From 8c48a0be63a17bb0550dae931c0c608d04beda65 Mon Sep 17 00:00:00 2001
From: giles <giles.bradshaw@rose-ash.com>
Date: Fri, 8 May 2026 11:32:33 +0000
Subject: [PATCH] =?UTF-8?q?mk:=20tako=20+=20dropo=20=E2=80=94=20Peano-inde?=
 =?UTF-8?q?xed=20prefix=20and=20suffix?=
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(tako n l prefix) — prefix is the first n elements of l.
(dropo n l suffix) — suffix is l after dropping the first n.

Both use a Peano natural for the count. Round-trip holds:
  (tako n l) ⊕ (dropo n l) = l   (verified by an end-to-end test)

9 new tests, 368/368 cumulative.
---
 lib/minikanren/relations.sx       | 16 ++++++
 lib/minikanren/tests/take-drop.sx | 92 +++++++++++++++++++++++++++++++
 plans/minikanren-on-sx.md         |  3 +
 3 files changed, 111 insertions(+)
 create mode 100644 lib/minikanren/tests/take-drop.sx

diff --git a/lib/minikanren/relations.sx b/lib/minikanren/relations.sx
index 60200c86..b9f382c5 100644
--- a/lib/minikanren/relations.sx
+++ b/lib/minikanren/relations.sx
@@ -172,3 +172,19 @@
     (conde
       ((fresh (x) (conso x (list) l) (== init (list))))
       ((fresh (a d d-init) (conso a d l) (conso a d-init init) (init-o d d-init))))))
+
+(define
+  tako
+  (fn
+    (n l prefix)
+    (conde
+      ((== n :z) (== prefix (list)))
+      ((fresh (n-1 a d p-rest) (== n (list :s n-1)) (conso a d l) (conso a p-rest prefix) (tako n-1 d p-rest))))))
+
+(define
+  dropo
+  (fn
+    (n l suffix)
+    (conde
+      ((== n :z) (== suffix l))
+      ((fresh (n-1 a d) (== n (list :s n-1)) (conso a d l) (dropo n-1 d suffix))))))
diff --git a/lib/minikanren/tests/take-drop.sx b/lib/minikanren/tests/take-drop.sx
new file mode 100644
index 00000000..c8c2959d
--- /dev/null
+++ b/lib/minikanren/tests/take-drop.sx
@@ -0,0 +1,92 @@
+;; lib/minikanren/tests/take-drop.sx — Peano-indexed prefix/suffix.
+
+(define
+  mk-nat
+  (fn (n) (if (= n 0) :z (list :s (mk-nat (- n 1))))))
+
+;; --- tako ---
+
+(mk-test
+  "tako-zero"
+  (run*
+    q
+    (tako (mk-nat 0) (list 1 2 3) q))
+  (list (list)))
+
+(mk-test
+  "tako-two"
+  (run*
+    q
+    (tako
+      (mk-nat 2)
+      (list 1 2 3 4 5)
+      q))
+  (list (list 1 2)))
+
+(mk-test
+  "tako-all"
+  (run*
+    q
+    (tako (mk-nat 3) (list 1 2 3) q))
+  (list (list 1 2 3)))
+
+(mk-test
+  "tako-too-many"
+  (run*
+    q
+    (tako (mk-nat 5) (list 1 2 3) q))
+  (list))
+
+;; --- dropo ---
+
+(mk-test
+  "dropo-zero"
+  (run*
+    q
+    (dropo (mk-nat 0) (list 1 2 3) q))
+  (list (list 1 2 3)))
+
+(mk-test
+  "dropo-two"
+  (run*
+    q
+    (dropo
+      (mk-nat 2)
+      (list 1 2 3 4 5)
+      q))
+  (list (list 3 4 5)))
+
+(mk-test
+  "dropo-all"
+  (run*
+    q
+    (dropo (mk-nat 3) (list 1 2 3) q))
+  (list (list)))
+
+(mk-test
+  "dropo-too-many"
+  (run*
+    q
+    (dropo (mk-nat 5) (list 1 2 3) q))
+  (list))
+
+;; --- take + drop round-trip ---
+
+(mk-test
+  "tako-dropo-roundtrip"
+  (run*
+    q
+    (fresh
+      (p s)
+      (tako
+        (mk-nat 2)
+        (list 1 2 3 4 5)
+        p)
+      (dropo
+        (mk-nat 2)
+        (list 1 2 3 4 5)
+        s)
+      (appendo p s q)))
+  (list (list 1 2 3 4 5)))
+
+(mk-tests-run!)
diff --git a/plans/minikanren-on-sx.md b/plans/minikanren-on-sx.md
index 9834c5c4..a2640338 100644
--- a/plans/minikanren-on-sx.md
+++ b/plans/minikanren-on-sx.md
@@ -173,6 +173,9 @@ _(none yet)_
 
 _Newest first._
 
+- **2026-05-08** — **tako + dropo (Peano-indexed prefix/suffix)**: takes / drops
+  the first n elements via a Peano-encoded count. Round-trip
+  `(tako n l) ⊕ (dropo n l) = l` holds. 9 new tests, 368/368 cumulative.
 - **2026-05-08** — **eveno / oddo Peano predicates**: classic miniKanren parity
   relations. eveno: 0 or successor-of-successor of even; oddo: 1 or
   successor-of-successor of odd. Both run forward (test) and backward