($constraint-names constraint))]
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#:when (cond
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[(eq? (first cnames) name)
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(($constraint-proc constraint) val aval)]
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[(eq? (second cnames) name)
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(($constraint-proc constraint) aval val)]
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[else #true]))
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val)]))
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(unless (pair? new-vals) (raise (inconsistency-signal csp)))
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new-vals)
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($csp
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(for/list ([var ($csp-vars csp)])
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(if ($avar? var)
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var
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($var ($var-name var) (filter-vals var))))
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($csp-constraints csp)))
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(check-equal?
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($csp-vars (forward-check ($csp (list ($avar 'a '(1)) ($var 'b (range 2))) null) 'a))
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(list ($avar 'a '(1)) ($var 'b '(0 1))))
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(check-equal?
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;; no inconsistency because b≠c not checked (because fc is relative to a)
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($csp-vars (forward-check ($csp (list ($avar 'a '(1)) ($var 'b (range 2)) ($var 'c '(0)))
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(list ($constraint '(a b) (negate =))
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($constraint '(b c) (negate =)))) 'a))
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(list ($avar 'a '(1)) ($var 'b '(0)) ($var 'c '(0))))
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(check-equal?
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;; no inconsistency because a≠b not checked (because fc ignores a, which is already assigned)
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($csp-vars (forward-check ($csp (list ($avar 'a '(1)) ($avar 'b '(1)) ($var 'c (range 2)))
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(list ($constraint '(a b) (negate =))
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($constraint '(b c) (negate =)))) 'b))
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(list ($avar 'a '(1)) ($avar 'b '(1)) ($var 'c '(0))))
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(check-exn inconsistency-signal?
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(λ () ($csp-vars (forward-check ($csp (list ($avar 'a '(1))
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($var 'b '(1)))
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(list ($constraint '(a b) (negate =)))) 'a))))
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(define/contract (backtrack-solution-generator csp
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[select-unassigned-variable (or (current-select-variable) first-unassigned-variable)]
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[order-domain-values (or (current-order-values) first-domain-value)]
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[inference (or (current-inference) no-inference)])
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(($csp?) (procedure? procedure? procedure?) . ->* . generator?)
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(generator ()
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(let backtrack ([csp csp])
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(match (select-unassigned-variable csp)
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[#false (yield csp)]
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[($var name vals)
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(for ([val (in-list (order-domain-values vals))])
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(with-handlers ([inconsistency-signal? void])
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(let* ([csp (assign-val csp name val)]
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[csp (inference csp name)])
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(backtrack csp))))]))))
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(define/contract (solve* csp [finish-proc $csp-vars][solution-limit +inf.0])
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(($csp?) (procedure? integer?) . ->* . (listof any/c))
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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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(define/contract (solve csp [finish-proc $csp-vars])
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(($csp?) (procedure?) . ->* . (or/c #false any/c))
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(match (solve* csp finish-proc 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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(parameterize ([current-inference forward-check])
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(time (solve* ($csp (list ($var 'a (range 3))
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($var 'b (range 3))
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($var 'c (range 3)))
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(list ($constraint '(a b) <>)
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($constraint '(a c) <>)
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($constraint '(b c) <>))))))
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(parameterize ([current-inference forward-check])
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(define vds (for/list ([k '(wa nsw t q nt v sa)])
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($var k '(red green blue))))
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(define cs (list
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($constraint '(wa nt) neq?)
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($constraint '(wa sa) neq?)
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($constraint '(nt sa) neq?)
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($constraint '(nt q) neq?)
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($constraint '(q sa) neq?)
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($constraint '(q nsw) neq?)
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($constraint '(nsw sa) neq?)
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($constraint '(nsw v) neq?)
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($constraint '(v sa) neq?)))
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(define csp ($csp vds cs))
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(check-equal? (time (length (solve* csp))) 18)) |