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The previous fd-fire-store fired every constraint exactly once. That left the propagation incomplete in chains like fd-plus c4 1 a; fd-neq c3 a where, on the round c4 binds, fd-plus binds a, but fd-neq c3 a was already past — so the conflict went undetected. New: fd-store-signature is sum-of-domain-sizes + count-of-bindings. fd-fire-store calls fd-fire-list and recurses while the signature strictly decreases. Reaches a fixed point or fails. This makes N-queens via FD tractable: 4-queens -> ((2 4 1 3) (3 1 4 2)) — exactly the two solutions. 5-queens -> 10 solutions (the canonical count), in seconds. Phase 6 marked complete in the plan: domains, fd-in, fd-eq, fd-neq, fd-lt, fd-lte, fd-plus, fd-times, fd-distinct, fd-label, all wired through the constraint-reactivation loop. Two new tests, 626/626 cumulative.
98 lines
2.1 KiB
Plaintext
98 lines
2.1 KiB
Plaintext
;; lib/minikanren/tests/queens-fd.sx — N-queens via CLP(FD).
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;;
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;; Native FD propagation makes N-queens tractable: 4-queens finds both
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;; solutions instantly; 5-queens finds all 10 in seconds. Compare with
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;; the naive enumerate-then-filter version in queens.sx, which struggles
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;; past N=4.
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(define
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fd-no-diag
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(fn
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(ci cj k)
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(fresh
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(a b)
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(fd-plus cj k a)
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(fd-plus ci k b)
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(fd-neq ci a)
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(fd-neq cj b))))
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(define
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n-queens-4-fd
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(fn
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(cs)
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(let
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((c1 (nth cs 0))
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(c2 (nth cs 1))
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(c3 (nth cs 2))
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(c4 (nth cs 3)))
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(mk-conj
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(fd-in c1 (list 1 2 3 4))
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(fd-in c2 (list 1 2 3 4))
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(fd-in c3 (list 1 2 3 4))
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(fd-in c4 (list 1 2 3 4))
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(fd-distinct cs)
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(fd-no-diag c1 c2 1)
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(fd-no-diag c1 c3 2)
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(fd-no-diag c1 c4 3)
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(fd-no-diag c2 c3 1)
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(fd-no-diag c2 c4 2)
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(fd-no-diag c3 c4 1)
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(fd-label cs)))))
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(define
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n-queens-5-fd
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(fn
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(cs)
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(let
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((c1 (nth cs 0))
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(c2 (nth cs 1))
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(c3 (nth cs 2))
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(c4 (nth cs 3))
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(c5 (nth cs 4)))
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(mk-conj
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(fd-in
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c1
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(list 1 2 3 4 5))
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(fd-in
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c2
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(list 1 2 3 4 5))
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(fd-in
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c3
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(list 1 2 3 4 5))
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(fd-in
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c4
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(list 1 2 3 4 5))
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(fd-in
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c5
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(list 1 2 3 4 5))
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(fd-distinct cs)
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(fd-no-diag c1 c2 1)
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(fd-no-diag c1 c3 2)
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(fd-no-diag c1 c4 3)
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(fd-no-diag c1 c5 4)
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(fd-no-diag c2 c3 1)
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(fd-no-diag c2 c4 2)
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(fd-no-diag c2 c5 3)
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(fd-no-diag c3 c4 1)
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(fd-no-diag c3 c5 2)
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(fd-no-diag c4 c5 1)
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(fd-label cs)))))
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(mk-test
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"n-queens-4-fd-two-solutions"
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(run*
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q
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(fresh (a b c d) (== q (list a b c d)) (n-queens-4-fd (list a b c d))))
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(list
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(list 2 4 1 3)
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(list 3 1 4 2)))
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(mk-test
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"n-queens-5-fd-ten-solutions"
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(let
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((sols (run* q (fresh (a b c d e) (== q (list a b c d e)) (n-queens-5-fd (list a b c d e))))))
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(= (len sols) 10))
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true)
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(mk-tests-run!)
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