mk: partitiono — split list by predicate

(partitiono pred l yes no) — yes is the elements of l where pred
succeeds; no is the rest. Conde dispatches on each element via the
predicate goal vs nafc-of-the-predicate, threading the head through
the matching output list.

Composes with intarith / membero / etc. for any predicate-shaped goal:
  (partitiono (fn (x) (lto-i x 5)) (list 1 7 2 8 3) yes no)
    yes -> (1 2 3); no -> (7 8)

5 new tests, 496/496 cumulative.

lib/minikanren/relations.sx

@@ -48,6 +48,14 @@
     (l1 l2 l3 result)
     (fresh (l12) (appendo l1 l2 l12) (appendo l12 l3 result))))
 
+(define
+  partitiono
+  (fn
+    (pred l yes no)
+    (conde
+      ((nullo l) (nullo yes) (nullo no))
+      ((fresh (a d y-rest n-rest) (conso a d l) (conde ((pred a) (conso a y-rest yes) (== no n-rest) (partitiono pred d y-rest n-rest)) ((nafc (pred a)) (== yes y-rest) (conso a n-rest no) (partitiono pred d y-rest n-rest))))))))
+
 (define
   membero
   (fn
@@ -80,6 +88,7 @@
       ((nullo l) (nullo r))
       ((fresh (a d res-rev) (conso a d l) (reverseo d res-rev) (appendo res-rev (list a) r))))))
 
+
 (define
   rev-acco
   (fn
@@ -88,7 +97,6 @@
       ((nullo l) (== result acc))
       ((fresh (a d acc-prime) (conso a d l) (conso a acc acc-prime) (rev-acco d acc-prime result))))))
 
-
 (define rev-2o (fn (l result) (rev-acco l (list) result)))
 
 (define palindromeo (fn (l) (fresh (rev) (reverseo l rev) (== l rev))))

lib/minikanren/tests/partitiono.sx

@@ -0,0 +1,75 @@
+;; lib/minikanren/tests/partitiono.sx — partition list by predicate.
+
+(mk-test
+  "partitiono-empty"
+  (run*
+    q
+    (fresh
+      (yes no)
+      (partitiono (fn (x) (== x 1)) (list) yes no)
+      (== q (list yes no))))
+  (list (list (list) (list))))
+
+(mk-test
+  "partitiono-by-equality"
+  (run*
+    q
+    (fresh
+      (yes no)
+      (partitiono
+        (fn (x) (== x 2))
+        (list 1 2 3 2 4)
+        yes
+        no)
+      (== q (list yes no))))
+  (list
+    (list
+      (list 2 2)
+      (list 1 3 4))))
+
+(mk-test
+  "partitiono-by-numeric-pred"
+  (run*
+    q
+    (fresh
+      (yes no)
+      (partitiono
+        (fn (x) (lto-i x 5))
+        (list 1 7 2 8 3)
+        yes
+        no)
+      (== q (list yes no))))
+  (list
+    (list
+      (list 1 2 3)
+      (list 7 8))))
+
+(mk-test
+  "partitiono-all-yes"
+  (run*
+    q
+    (fresh
+      (yes no)
+      (partitiono
+        (fn (x) (lto-i x 100))
+        (list 1 2 3)
+        yes
+        no)
+      (== q (list yes no))))
+  (list (list (list 1 2 3) (list))))
+
+(mk-test
+  "partitiono-all-no"
+  (run*
+    q
+    (fresh
+      (yes no)
+      (partitiono
+        (fn (x) (lto-i 100 x))
+        (list 1 2 3)
+        yes
+        no)
+      (== q (list yes no))))
+  (list (list (list) (list 1 2 3))))
+
+(mk-tests-run!)

plans/minikanren-on-sx.md

@@ -173,6 +173,7 @@ _(none yet)_
 
 _Newest first._
 
+- **2026-05-08** — **partitiono**: relational partition. (partitiono pred l yes no) splits l so yes contains elements where pred succeeds and no contains the rest. Composes with intarith for numeric predicates. 5 new tests, 496/496 cumulative.
 - **2026-05-08** — **appendo3**: 3-list append via two appendos. (appendo3 a b c r) is (appendo a b mid) ∧ (appendo mid c r). Recovers any of the three lists given the other two and the result. 5 new tests, 491/491 cumulative.
 - **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.