mk: lasto + init-o — last and not-last list relations

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

@@ -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))))))

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!)

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