;; lib/minikanren/tests/pythag.sx — Pythagorean triple search.
;;
;; Uses ino + intarith goals to find triples (a, b, c) with
;; a, b, c ∈ [1..N], a ≤ b, a² + b² = c². With intarith escapes
;; the search runs at host-arithmetic speed.

(define
  digits-1-10
  (list
    1
    2
    3
    4
    5
    6
    7
    8
    9
    10))

(mk-test
  "pythag-triples-1-to-10"
  (let
    ((triples (run* q (fresh (a b c a-sq b-sq sum c-sq) (ino a digits-1-10) (ino b digits-1-10) (ino c digits-1-10) (lteo-i a b) (*o-i a a a-sq) (*o-i b b b-sq) (*o-i c c c-sq) (pluso-i a-sq b-sq sum) (== sum c-sq) (== q (list a b c))))))
    (and
      (= (len triples) 2)
      (and
        (some
          (fn (t) (= t (list 3 4 5)))
          triples)
        (some
          (fn (t) (= t (list 6 8 10)))
          triples))))
  true)

(mk-tests-run!)