From 7ff72cefb24f3c88d12049776e5606496ad01dc0 Mon Sep 17 00:00:00 2001
From: giles <giles.bradshaw@rose-ash.com>
Date: Fri, 8 May 2026 12:15:53 +0000
Subject: [PATCH] =?UTF-8?q?mk:=20lengtho-i=20=E2=80=94=20integer-indexed?=
 =?UTF-8?q?=20length?=
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Drop-in fast replacement for Peano lengtho when the count fits in a
host integer. Two conde clauses: empty list -> 0; recurse, n = 1 +
length(tail). Uses pluso-i so the length walks to a native int.

5 new tests, 486/486 cumulative.
---
 lib/minikanren/intarith.sx        |  8 ++++++++
 lib/minikanren/tests/lengtho-i.sx | 28 ++++++++++++++++++++++++++++
 plans/minikanren-on-sx.md         |  1 +
 3 files changed, 37 insertions(+)
 create mode 100644 lib/minikanren/tests/lengtho-i.sx

diff --git a/lib/minikanren/intarith.sx b/lib/minikanren/intarith.sx
index 015bea2d..e9548b4b 100644
--- a/lib/minikanren/intarith.sx
+++ b/lib/minikanren/intarith.sx
@@ -109,3 +109,11 @@
     (conde
       ((nullo l) (== total 1))
       ((fresh (a d rest-prod) (conso a d l) (producto d rest-prod) (*o-i a rest-prod total))))))
+
+(define
+  lengtho-i
+  (fn
+    (l n)
+    (conde
+      ((nullo l) (== n 0))
+      ((fresh (a d n-1) (conso a d l) (lengtho-i d n-1) (pluso-i 1 n-1 n))))))
diff --git a/lib/minikanren/tests/lengtho-i.sx b/lib/minikanren/tests/lengtho-i.sx
new file mode 100644
index 00000000..6759e24e
--- /dev/null
+++ b/lib/minikanren/tests/lengtho-i.sx
@@ -0,0 +1,28 @@
+;; lib/minikanren/tests/lengtho-i.sx — integer-indexed length (fast).
+
+(mk-test "lengtho-i-empty" (run* q (lengtho-i (list) q)) (list 0))
+(mk-test
+  "lengtho-i-singleton"
+  (run* q (lengtho-i (list :a) q))
+  (list 1))
+(mk-test
+  "lengtho-i-three"
+  (run* q (lengtho-i (list 1 2 3) q))
+  (list 3))
+(mk-test
+  "lengtho-i-five"
+  (run*
+    q
+    (lengtho-i
+      (list 1 2 3 4 5)
+      q))
+  (list 5))
+
+(mk-test
+  "lengtho-i-mixed-types"
+  (run*
+    q
+    (lengtho-i (list 1 "two" :three (list 4 5)) q))
+  (list 4))
+
+(mk-tests-run!)
diff --git a/plans/minikanren-on-sx.md b/plans/minikanren-on-sx.md
index 5ba00636..c55abc7d 100644
--- a/plans/minikanren-on-sx.md
+++ b/plans/minikanren-on-sx.md
@@ -173,6 +173,7 @@ _(none yet)_
 
 _Newest first._
 
+- **2026-05-08** — **lengtho-i**: integer-indexed length (intarith). Empty list -> 0; recurse with pluso-i. Drop-in fast replacement for Peano lengtho when the count fits in a host integer. 5 new tests, 486/486 cumulative.
 - **2026-05-08** — **sumo + producto (intarith)**: fold a list of ground integers to its sum or product. Empty list -> identity (0 / 1). Recurse via pluso-i / *o-i. 9 new tests, 481/481 cumulative.
 - **2026-05-08** — **mino + maxo (intarith)**: find the minimum/maximum of a non-empty list of ground integers. Two conde clauses each: singleton (return the element) / multi (compare head against recursive min/max of tail). 9 new tests, 472/472 cumulative.
 - **2026-05-08** — **sortedo (intarith)**: list is non-decreasing under integer ordering. Three conde clauses: empty / singleton / pair-and-recurse. Uses lteo-i for the adjacent-pair check (ground integers). 7 new tests, 463/463 cumulative.