From 7b6cb64548d3eaf9d4bd39a8239d8f14f18ff460 Mon Sep 17 00:00:00 2001
From: giles <giles.bradshaw@rose-ash.com>
Date: Fri, 8 May 2026 11:36:14 +0000
Subject: [PATCH] =?UTF-8?q?mk:=20not-membero=20=E2=80=94=20relational=20"x?=
 =?UTF-8?q?=20is=20not=20in=20l"?=
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Mirrors the structure all-distincto already uses internally: walk the
list, ensure each element is not equal to x via nafc, recurse on tail.
Useful as a constraint-style filter:

  (membero x (list 1 2 3 4 5))
  (not-membero x (list 2 4))
    -> x in {1, 3, 5}

4 new tests, 382/382 cumulative.
---
 lib/minikanren/relations.sx         | 10 +++++++++-
 lib/minikanren/tests/not-membero.sx | 29 +++++++++++++++++++++++++++++
 plans/minikanren-on-sx.md           |  4 ++++
 3 files changed, 42 insertions(+), 1 deletion(-)
 create mode 100644 lib/minikanren/tests/not-membero.sx

diff --git a/lib/minikanren/relations.sx b/lib/minikanren/relations.sx
index 6423a759..b04768d7 100644
--- a/lib/minikanren/relations.sx
+++ b/lib/minikanren/relations.sx
@@ -50,6 +50,14 @@
       ((fresh (d) (conso x d l)))
       ((fresh (a d) (conso a d l) (membero x d))))))
 
+(define
+  not-membero
+  (fn
+    (x l)
+    (conde
+      ((nullo l))
+      ((fresh (a d) (conso a d l) (nafc (== a x)) (not-membero x d))))))
+
 (define
   reverseo
   (fn
@@ -82,6 +90,7 @@
       ((nullo l) (nullo p))
       ((fresh (a d perm-d) (conso a d l) (permuteo d perm-d) (inserto a perm-d p))))))
 
+
 (define
   flatteno
   (fn
@@ -97,7 +106,6 @@
           (appendo hf tf flat)))
       ((nafc (nullo tree)) (nafc (pairo tree)) (== flat (list tree))))))
 
-
 (define
   rembero
   (fn
diff --git a/lib/minikanren/tests/not-membero.sx b/lib/minikanren/tests/not-membero.sx
new file mode 100644
index 00000000..8952f79e
--- /dev/null
+++ b/lib/minikanren/tests/not-membero.sx
@@ -0,0 +1,29 @@
+;; lib/minikanren/tests/not-membero.sx — relational "not in list".
+
+(mk-test
+  "not-membero-absent"
+  (run* q (not-membero 99 (list 1 2 3)))
+  (list (make-symbol "_.0")))
+(mk-test
+  "not-membero-present"
+  (run* q (not-membero 2 (list 1 2 3)))
+  (list))
+(mk-test
+  "not-membero-empty"
+  (run* q (not-membero 1 (list)))
+  (list (make-symbol "_.0")))
+
+(mk-test
+  "not-membero-as-filter"
+  (run*
+    q
+    (fresh
+      (x)
+      (membero
+        x
+        (list 1 2 3 4 5))
+      (not-membero x (list 2 4))
+      (== q x)))
+  (list 1 3 5))
+
+(mk-tests-run!)
diff --git a/plans/minikanren-on-sx.md b/plans/minikanren-on-sx.md
index 9f5749a6..733eaea6 100644
--- a/plans/minikanren-on-sx.md
+++ b/plans/minikanren-on-sx.md
@@ -173,6 +173,10 @@ _(none yet)_
 
 _Newest first._
 
+- **2026-05-08** — **not-membero**: relational "x is not a member of l".
+  Uses `nafc + ==` per element (the same skeleton all-distincto uses).
+  Useful as a constraint-style filter: `(membero x dom) (not-membero x
+  excluded)`. 4 new tests, 382/382 cumulative.
 - **2026-05-08** — **repeato + concato**: repeato builds a list of n copies
   (Peano n); concato is fold-appendo over a list of lists. Both run forward
   and backward — repeato can recover the count from a uniform list. 10 new