;; lib/minikanren/tests/path-cycle-free.sx — cycle-free reachability search.
;;
;; Threads a "visited" accumulator through the recursion, using nafc +
;; membero to prevent revisiting nodes. Demonstrates how to make the
;; cyclic-graph divergence problem (see tests/cyclic-graph.sx) tractable
;; for graphs with cycles, without invoking Phase-7 tabling.

(define
  cf-edges
  (list (list :a :b) (list :b :a) (list :b :c) (list :c :d) (list :d :a)))      ; another cycle

(define cf-edgeo (fn (from to) (membero (list from to) cf-edges)))

(define
  patho-no-cycles
  (fn
    (x y visited path)
    (conde
      ((cf-edgeo x y) (nafc (membero y visited)) (== path (list x y)))
      ((fresh (z mid v-prime) (cf-edgeo x z) (nafc (membero z visited)) (conso z visited v-prime) (patho-no-cycles z y v-prime mid) (conso x mid path))))))

(define cf-patho (fn (x y path) (patho-no-cycles x y (list x) path)))

(mk-test
  "cycle-free-finds-finitely"
  (let
    ((paths (run* q (cf-patho :a :d q))))
    (and
      (>= (len paths) 1)
      (every? (fn (p) (and (= (first p) :a) (= (last p) :d))) paths)))
  true)

(mk-test
  "cycle-free-direct-edge"
  (run* q (cf-patho :a :b q))
  (list (list :a :b)))

(mk-test "cycle-free-no-self-loop" (run* q (cf-patho :a :a q)) (list))

(mk-tests-run!)