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queens.sx encodes a queen in row i at column ci. ino-each constrains
each ci to {1..n}; all-distincto handles the row/column distinct
property; safe-diag uses project to escape into host arithmetic for the
|c_i - c_j| != |i - j| diagonal guard. all-cells-safe iterates pairs at
goal-construction time so the constraint set is materialised once,
then driven by the search.
(run* q (fresh (a b c d) (== q (list a b c d))
(queens-cols (list a b c d) 4)))
-> ((2 4 1 3) (3 1 4 2))
Both valid 4-queens placements found. 6 new tests including the
two-solution invariant; 243/243 cumulative.
68 lines
1.5 KiB
Plaintext
68 lines
1.5 KiB
Plaintext
;; lib/minikanren/queens.sx — N-queens via ino + all-distincto + project.
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;;
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;; Encoding: q = (c1 c2 ... cn) where ci is the column of the queen in
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;; row i. Each ci ∈ {1..n}; all distinct (no two queens share a column);
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;; no two queens on the same diagonal (|ci - cj| ≠ |i - j| for i ≠ j).
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;;
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;; The diagonal check uses `project` to escape into host arithmetic
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;; once both column values are ground.
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(define
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safe-diag
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(fn
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(a b dist)
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(project (a b) (if (= (abs (- a b)) dist) fail succeed))))
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(define
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safe-cell-vs-rest
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(fn
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(c c-row others next-row)
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(cond
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((empty? others) succeed)
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(:else
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(mk-conj
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(safe-diag c (first others) (- next-row c-row))
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(safe-cell-vs-rest c c-row (rest others) (+ next-row 1)))))))
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(define
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all-cells-safe
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(fn
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(cols start-row)
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(cond
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((empty? cols) succeed)
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(:else
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(mk-conj
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(safe-cell-vs-rest
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(first cols)
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start-row
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(rest cols)
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(+ start-row 1))
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(all-cells-safe (rest cols) (+ start-row 1)))))))
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(define
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range-1-to-n
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(fn
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(n)
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(cond
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((= n 0) (list))
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(:else (append (range-1-to-n (- n 1)) (list n))))))
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(define
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ino-each
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(fn
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(cols dom)
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(cond
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((empty? cols) succeed)
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(:else (mk-conj (ino (first cols) dom) (ino-each (rest cols) dom))))))
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(define
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queens-cols
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(fn
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(cols n)
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(let
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((dom (range-1-to-n n)))
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(mk-conj
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(ino-each cols dom)
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(all-distincto cols)
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(all-cells-safe cols 1)))))
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