mk: intarith.sx — ground-only integer arithmetic via project

pluso-i / minuso-i / *o-i / lto-i / lteo-i / neqo-i wrap host arithmetic
in project. They run at native speed but require their inputs to walk
to ground numbers — they are NOT relational the way Peano pluso is.
Use them when puzzle size makes Peano impractical (which is most cases
beyond toy examples).

Composes with relational goals — for instance,
  (fresh (x) (membero x (1 2 3 4 5)) (lto-i x 3) (== q x))
filters the domain by < 3 and returns (1 2).

18 new tests, 287/287 cumulative.

lib/minikanren/intarith.sx

@@ -0,0 +1,56 @@
+;; lib/minikanren/intarith.sx — fast integer arithmetic via project.
+;;
+;; These are ground-only escapes into host arithmetic. They run at native
+;; speed (host ints) but require their arguments to walk to actual numbers
+;; — they are not relational the way `pluso` (Peano) is. Use them when
+;; the puzzle size makes Peano impractical.
+;;
+;; Naming: `-i` suffix marks "integer-only" goals.
+
+(define
+  pluso-i
+  (fn
+    (a b c)
+    (project
+      (a b)
+      (if (and (number? a) (number? b)) (== c (+ a b)) fail))))
+
+(define
+  minuso-i
+  (fn
+    (a b c)
+    (project
+      (a b)
+      (if (and (number? a) (number? b)) (== c (- a b)) fail))))
+
+(define
+  *o-i
+  (fn
+    (a b c)
+    (project
+      (a b)
+      (if (and (number? a) (number? b)) (== c (* a b)) fail))))
+
+(define
+  lto-i
+  (fn
+    (a b)
+    (project
+      (a b)
+      (if (and (number? a) (and (number? b) (< a b))) succeed fail))))
+
+(define
+  lteo-i
+  (fn
+    (a b)
+    (project
+      (a b)
+      (if (and (number? a) (and (number? b) (<= a b))) succeed fail))))
+
+(define
+  neqo-i
+  (fn
+    (a b)
+    (project
+      (a b)
+      (if (and (number? a) (and (number? b) (not (= a b)))) succeed fail))))

lib/minikanren/tests/intarith.sx

@@ -0,0 +1,89 @@
+;; lib/minikanren/tests/intarith.sx — ground-only integer arithmetic
+;; goals that escape into host operations via project.
+
+;; --- pluso-i ---
+
+(mk-test
+  "pluso-i-forward"
+  (run* q (pluso-i 7 8 q))
+  (list 15))
+(mk-test
+  "pluso-i-zero"
+  (run* q (pluso-i 0 0 q))
+  (list 0))
+(mk-test
+  "pluso-i-negatives"
+  (run* q (pluso-i -5 3 q))
+  (list -2))
+(mk-test
+  "pluso-i-non-ground-fails"
+  (run* q (fresh (a) (pluso-i a 3 5)))
+  (list))
+
+;; --- minuso-i ---
+
+(mk-test
+  "minuso-i-forward"
+  (run* q (minuso-i 10 4 q))
+  (list 6))
+(mk-test
+  "minuso-i-zero"
+  (run* q (minuso-i 5 5 q))
+  (list 0))
+
+;; --- *o-i ---
+
+(mk-test
+  "times-i-forward"
+  (run* q (*o-i 6 7 q))
+  (list 42))
+(mk-test
+  "times-i-by-zero"
+  (run* q (*o-i 0 99 q))
+  (list 0))
+(mk-test
+  "times-i-by-one"
+  (run* q (*o-i 1 17 q))
+  (list 17))
+
+;; --- comparisons ---
+
+(mk-test
+  "lto-i-true"
+  (run 1 q (lto-i 2 5))
+  (list (make-symbol "_.0")))
+(mk-test "lto-i-false" (run* q (lto-i 5 2)) (list))
+(mk-test "lto-i-equal-false" (run* q (lto-i 3 3)) (list))
+
+(mk-test
+  "lteo-i-equal"
+  (run 1 q (lteo-i 4 4))
+  (list (make-symbol "_.0")))
+(mk-test
+  "lteo-i-less"
+  (run 1 q (lteo-i 1 4))
+  (list (make-symbol "_.0")))
+(mk-test "lteo-i-more" (run* q (lteo-i 9 4)) (list))
+
+(mk-test
+  "neqo-i-different"
+  (run 1 q (neqo-i 3 5))
+  (list (make-symbol "_.0")))
+(mk-test "neqo-i-same" (run* q (neqo-i 3 3)) (list))
+
+;; --- composition with relational vars ---
+
+(mk-test
+  "intarith-with-membero"
+  (run*
+    q
+    (fresh
+      (x)
+      (membero
+        x
+        (list 1 2 3 4 5))
+      (lto-i x 3)
+      (== q x)))
+  (list 1 2))
+
+(mk-tests-run!)

plans/minikanren-on-sx.md

@@ -173,6 +173,13 @@ _(none yet)_
 
 _Newest first._
 
+- **2026-05-08** — **intarith.sx — fast ground-only integer arithmetic**:
+  pluso-i / minuso-i / *o-i / lto-i / lteo-i / neqo-i wrap host arithmetic
+  via `project`. They are not relational like Peano `pluso` (require args
+  to walk to numbers), but run at native host speed — a viable escape
+  hatch when puzzle size makes Peano impractical. Composes with relational
+  goals: `(membero x dom) (lto-i x 3)` filters dom by `< 3`. 18 new tests,
+  287/287 cumulative.
 - **2026-05-08** — **2x2 Latin square**: small classic constraint demo using
   `ino` + 4 `all-distincto` constraints. Enumerates exactly 2 squares
   (`((1 2)(2 1))` and `((2 1)(1 2))`); a clue (top-left = 1) narrows to one.