diff --git a/lib/lua/runtime.sx b/lib/lua/runtime.sx
index 71b37373..82cf1ace 100644
--- a/lib/lua/runtime.sx
+++ b/lib/lua/runtime.sx
@@ -123,7 +123,7 @@
               (fn
                 (i)
                 (if
-                  (has? a (str i))
+                  (not (= (get a (str i)) nil))
                   (begin (set! n i) (count-loop (+ i 1)))
                   n)))
             (count-loop 1))))
@@ -152,7 +152,9 @@
                   (cond
                     ((= (first f) "pos")
                       (begin
-                        (set! t (assoc t (str array-idx) (nth f 1)))
+                        (set!
+                          t
+                          (assoc t (str array-idx) (nth f 1)))
                         (set! array-idx (+ array-idx 1))))
                     ((= (first f) "kv")
                       (let
@@ -169,3 +171,108 @@
     (if (= t nil) nil (let ((v (get t (str k)))) (if (= v nil) nil v)))))
 
 (define lua-set! (fn (t k v) (assoc t (str k) v)))
+
+;; ---------------------------------------------------------------------------
+;; Helpers for stdlib
+;; ---------------------------------------------------------------------------
+
+;; Apply a char function to every character in a string
+(define (lua-str-map s fn) (list->string (map fn (string->list s))))
+
+;; Repeat string s n times
+(define
+  (lua-str-rep s n)
+  (letrec
+    ((go (fn (acc i) (if (= i 0) acc (go (str acc s) (- i 1))))))
+    (go "" n)))
+
+;; Force a promise created by delay
+(define
+  (lua-force p)
+  (if
+    (and (dict? p) (get p :_promise))
+    (if (get p :forced) (get p :value) ((get p :thunk)))
+    p))
+
+;; ---------------------------------------------------------------------------
+;; math — Lua math library
+;; ---------------------------------------------------------------------------
+
+(define math {:asin asin :floor floor :exp exp :huge 1e+308 :tan tan :sqrt sqrt :log log :abs abs :ceil ceil :sin sin :max (fn (a b) (if (> a b) a b)) :acos acos :min (fn (a b) (if (< a b) a b)) :cos cos :pi 3.14159 :atan atan})
+
+;; ---------------------------------------------------------------------------
+;; string — Lua string library
+;; ---------------------------------------------------------------------------
+
+(define
+  (lua-string-find s pat)
+  (let
+    ((m (regexp-match (make-regexp pat) s)))
+    (if (= m nil) nil (list (+ (get m :start) 1) (get m :end)))))
+
+(define
+  (lua-string-match s pat)
+  (let
+    ((m (regexp-match (make-regexp pat) s)))
+    (if
+      (= m nil)
+      nil
+      (let
+        ((groups (get m :groups)))
+        (if (= (len groups) 0) (get m :match) (first groups))))))
+
+(define
+  (lua-string-gmatch s pat)
+  (map (fn (m) (get m :match)) (regexp-match-all (make-regexp pat) s)))
+
+(define
+  (lua-string-gsub s pat repl)
+  (regexp-replace-all (make-regexp pat) s repl))
+
+(define string {:rep lua-str-rep :sub (fn (s i &rest j-args) (let ((slen (len s)) (j (if (= (len j-args) 0) -1 (first j-args)))) (let ((from (if (< i 0) (let ((r (+ slen i))) (if (< r 0) 0 r)) (- i 1))) (to (if (< j 0) (let ((r (+ slen j 1))) (if (< r 0) 0 r)) (if (> j slen) slen j)))) (if (> from to) "" (substring s from to))))) :len (fn (s) (len s)) :upper (fn (s) (lua-str-map s char-upcase)) :char (fn (&rest codes) (list->string (map (fn (c) (integer->char (truncate c))) codes))) :gmatch lua-string-gmatch :gsub lua-string-gsub :lower (fn (s) (lua-str-map s char-downcase)) :byte (fn (s &rest args) (char->integer (nth (string->list s) (- (if (= (len args) 0) 1 (first args)) 1)))) :match lua-string-match :find lua-string-find :reverse (fn (s) (list->string (reverse (string->list s))))})
+
+;; ---------------------------------------------------------------------------
+;; table — Lua table library
+;; ---------------------------------------------------------------------------
+
+(define
+  (lua-table-insert t v)
+  (assoc t (str (+ (lua-len t) 1)) v))
+
+(define
+  (lua-table-remove t &rest args)
+  (let
+    ((n (lua-len t))
+      (pos (if (= (len args) 0) (lua-len t) (first args))))
+    (letrec
+      ((slide (fn (t i) (if (< i n) (assoc (slide t (+ i 1)) (str i) (lua-get t (+ i 1))) (assoc t (str n) nil)))))
+      (slide t pos))))
+
+(define
+  (lua-table-concat t &rest args)
+  (let
+    ((sep (if (= (len args) 0) "" (first args)))
+      (n (lua-len t)))
+    (letrec
+      ((go (fn (acc i) (if (> i n) acc (go (str acc (if (= i 1) "" sep) (lua-to-string (lua-get t i))) (+ i 1))))))
+      (go "" 1))))
+
+(define
+  (lua-table-sort t)
+  (let
+    ((n (lua-len t)))
+    (letrec
+      ((collect (fn (i acc) (if (< i 1) acc (collect (- i 1) (cons (lua-get t i) acc)))))
+        (rebuild
+          (fn
+            (t i items)
+            (if
+              (= (len items) 0)
+              t
+              (rebuild
+                (assoc t (str i) (first items))
+                (+ i 1)
+                (rest items))))))
+      (rebuild t 1 (sort (collect n (list)))))))
+
+(define table {:sort lua-table-sort :concat lua-table-concat :insert lua-table-insert :remove lua-table-remove})
diff --git a/lib/lua/test.sh b/lib/lua/test.sh
index 96a2e495..719f3750 100755
--- a/lib/lua/test.sh
+++ b/lib/lua/test.sh
@@ -633,6 +633,116 @@ check 482 "while i<5 count"                 '5'
 check 483 "repeat until i>=3"               '3'
 check 484 "for 1..100 sum"                  '5050'
 
+# ── Phase 3: stdlib — math, string, table ──────────────────────────────────
+
+cat >> "$TMPFILE" << 'EPOCHS2'
+
+;; ── math library ───────────────────────────────────────────────
+(epoch 500)
+(eval "(lua-eval-ast \"return math.abs(-7)\")")
+(epoch 501)
+(eval "(lua-eval-ast \"return math.floor(3.9)\")")
+(epoch 502)
+(eval "(lua-eval-ast \"return math.ceil(3.1)\")")
+(epoch 503)
+(eval "(lua-eval-ast \"return math.sqrt(9)\")")
+(epoch 504)
+(eval "(lua-eval-ast \"return math.sin(0)\")")
+(epoch 505)
+(eval "(lua-eval-ast \"return math.cos(0)\")")
+(epoch 506)
+(eval "(lua-eval-ast \"return math.max(3, 7)\")")
+(epoch 507)
+(eval "(lua-eval-ast \"return math.min(3, 7)\")")
+(epoch 508)
+(eval "(lua-eval-ast \"return math.pi > 3\")")
+(epoch 509)
+(eval "(lua-eval-ast \"return math.huge > 0\")")
+
+;; ── string library ─────────────────────────────────────────────
+(epoch 520)
+(eval "(lua-eval-ast \"return string.len(\\\"hello\\\")\")")
+(epoch 521)
+(eval "(lua-eval-ast \"return string.upper(\\\"hello\\\")\")")
+(epoch 522)
+(eval "(lua-eval-ast \"return string.lower(\\\"WORLD\\\")\")")
+(epoch 523)
+(eval "(lua-eval-ast \"return string.sub(\\\"hello\\\", 2, 4)\")")
+(epoch 524)
+(eval "(lua-eval-ast \"return string.rep(\\\"ab\\\", 3)\")")
+(epoch 525)
+(eval "(lua-eval-ast \"return string.reverse(\\\"hello\\\")\")")
+(epoch 526)
+(eval "(lua-eval-ast \"return string.byte(\\\"A\\\")\")")
+(epoch 527)
+(eval "(lua-eval-ast \"return string.char(72, 105)\")")
+(epoch 528)
+(eval "(lua-eval-ast \"return string.find(\\\"hello\\\", \\\"ll\\\")\")")
+(epoch 529)
+(eval "(lua-eval-ast \"return string.match(\\\"hello\\\", \\\"ell\\\")\")")
+(epoch 530)
+(eval "(lua-eval-ast \"return string.gsub(\\\"hello\\\", \\\"l\\\", \\\"r\\\")\")")
+
+;; ── table library ──────────────────────────────────────────────
+(epoch 540)
+(eval "(lua-eval-ast \"local t = {10, 20, 30} t = table.insert(t, 40) return t[4]\")")
+(epoch 541)
+(eval "(lua-eval-ast \"local t = {10, 20, 30} t = table.remove(t) return t[3]\")")
+(epoch 542)
+(eval "(lua-eval-ast \"local t = {\\\"a\\\", \\\"b\\\", \\\"c\\\"} return table.concat(t, \\\",\\\")\")")
+(epoch 543)
+(eval "(lua-eval-ast \"local t = {3, 1, 2} t = table.sort(t) return t[1]\")")
+(epoch 544)
+(eval "(lua-eval-ast \"local t = {3, 1, 2} t = table.sort(t) return t[3]\")")
+
+;; ── delay / force ──────────────────────────────────────────────
+(epoch 550)
+(eval "(lua-force (delay (+ 10 5)))")
+(epoch 551)
+(eval "(lua-force 42)")
+
+EPOCHS2
+
+OUTPUT2=$(timeout 30 "$SX_SERVER" < "$TMPFILE" 2>/dev/null)
+OUTPUT="$OUTPUT
+$OUTPUT2"
+
+# math
+check 500 "math.abs(-7)"         '7'
+check 501 "math.floor(3.9)"      '3'
+check 502 "math.ceil(3.1)"       '4'
+check 503 "math.sqrt(9)"         '3'
+check 504 "math.sin(0)"          '0'
+check 505 "math.cos(0)"          '1'
+check 506 "math.max(3,7)"        '7'
+check 507 "math.min(3,7)"        '3'
+check 508 "math.pi > 3"          'true'
+check 509 "math.huge > 0"        'true'
+
+# string
+check 520 "string.len"           '5'
+check 521 "string.upper"         '"HELLO"'
+check 522 "string.lower"         '"world"'
+check 523 "string.sub(2,4)"      '"ell"'
+check 524 "string.rep(ab,3)"     '"ababab"'
+check 525 "string.reverse"       '"olleh"'
+check 526 "string.byte(A)"       '65'
+check 527 "string.char(72,105)"  '"Hi"'
+check 528 "string.find ll"       '3'
+check 529 "string.match ell"     '"ell"'
+check 530 "string.gsub l->r"     '"herro"'
+
+# table
+check 540 "table.insert"         '40'
+check 541 "table.remove"         'nil'
+check 542 "table.concat ,"       '"a,b,c"'
+check 543 "table.sort [1]"       '1'
+check 544 "table.sort [3]"       '3'
+
+# delay/force
+check 550 "lua-force delay"      '15'
+check 551 "lua-force non-promise" '42'
+
 TOTAL=$((PASS + FAIL))
 if [ $FAIL -eq 0 ]; then
   echo "ok $PASS/$TOTAL Lua-on-SX tests passed"