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Two CLP(FD) demo puzzles plus an underlying improvement.
clpfd.sx: each fd-* posting goal now wraps its post-time propagation
in fd-fire-store, so cross-constraint narrowing happens BEFORE
labelling. Without this, a chain like fd-eq xyc z-plus-tenc1 followed
by fd-plus 2 ten-c1 z-plus-tenc1 wouldn't deduce ten-c1 = 10 until
labelling kicked in. Now the deduction happens at goal-construction
time. Guard against (c s2) returning nil before fd-fire-store runs.
tests/send-more-money.sx: full column-by-column carry encoding
(D+E = Y+10*c1; N+R+c1 = E+10*c2; E+O+c2 = N+10*c3; S+M+c3 = O+10*M).
Verifies the encoding against the known answer (9 5 6 7 1 0 8 2);
the full search labelling 11 vars from {0..9} is too slow for naive
labelling order — documented as a known limitation. Real CLP(FD)
needs first-fail / failure-driven heuristics for SMM to be fast.
tests/sudoku-4x4.sx: 16 cells / 12 distinctness constraints. The
empty grid enumerates exactly 288 distinct fillings (the known count
for 4x4 Latin squares with 2x2 box constraints). An impossible-clue
test (two 1s in row 0) fails immediately.
50/50 sudoku + smm tests, full clpfd suite green at 132/132.
98 lines
2.0 KiB
Plaintext
98 lines
2.0 KiB
Plaintext
;; lib/minikanren/tests/send-more-money.sx — classic cryptarithmetic
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;;
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;; S E N D
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;; + M O R E
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;; ---------
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;; M O N E Y
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;;
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;; Column-by-column encoding with carries c1, c2, c3, and the
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;; leftmost column produces a carry which equals M (the result is 5 digits).
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;; All 8 letters distinct; S ≠ 0, M ≠ 0.
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;; Unique solution: S=9, E=5, N=6, D=7, M=1, O=0, R=8, Y=2.
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;;
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;; Note: the full search labelling 11 variables from {0..9} is too slow
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;; for naive labelling order (10^11 combinations naively, even with
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;; bounds-consistency the branching factor dominates). Real CLP(FD)
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;; systems use first-fail heuristics. Here we only verify the encoding
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;; against the known answer.
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(define
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digits-0-9
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(list
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0
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1
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2
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3
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4
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5
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6
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7
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8
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9))
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(define
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digits-1-9
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(list
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1
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2
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3
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4
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5
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6
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7
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8
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9))
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(define
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smm-col-with-carry
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(fn
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(x y carry-in z carry-out)
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(fresh
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(xy xyc ten-cout z-plus-ten-cout)
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(fd-plus x y xy)
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(fd-plus xy carry-in xyc)
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(fd-times 10 carry-out ten-cout)
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(fd-plus z ten-cout z-plus-ten-cout)
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(fd-eq xyc z-plus-ten-cout))))
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(define
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send-more-money
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(fn
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(S E N D M O R Y)
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(fresh
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(c1 c2 c3)
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(mk-conj
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(fd-in S digits-1-9)
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(fd-in M digits-1-9)
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(fd-in E digits-0-9)
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(fd-in N digits-0-9)
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(fd-in D digits-0-9)
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(fd-in O digits-0-9)
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(fd-in R digits-0-9)
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(fd-in Y digits-0-9)
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(fd-in c1 (list 0 1))
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(fd-in c2 (list 0 1))
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(fd-in c3 (list 0 1))
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(fd-distinct (list S E N D M O R Y))
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(smm-col-with-carry D E 0 Y c1)
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(smm-col-with-carry N R c1 E c2)
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(smm-col-with-carry E O c2 N c3)
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(smm-col-with-carry S M c3 O M)
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(fd-label (list S E N D M O R Y c1 c2 c3))))))
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(mk-test
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"send-more-money-verify-known-solution"
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(run*
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q
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(send-more-money
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9
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5
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6
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7
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1
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0
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8
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2))
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(list (make-symbol "_.0")))
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(mk-tests-run!)
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