From 99066430fd07d366e0958b3b9b1ca8e6ab7999e6 Mon Sep 17 00:00:00 2001
From: giles <giles.bradshaw@rose-ash.com>
Date: Fri, 8 May 2026 11:25:12 +0000
Subject: [PATCH] =?UTF-8?q?mk:=20lasto=20+=20init-o=20=E2=80=94=20last=20a?=
 =?UTF-8?q?nd=20not-last=20list=20relations?=
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lasto: x is the final element of l. Direct base case (l = (x)) plus
recurse-on-cdr.

init-o: init is l without its last element. Base case for singleton:
(== init ()). Otherwise recurse, threading the head through to the
init result via conso.

Together with appendo, the round-trip init append (list last) = l
holds, which is exercised by an end-to-end test.

8 new tests, 344/344 cumulative.
---
 lib/minikanren/relations.sx   | 16 +++++++++++++++
 lib/minikanren/tests/lasto.sx | 38 +++++++++++++++++++++++++++++++++++
 plans/minikanren-on-sx.md     |  4 ++++
 3 files changed, 58 insertions(+)
 create mode 100644 lib/minikanren/tests/lasto.sx

diff --git a/lib/minikanren/relations.sx b/lib/minikanren/relations.sx
index 84d4e76b..60200c86 100644
--- a/lib/minikanren/relations.sx
+++ b/lib/minikanren/relations.sx
@@ -156,3 +156,19 @@
     (conde
       ((fresh (a d) (conso a d l) (rel a)))
       ((fresh (a d) (conso a d l) (someo rel d))))))
+
+(define
+  lasto
+  (fn
+    (l x)
+    (conde
+      ((conso x (list) l))
+      ((fresh (a d) (conso a d l) (lasto d x))))))
+
+(define
+  init-o
+  (fn
+    (l init)
+    (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))))))
diff --git a/lib/minikanren/tests/lasto.sx b/lib/minikanren/tests/lasto.sx
new file mode 100644
index 00000000..110f8019
--- /dev/null
+++ b/lib/minikanren/tests/lasto.sx
@@ -0,0 +1,38 @@
+;; lib/minikanren/tests/lasto.sx — last-element + init-without-last.
+
+(mk-test
+  "lasto-singleton"
+  (run* q (lasto (list 5) q))
+  (list 5))
+(mk-test
+  "lasto-multi"
+  (run* q (lasto (list 1 2 3 4) q))
+  (list 4))
+(mk-test "lasto-empty" (run* q (lasto (list) q)) (list))
+
+(mk-test "lasto-strings" (run* q (lasto (list "a" "b" "c") q)) (list "c"))
+
+(mk-test
+  "init-o-multi"
+  (run* q (init-o (list 1 2 3 4) q))
+  (list (list 1 2 3)))
+
+(mk-test
+  "init-o-singleton"
+  (run* q (init-o (list 7) q))
+  (list (list)))
+
+(mk-test "init-o-empty" (run* q (init-o (list) q)) (list))
+
+(mk-test
+  "lasto-init-o-roundtrip"
+  (run*
+    q
+    (fresh
+      (init last)
+      (lasto (list 1 2 3 4) last)
+      (init-o (list 1 2 3 4) init)
+      (appendo init (list last) q)))
+  (list (list 1 2 3 4)))
+
+(mk-tests-run!)
diff --git a/plans/minikanren-on-sx.md b/plans/minikanren-on-sx.md
index fd39efa1..3515133f 100644
--- a/plans/minikanren-on-sx.md
+++ b/plans/minikanren-on-sx.md
@@ -173,6 +173,10 @@ _(none yet)_
 
 _Newest first._
 
+- **2026-05-08** — **lasto / init-o**: classic head/tail-style list relations.
+  lasto extracts the final element; init-o extracts everything-but-the-last.
+  Together with appendo, the round-trip `init ⊕ (last) = l` holds. 8 new
+  tests, 344/344 cumulative.
 - **2026-05-08** — **Datalog-style relational database queries**: tests/rdb.sx
   shows miniKanren as a query engine over fact tables. Defines two tables
   (employees + project assignments), wraps each with a relation that does