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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.
120 lines
2.2 KiB
Plaintext
120 lines
2.2 KiB
Plaintext
;; lib/minikanren/tests/peano.sx — Peano arithmetic.
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;;
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;; Builds Peano numbers via a host-side helper so tests stay readable.
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;; (mk-nat 3) → (:s (:s (:s :z))).
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(define
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mk-nat
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(fn (n) (if (= n 0) :z (list :s (mk-nat (- n 1))))))
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;; --- zeroo ---
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(mk-test
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"zeroo-zero-succeeds"
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(run* q (zeroo :z))
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(list (make-symbol "_.0")))
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(mk-test
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"zeroo-non-zero-fails"
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(run* q (zeroo (mk-nat 1)))
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(list))
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;; --- pluso forward ---
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(mk-test
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"pluso-forward-2-3"
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(run* q (pluso (mk-nat 2) (mk-nat 3) q))
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(list (mk-nat 5)))
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(mk-test "pluso-forward-zero-zero" (run* q (pluso :z :z q)) (list :z))
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(mk-test
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"pluso-forward-zero-n"
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(run* q (pluso :z (mk-nat 4) q))
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(list (mk-nat 4)))
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(mk-test
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"pluso-forward-n-zero"
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(run* q (pluso (mk-nat 4) :z q))
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(list (mk-nat 4)))
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;; --- pluso backward ---
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(mk-test
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"pluso-recover-augend"
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(run* q (pluso q (mk-nat 2) (mk-nat 5)))
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(list (mk-nat 3)))
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(mk-test
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"pluso-recover-addend"
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(run* q (pluso (mk-nat 2) q (mk-nat 5)))
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(list (mk-nat 3)))
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(mk-test
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"pluso-enumerate-pairs-summing-to-3"
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(run*
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q
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(fresh (a b) (pluso a b (mk-nat 3)) (== q (list a b))))
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(list
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(list :z (mk-nat 3))
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(list (mk-nat 1) (mk-nat 2))
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(list (mk-nat 2) (mk-nat 1))
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(list (mk-nat 3) :z)))
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;; --- minuso ---
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(mk-test
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"minuso-5-2-3"
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(run* q (minuso (mk-nat 5) (mk-nat 2) q))
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(list (mk-nat 3)))
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(mk-test
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"minuso-n-n-zero"
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(run* q (minuso (mk-nat 7) (mk-nat 7) q))
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(list :z))
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;; --- *o ---
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(mk-test
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"times-2-3"
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(run* q (*o (mk-nat 2) (mk-nat 3) q))
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(list (mk-nat 6)))
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(mk-test
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"times-zero-anything-zero"
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(run* q (*o :z (mk-nat 99) q))
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(list :z))
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(mk-test
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"times-3-4"
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(run* q (*o (mk-nat 3) (mk-nat 4) q))
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(list (mk-nat 12)))
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;; --- lteo / lto ---
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(mk-test
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"lteo-success"
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(run 1 q (lteo (mk-nat 2) (mk-nat 5)))
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(list (make-symbol "_.0")))
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(mk-test
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"lteo-equal-success"
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(run 1 q (lteo (mk-nat 3) (mk-nat 3)))
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(list (make-symbol "_.0")))
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(mk-test
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"lteo-greater-fails"
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(run* q (lteo (mk-nat 5) (mk-nat 2)))
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(list))
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(mk-test
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"lto-strict-success"
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(run 1 q (lto (mk-nat 2) (mk-nat 5)))
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(list (make-symbol "_.0")))
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(mk-test
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"lto-equal-fails"
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(run* q (lto (mk-nat 3) (mk-nat 3)))
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(list))
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(mk-tests-run!)
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