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Classic miniKanren Peano arithmetic on (:z / (:s n)) naturals. pluso runs relationally in all directions: 2+3=5 forward, x+2=5 → 3 backward, enumerates the four pairs summing to 3. *o is iterated pluso. lteo/lto via existential successor decomposition. 19 new tests, 188/188 cumulative. Phase-tagged in the plan separately from Phase 6 CLP(FD), which will eventually replace this with native integers + arc-consistency propagation.
36 lines
1.0 KiB
Plaintext
36 lines
1.0 KiB
Plaintext
;; lib/minikanren/peano.sx — Peano-encoded natural-number relations.
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;;
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;; Same encoding as `lengtho`: zero is the keyword `:z`; successors are
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;; `(:s n)`. So 3 = `(:s (:s (:s :z)))`. `(:z)` and `(:s ...)` are normal
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;; SX values that unify positionally — no special primitives needed.
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;;
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;; Peano arithmetic is the canonical miniKanren way to test addition /
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;; multiplication / less-than relationally without an FD constraint store.
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;; (CLP(FD) integers come in Phase 6.)
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(define zeroo (fn (n) (== n :z)))
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(define succ-of (fn (n m) (== m (list :s n))))
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(define
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pluso
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(fn
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(a b c)
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(conde
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((== a :z) (== b c))
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((fresh (a-1 c-1) (== a (list :s a-1)) (== c (list :s c-1)) (pluso a-1 b c-1))))))
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(define minuso (fn (a b c) (pluso b c a)))
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(define lteo (fn (a b) (fresh (k) (pluso a k b))))
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(define lto (fn (a b) (fresh (sa) (succ-of a sa) (lteo sa b))))
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(define
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*o
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(fn
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(a b c)
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(conde
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((== a :z) (== c :z))
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((fresh (a-1 ab-1) (== a (list :s a-1)) (*o a-1 b ab-1) (pluso b ab-1 c))))))
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