mk: phase 6A — minimal FD (ino + all-distincto)

ino is membero with the constraint-store-friendly argument order
(`(ino x dom)` reads as "x in dom"). all-distincto checks pairwise
distinctness via nafc + membero on the recursive tail. These two are
enough to express the enumerate-then-filter style of finite-domain
solving:

  (fresh (a b c)
    (ino a (list 1 2 3)) (ino b (list 1 2 3)) (ino c (list 1 2 3))
    (all-distincto (list a b c)))

enumerates all 6 distinct triples from {1, 2, 3}. Full CLP(FD) with
arc-consistency, fd-plus, etc. remains pending under Phase 6 proper.

9 new tests, 237/237 cumulative.

lib/minikanren/fd.sx

@@ -0,0 +1,25 @@
+;; lib/minikanren/fd.sx — Phase 6 piece A: minimal finite-domain helpers.
+;;
+;; A full CLP(FD) engine (arc consistency, native integer domains, fd-plus
+;; etc.) is Phase 6 proper. For now we expose two small relations layered
+;; on the existing list machinery — they're sufficient for permutation
+;; puzzles, the N-queens-style core of constraint solving:
+;;
+;;   (ino x dom)         — x is a member of dom (alias for membero with the
+;;                         constraint-store-friendly argument order).
+;;   (all-distincto l)   — all elements of l are pairwise distinct.
+;;
+;; all-distincto uses nafc + membero on the tail — it requires the head
+;; element of each recursive step to be ground enough for membero to be
+;; finitary, so order matters: prefer (in x dom) goals BEFORE
+;; (all-distincto (list x ...)) so values get committed first.
+
+(define ino (fn (x dom) (membero x dom)))
+
+(define
+  all-distincto
+  (fn
+    (l)
+    (conde
+      ((nullo l))
+      ((fresh (a d) (conso a d l) (nafc (membero a d)) (all-distincto d))))))

lib/minikanren/tests/fd.sx

@@ -0,0 +1,75 @@
+;; lib/minikanren/tests/fd.sx — Phase 6 piece A: ino + all-distincto.
+
+;; --- ino ---
+
+(mk-test
+  "ino-element-in-domain"
+  (run* q (ino q (list 1 2 3)))
+  (list 1 2 3))
+
+(mk-test "ino-empty-domain" (run* q (ino q (list))) (list))
+
+(mk-test
+  "ino-singleton-domain"
+  (run* q (ino q (list 42)))
+  (list 42))
+
+;; --- all-distincto ---
+
+(mk-test
+  "all-distincto-empty"
+  (run* q (all-distincto (list)))
+  (list (make-symbol "_.0")))
+
+(mk-test
+  "all-distincto-singleton"
+  (run* q (all-distincto (list 1)))
+  (list (make-symbol "_.0")))
+
+(mk-test
+  "all-distincto-distinct-three"
+  (run* q (all-distincto (list 1 2 3)))
+  (list (make-symbol "_.0")))
+
+(mk-test
+  "all-distincto-duplicate-fails"
+  (run* q (all-distincto (list 1 2 1)))
+  (list))
+
+(mk-test
+  "all-distincto-adjacent-duplicate-fails"
+  (run* q (all-distincto (list 1 1 2)))
+  (list))
+
+;; --- ino + all-distincto: classic enumerate-all-permutations ---
+
+(mk-test
+  "fd-puzzle-three-distinct-from-domain"
+  (let
+    ((perms (run* q (fresh (a b c) (== q (list a b c)) (ino a (list 1 2 3)) (ino b (list 1 2 3)) (ino c (list 1 2 3)) (all-distincto (list a b c))))))
+    (and
+      (= (len perms) 6)
+      (and
+        (some (fn (p) (= p (list 1 2 3))) perms)
+        (and
+          (some
+            (fn (p) (= p (list 1 3 2)))
+            perms)
+          (and
+            (some
+              (fn (p) (= p (list 2 1 3)))
+              perms)
+            (and
+              (some
+                (fn (p) (= p (list 2 3 1)))
+                perms)
+              (and
+                (some
+                  (fn (p) (= p (list 3 1 2)))
+                  perms)
+                (some
+                  (fn (p) (= p (list 3 2 1)))
+                  perms))))))))
+  true)
+
+(mk-tests-run!)

plans/minikanren-on-sx.md

@@ -142,7 +142,10 @@ Key semantic mappings:
 
 ### Phase 6 — arithmetic constraints CLP(FD)
 - [ ] Finite domain variables: `fd-var` with domain `[lo..hi]`
-- [ ] `in` `x` `domain` — constrain x to domain
+- [x] `ino` `x` `domain` — alias for `(membero x domain)` with the
+      constraint-store-friendly argument order. Sufficient for the
+      enumerate-then-filter style of finite-domain solving.
+- [x] `all-distincto` `l` — pairwise-distinct elements via `nafc + membero`.
 - [ ] `fd-eq` `x` `y` — x = y (constraint propagation)
 - [ ] `fd-neq` `x` `y` — x ≠ y
 - [ ] `fd-lt` `fd-lte` `fd-gt` `fd-gte` — ordering constraints
@@ -166,6 +169,13 @@ _(none yet)_
 
 _Newest first._
 
+- **2026-05-08** — **Phase 6 piece A — minimal FD (ino + all-distincto)**:
+  `lib/minikanren/fd.sx`. `ino` is `membero` with the FD-style argument
+  order; `all-distincto` is `nafc + membero` walking the list. Together
+  they cover the enumerate-then-filter style of finite-domain solving —
+  `(fresh (a b c) (ino a D) (ino b D) (ino c D) (all-distincto (list a b c)))`
+  enumerates all distinct triples from D. Full FD with arc-consistency,
+  fd-plus etc. is still pending. 9 new tests, 237/237 cumulative.
 - **2026-05-08** — **Classic puzzles + matche keyword fix**: matche now emits
   keywords bare in the pattern->expr conversion so they self-evaluate to their
   string name and unify with the same-keyword target value (instead of becoming