mk: sumo + producto — fold list to integer

Sum and product over a list of ground integers via fold + intarith.
Empty list yields the identity (0 for sum, 1 for product). Recurse
combines the head with the recursively-computed tail value via
pluso-i / *o-i.

9 new tests, 481/481 cumulative.

lib/minikanren/intarith.sx

@@ -93,3 +93,19 @@
     (conde
       ((fresh (a) (== l (list a)) (== m a)))
       ((fresh (a d rest-max) (conso a d l) (maxo d rest-max) (conde ((lteo-i rest-max a) (== m a)) ((lto-i a rest-max) (== m rest-max))))))))
+
+(define
+  sumo
+  (fn
+    (l total)
+    (conde
+      ((nullo l) (== total 0))
+      ((fresh (a d rest-sum) (conso a d l) (sumo d rest-sum) (pluso-i a rest-sum total))))))
+
+(define
+  producto
+  (fn
+    (l total)
+    (conde
+      ((nullo l) (== total 1))
+      ((fresh (a d rest-prod) (conso a d l) (producto d rest-prod) (*o-i a rest-prod total))))))

lib/minikanren/tests/sum-product.sx

@@ -0,0 +1,44 @@
+;; lib/minikanren/tests/sum-product.sx — fold list to integer.
+
+(mk-test "sumo-empty" (run* q (sumo (list) q)) (list 0))
+(mk-test
+  "sumo-1-to-5"
+  (run*
+    q
+    (sumo (list 1 2 3 4 5) q))
+  (list 15))
+(mk-test
+  "sumo-zeros"
+  (run* q (sumo (list 0 0 0) q))
+  (list 0))
+(mk-test
+  "sumo-negs"
+  (run* q (sumo (list 5 -3 8) q))
+  (list 10))
+
+(mk-test "producto-empty" (run* q (producto (list) q)) (list 1))
+(mk-test
+  "producto-1-to-4"
+  (run* q (producto (list 1 2 3 4) q))
+  (list 24))
+(mk-test
+  "producto-with-0"
+  (run* q (producto (list 5 0 7) q))
+  (list 0))
+(mk-test
+  "producto-of-1s"
+  (run* q (producto (list 1 1 1) q))
+  (list 1))
+
+(mk-test
+  "sum-product-pythagorean-square"
+  (run*
+    q
+    (fresh
+      (s sq2)
+      (sumo (list 3 4 5) s)
+      (producto (list 3 3) sq2)
+      (== q (list s sq2))))
+  (list (list 12 9)))
+
+(mk-tests-run!)

plans/minikanren-on-sx.md

@@ -173,6 +173,7 @@ _(none yet)_
 
 _Newest first._
 
+- **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.
 - **2026-05-08** — **subseto**: every element of l1 is a member of l2. Recurses on l1, checking each element via membero. Allows duplicates in l1 (each independently in l2). 7 new tests, 456/456 cumulative.