mk: samelengtho — equal-length relation

Recurses positionally, dropping a head from each list each step. Both
arguments can be unbound, giving the natural enumeration:

  (run 3 q (fresh (l1 l2) (samelengtho l1 l2) (== q (list l1 l2))))
    -> (((), ())                         empty/empty
        ((_.0), (_.1))                   pair of 1-element lists
        ((_.0 _.1), (_.2 _.3)))          pair of 2-element lists

5 new tests, 293/293 cumulative.

lib/minikanren/relations.sx

@@ -124,3 +124,11 @@
     (conde
       ((== n :z) (fresh (d) (conso elem d l)))
       ((fresh (n-1 a d) (== n (list :s n-1)) (conso a d l) (nth-o n-1 d elem))))))
+
+(define
+  samelengtho
+  (fn
+    (l1 l2)
+    (conde
+      ((nullo l1) (nullo l2))
+      ((fresh (a d a-prime d-prime) (conso a d l1) (conso a-prime d-prime l2) (samelengtho d d-prime))))))

lib/minikanren/tests/list-relations.sx

@@ -1,4 +1,4 @@
-;; lib/minikanren/tests/list-relations.sx — rembero, assoco, nth-o.
+;; lib/minikanren/tests/list-relations.sx — rembero, assoco, nth-o, samelengtho.
 
 ;; --- rembero (remove first occurrence) ---
 
@@ -86,4 +86,41 @@
       q))
   (list))
 
+;; --- samelengtho ---
+
+(mk-test
+  "samelengtho-equal"
+  (run*
+    q
+    (samelengtho (list 1 2 3) (list :a :b :c)))
+  (list (make-symbol "_.0")))
+
+(mk-test
+  "samelengtho-different-fails"
+  (run* q (samelengtho (list 1 2) (list :a :b :c)))
+  (list))
+
+(mk-test
+  "samelengtho-empty-equal"
+  (run* q (samelengtho (list) (list)))
+  (list (make-symbol "_.0")))
+
+(mk-test
+  "samelengtho-builds-vars"
+  (run 1 q (samelengtho (list 1 2 3) q))
+  (list (list (make-symbol "_.0") (make-symbol "_.1") (make-symbol "_.2"))))
+
+(mk-test
+  "samelengtho-enumerates-pairs"
+  (run
+    3
+    q
+    (fresh (l1 l2) (samelengtho l1 l2) (== q (list l1 l2))))
+  (list
+    (list (list) (list))
+    (list (list (make-symbol "_.0")) (list (make-symbol "_.1")))
+    (list
+      (list (make-symbol "_.0") (make-symbol "_.1"))
+      (list (make-symbol "_.2") (make-symbol "_.3")))))
+
 (mk-tests-run!)

plans/minikanren-on-sx.md

@@ -173,6 +173,11 @@ _(none yet)_
 
 _Newest first._
 
+- **2026-05-08** — **samelengtho**: classic miniKanren relation that
+  succeeds when two lists have equal length. Symmetric — works to enumerate
+  both lists fresh: `(run 3 q (fresh (l1 l2) (samelengtho l1 l2) (== q
+  (list l1 l2))))` produces empty/empty, then 1-elem pairs, then 2-elem.
+  5 new tests, 293/293 cumulative.
 - **2026-05-08** — **Pythagorean triples (intarith showcase)**: search for
   (a, b, c) ∈ [1..10]³, a ≤ b, a² + b² = c² via `ino + lteo-i + *o-i +
   pluso-i + ==`. Finds exactly `(3 4 5)` and `(6 8 10)`. Demonstrates the