diff --git a/lib/apl/runtime.sx b/lib/apl/runtime.sx
new file mode 100644
index 00000000..43addb91
--- /dev/null
+++ b/lib/apl/runtime.sx
@@ -0,0 +1,349 @@
+; APL Runtime — array model + scalar primitives
+;
+; Array = SX dict {:shape (d1 d2 ...) :ravel (v1 v2 ...)}
+; Scalar: rank 0, shape (), one element in ravel
+; Vector: rank 1, shape (n), n elements in ravel
+; Matrix: rank 2, shape (r c), r*c elements in ravel
+
+; ============================================================
+; Array constructors
+; ============================================================
+
+(define make-array (fn (shape ravel) {:ravel ravel :shape shape}))
+
+(define apl-scalar (fn (v) {:ravel (list v) :shape (list)}))
+
+(define apl-vector (fn (elems) {:ravel elems :shape (list (len elems))}))
+
+; enclose — wrap any value in a rank-0 box
+(define enclose (fn (v) (apl-scalar v)))
+
+; disclose — unwrap rank-0 box, returning the first element
+(define disclose (fn (arr) (first (get arr :ravel))))
+
+; ============================================================
+; Array accessors
+; ============================================================
+
+(define array-rank (fn (arr) (len (get arr :shape))))
+
+(define scalar? (fn (arr) (= (len (get arr :shape)) 0)))
+
+(define array-ref (fn (arr i) (nth (get arr :ravel) i)))
+
+; ============================================================
+; System variables
+; ============================================================
+
+(define apl-io 1)
+
+; ============================================================
+; Broadcast engine
+; ============================================================
+
+(define
+  broadcast-monadic
+  (fn (f arr) (make-array (get arr :shape) (map f (get arr :ravel)))))
+
+(define
+  broadcast-dyadic
+  (fn
+    (f a b)
+    (cond
+      ((and (scalar? a) (scalar? b))
+        (apl-scalar (f (first (get a :ravel)) (first (get b :ravel)))))
+      ((scalar? a)
+        (let
+          ((sv (first (get a :ravel))))
+          (make-array
+            (get b :shape)
+            (map (fn (x) (f sv x)) (get b :ravel)))))
+      ((scalar? b)
+        (let
+          ((sv (first (get b :ravel))))
+          (make-array
+            (get a :shape)
+            (map (fn (x) (f x sv)) (get a :ravel)))))
+      (else
+        (if
+          (equal? (get a :shape) (get b :shape))
+          (make-array (get a :shape) (map f (get a :ravel) (get b :ravel)))
+          (error "length error: shape mismatch"))))))
+
+; ============================================================
+; Arithmetic primitives
+; ============================================================
+
+; Monadic + : identity
+(define apl-plus-m (fn (a) (broadcast-monadic (fn (x) x) a)))
+
+; Dyadic +
+(define apl-add (fn (a b) (broadcast-dyadic (fn (x y) (+ x y)) a b)))
+
+; Monadic - : negate
+(define apl-neg-m (fn (a) (broadcast-monadic (fn (x) (- 0 x)) a)))
+
+; Dyadic -
+(define apl-sub (fn (a b) (broadcast-dyadic (fn (x y) (- x y)) a b)))
+
+; Monadic × : signum
+(define
+  apl-signum
+  (fn
+    (a)
+    (broadcast-monadic
+      (fn (x) (cond ((> x 0) 1) ((< x 0) -1) (else 0)))
+      a)))
+
+; Dyadic ×
+(define apl-mul (fn (a b) (broadcast-dyadic (fn (x y) (* x y)) a b)))
+
+; Monadic ÷ : reciprocal
+(define apl-recip (fn (a) (broadcast-monadic (fn (x) (/ 1 x)) a)))
+
+; Dyadic ÷
+(define apl-div (fn (a b) (broadcast-dyadic (fn (x y) (/ x y)) a b)))
+
+; Monadic ⌈ : ceiling
+(define apl-ceil (fn (a) (broadcast-monadic (fn (x) (ceil x)) a)))
+
+; Dyadic ⌈ : max
+(define
+  apl-max
+  (fn (a b) (broadcast-dyadic (fn (x y) (if (>= x y) x y)) a b)))
+
+; Monadic ⌊ : floor
+(define apl-floor (fn (a) (broadcast-monadic (fn (x) (floor x)) a)))
+
+; Dyadic ⌊ : min
+(define
+  apl-min
+  (fn (a b) (broadcast-dyadic (fn (x y) (if (<= x y) x y)) a b)))
+
+; Monadic * : e^x
+(define apl-exp (fn (a) (broadcast-monadic (fn (x) (exp x)) a)))
+
+; Dyadic * : power
+(define apl-pow (fn (a b) (broadcast-dyadic (fn (x y) (pow x y)) a b)))
+
+; Monadic ⍟ : natural log
+(define apl-ln (fn (a) (broadcast-monadic (fn (x) (log x)) a)))
+
+; Dyadic ⍟ : log base (a⍟b = log base a of b)
+(define
+  apl-log
+  (fn (a b) (broadcast-dyadic (fn (x y) (/ (log y) (log x))) a b)))
+
+; Monadic | : absolute value
+(define
+  apl-abs
+  (fn (a) (broadcast-monadic (fn (x) (if (< x 0) (- 0 x) x)) a)))
+
+; Dyadic | : modulo (a|b = b mod a)
+(define
+  apl-mod
+  (fn
+    (a b)
+    (broadcast-dyadic
+      (fn (x y) (if (= x 0) y (- y (* x (floor (/ y x))))))
+      a
+      b)))
+
+; Monadic ! : factorial
+(define
+  apl-fact
+  (fn
+    (a)
+    (broadcast-monadic
+      (fn
+        (n)
+        (let
+          ((loop nil))
+          (begin
+            (set!
+              loop
+              (fn (i acc) (if (> i n) acc (loop (+ i 1) (* acc i)))))
+            (loop 1 1))))
+      a)))
+
+; Dyadic ! : binomial coefficient n!k  (a=n, b=k => a choose b)
+(define
+  apl-binomial
+  (fn
+    (a b)
+    (broadcast-dyadic
+      (fn
+        (n k)
+        (let
+          ((loop nil))
+          (begin
+            (set!
+              loop
+              (fn
+                (i num den)
+                (if
+                  (> i k)
+                  (/ num den)
+                  (loop (+ i 1) (* num (- (+ n 1) i)) (* den i)))))
+            (loop 1 1 1))))
+      a
+      b)))
+
+; Monadic ○ : pi times x
+(define
+  apl-pi-times
+  (fn (a) (broadcast-monadic (fn (x) (* 3.14159 x)) a)))
+
+; Dyadic ○ : trig functions (a○b, a=code, b=value)
+(define
+  apl-trig
+  (fn
+    (a b)
+    (broadcast-dyadic
+      (fn
+        (n x)
+        (cond
+          ((= n 0) (pow (- 1 (* x x)) 0.5))
+          ((= n 1) (sin x))
+          ((= n 2) (cos x))
+          ((= n 3) (tan x))
+          ((= n -1) (asin x))
+          ((= n -2) (acos x))
+          ((= n -3) (atan x))
+          (else (error "circle: unsupported trig code"))))
+      a
+      b)))
+
+; ============================================================
+; Comparison primitives (return 0 or 1)
+; ============================================================
+
+(define
+  apl-lt
+  (fn (a b) (broadcast-dyadic (fn (x y) (if (< x y) 1 0)) a b)))
+
+(define
+  apl-le
+  (fn (a b) (broadcast-dyadic (fn (x y) (if (<= x y) 1 0)) a b)))
+
+(define
+  apl-eq
+  (fn (a b) (broadcast-dyadic (fn (x y) (if (= x y) 1 0)) a b)))
+
+(define
+  apl-ge
+  (fn (a b) (broadcast-dyadic (fn (x y) (if (>= x y) 1 0)) a b)))
+
+(define
+  apl-gt
+  (fn (a b) (broadcast-dyadic (fn (x y) (if (> x y) 1 0)) a b)))
+
+(define
+  apl-ne
+  (fn (a b) (broadcast-dyadic (fn (x y) (if (= x y) 0 1)) a b)))
+
+; ============================================================
+; Logical primitives
+; ============================================================
+
+; Monadic ~ : logical not
+(define
+  apl-not
+  (fn (a) (broadcast-monadic (fn (x) (if (= x 0) 1 0)) a)))
+
+; Dyadic ∧ : logical and
+(define
+  apl-and
+  (fn
+    (a b)
+    (broadcast-dyadic
+      (fn (x y) (if (and (not (= x 0)) (not (= y 0))) 1 0))
+      a
+      b)))
+
+; Dyadic ∨ : logical or
+(define
+  apl-or
+  (fn
+    (a b)
+    (broadcast-dyadic
+      (fn (x y) (if (or (not (= x 0)) (not (= y 0))) 1 0))
+      a
+      b)))
+
+; Dyadic ⍱ : logical nor
+(define
+  apl-nor
+  (fn
+    (a b)
+    (broadcast-dyadic
+      (fn (x y) (if (or (not (= x 0)) (not (= y 0))) 0 1))
+      a
+      b)))
+
+; Dyadic ⍲ : logical nand
+(define
+  apl-nand
+  (fn
+    (a b)
+    (broadcast-dyadic
+      (fn (x y) (if (and (not (= x 0)) (not (= y 0))) 0 1))
+      a
+      b)))
+
+; ============================================================
+; Shape primitives
+; ============================================================
+
+; Monadic ⍴ : shape — returns shape as a vector array
+(define apl-shape (fn (arr) (apl-vector (get arr :shape))))
+
+; Monadic , : ravel — returns a rank-1 vector of all elements
+(define apl-ravel (fn (arr) (apl-vector (get arr :ravel))))
+
+; Monadic ≢ : tally — first dimension (1 for scalar)
+(define
+  apl-tally
+  (fn
+    (arr)
+    (if
+      (scalar? arr)
+      (apl-scalar 1)
+      (apl-scalar (first (get arr :shape))))))
+
+; Monadic ≡ : depth
+; simple number/string value → 0
+; array containing only non-arrays → 0
+; array containing arrays → 1 + max depth of elements
+(define
+  apl-depth
+  (fn
+    (arr)
+    (define item-depth nil)
+    (set!
+      item-depth
+      (fn
+        (v)
+        (if
+          (and
+            (dict? v)
+            (not (= nil (get v :shape nil)))
+            (not (= nil (get v :ravel nil))))
+          (+ 1 (first (get (apl-depth v) :ravel)))
+          0)))
+    (let
+      ((depths (map item-depth (get arr :ravel))))
+      (apl-scalar (reduce (fn (a b) (if (> a b) a b)) 0 depths)))))
+
+; Monadic ⍳ : iota — vector 1..n (with ⎕IO=1)
+(define
+  apl-iota
+  (fn
+    (n-arr)
+    (let
+      ((n (first (get n-arr :ravel))) (build nil))
+      (begin
+        (set!
+          build
+          (fn (i acc) (if (< i 1) acc (build (- i 1) (cons i acc)))))
+        (apl-vector (build n (list)))))))
diff --git a/lib/apl/tests/scalar.sx b/lib/apl/tests/scalar.sx
new file mode 100644
index 00000000..26a2c1e2
--- /dev/null
+++ b/lib/apl/tests/scalar.sx
@@ -0,0 +1,369 @@
+; APL scalar primitives test suite
+; Requires: lib/apl/runtime.sx
+
+; ============================================================
+; Test framework
+; ============================================================
+
+(define apl-rt-count 0)
+(define apl-rt-pass 0)
+(define apl-rt-fails (list))
+
+; Element-wise list comparison (handles both List and ListRef)
+(define
+  lists-eq
+  (fn
+    (a b)
+    (if
+      (and (= (len a) 0) (= (len b) 0))
+      true
+      (if
+        (not (= (len a) (len b)))
+        false
+        (if
+          (not (= (first a) (first b)))
+          false
+          (lists-eq (rest a) (rest b)))))))
+
+(define
+  apl-rt-test
+  (fn
+    (name actual expected)
+    (begin
+      (set! apl-rt-count (+ apl-rt-count 1))
+      (if
+        (equal? actual expected)
+        (set! apl-rt-pass (+ apl-rt-pass 1))
+        (append! apl-rt-fails {:actual actual :expected expected :name name})))))
+
+; Test that a ravel equals a plain list (handles ListRef vs List)
+(define
+  ravel-test
+  (fn
+    (name arr expected-list)
+    (begin
+      (set! apl-rt-count (+ apl-rt-count 1))
+      (let
+        ((actual (get arr :ravel)))
+        (if
+          (lists-eq actual expected-list)
+          (set! apl-rt-pass (+ apl-rt-pass 1))
+          (append! apl-rt-fails {:actual actual :expected expected-list :name name}))))))
+
+; Test a scalar ravel value (single-element list)
+(define
+  scalar-test
+  (fn (name arr expected-val) (ravel-test name arr (list expected-val))))
+
+; ============================================================
+; Array constructor tests
+; ============================================================
+
+(apl-rt-test
+  "scalar: shape is empty list"
+  (get (apl-scalar 5) :shape)
+  (list))
+
+(apl-rt-test
+  "scalar: ravel has one element"
+  (get (apl-scalar 5) :ravel)
+  (list 5))
+
+(apl-rt-test "scalar: rank 0" (array-rank (apl-scalar 5)) 0)
+
+(apl-rt-test "scalar? returns true for scalar" (scalar? (apl-scalar 5)) true)
+
+(apl-rt-test "scalar: zero" (get (apl-scalar 0) :ravel) (list 0))
+
+(apl-rt-test
+  "vector: shape is (3)"
+  (get (apl-vector (list 1 2 3)) :shape)
+  (list 3))
+
+(apl-rt-test
+  "vector: ravel matches input"
+  (get (apl-vector (list 1 2 3)) :ravel)
+  (list 1 2 3))
+
+(apl-rt-test "vector: rank 1" (array-rank (apl-vector (list 1 2 3))) 1)
+
+(apl-rt-test
+  "scalar? returns false for vector"
+  (scalar? (apl-vector (list 1 2 3)))
+  false)
+
+(apl-rt-test
+  "make-array: rank 2"
+  (array-rank (make-array (list 2 3) (list 1 2 3 4 5 6)))
+  2)
+
+(apl-rt-test
+  "make-array: shape"
+  (get (make-array (list 2 3) (list 1 2 3 4 5 6)) :shape)
+  (list 2 3))
+
+(apl-rt-test
+  "array-ref: first element"
+  (array-ref (apl-vector (list 10 20 30)) 0)
+  10)
+
+(apl-rt-test
+  "array-ref: last element"
+  (array-ref (apl-vector (list 10 20 30)) 2)
+  30)
+
+(apl-rt-test "enclose: wraps in rank-0" (scalar? (enclose 42)) true)
+
+(apl-rt-test
+  "enclose: ravel contains value"
+  (get (enclose 42) :ravel)
+  (list 42))
+
+(apl-rt-test "disclose: unwraps rank-0" (disclose (enclose 42)) 42)
+
+; ============================================================
+; Shape primitive tests
+; ============================================================
+
+(ravel-test "⍴ scalar: returns empty" (apl-shape (apl-scalar 5)) (list))
+
+(ravel-test
+  "⍴ vector: returns (3)"
+  (apl-shape (apl-vector (list 1 2 3)))
+  (list 3))
+
+(ravel-test
+  "⍴ matrix: returns (2 3)"
+  (apl-shape (make-array (list 2 3) (list 1 2 3 4 5 6)))
+  (list 2 3))
+
+(ravel-test
+  ", ravel scalar: vector of 1"
+  (apl-ravel (apl-scalar 5))
+  (list 5))
+
+(apl-rt-test
+  ", ravel vector: same elements"
+  (get (apl-ravel (apl-vector (list 1 2 3))) :ravel)
+  (list 1 2 3))
+
+(apl-rt-test
+  ", ravel matrix: all elements"
+  (get (apl-ravel (make-array (list 2 3) (list 1 2 3 4 5 6))) :ravel)
+  (list 1 2 3 4 5 6))
+
+(scalar-test "≢ tally scalar: 1" (apl-tally (apl-scalar 5)) 1)
+
+(scalar-test
+  "≢ tally vector: first dimension"
+  (apl-tally (apl-vector (list 1 2 3)))
+  3)
+
+(scalar-test
+  "≢ tally matrix: first dimension"
+  (apl-tally (make-array (list 2 3) (list 1 2 3 4 5 6)))
+  2)
+
+(scalar-test
+  "≡ depth flat vector: 0"
+  (apl-depth (apl-vector (list 1 2 3)))
+  0)
+
+(scalar-test "≡ depth scalar: 0" (apl-depth (apl-scalar 5)) 0)
+
+(scalar-test
+  "≡ depth nested (enclose in vector): 1"
+  (apl-depth (enclose (apl-vector (list 1 2 3))))
+  1)
+
+; ============================================================
+; ⍳ iota tests
+; ============================================================
+
+(apl-rt-test
+  "⍳5 shape is (5)"
+  (get (apl-iota (apl-scalar 5)) :shape)
+  (list 5))
+
+(ravel-test "⍳5 ravel is 1..5" (apl-iota (apl-scalar 5)) (list 1 2 3 4 5))
+
+(ravel-test "⍳1 ravel is (1)" (apl-iota (apl-scalar 1)) (list 1))
+
+(ravel-test "⍳0 ravel is empty" (apl-iota (apl-scalar 0)) (list))
+
+(apl-rt-test "apl-io is 1" apl-io 1)
+
+; ============================================================
+; Arithmetic broadcast tests
+; ============================================================
+
+(scalar-test
+  "+ scalar scalar: 3+4=7"
+  (apl-add (apl-scalar 3) (apl-scalar 4))
+  7)
+
+(ravel-test
+  "+ vector scalar: +10"
+  (apl-add (apl-vector (list 1 2 3)) (apl-scalar 10))
+  (list 11 12 13))
+
+(ravel-test
+  "+ scalar vector: 10+"
+  (apl-add (apl-scalar 10) (apl-vector (list 1 2 3)))
+  (list 11 12 13))
+
+(ravel-test
+  "+ vector vector"
+  (apl-add (apl-vector (list 1 2 3)) (apl-vector (list 4 5 6)))
+  (list 5 7 9))
+
+(scalar-test "- negate monadic" (apl-neg-m (apl-scalar 5)) -5)
+
+(scalar-test "- dyadic 10-3=7" (apl-sub (apl-scalar 10) (apl-scalar 3)) 7)
+
+(scalar-test "× signum positive" (apl-signum (apl-scalar 7)) 1)
+
+(scalar-test "× signum negative" (apl-signum (apl-scalar -3)) -1)
+
+(scalar-test "× signum zero" (apl-signum (apl-scalar 0)) 0)
+
+(scalar-test "× dyadic 3×4=12" (apl-mul (apl-scalar 3) (apl-scalar 4)) 12)
+
+(scalar-test "÷ reciprocal 1÷4=0.25" (apl-recip (apl-scalar 4)) 0.25)
+
+(scalar-test
+  "÷ dyadic 10÷4=2.5"
+  (apl-div (apl-scalar 10) (apl-scalar 4))
+  2.5)
+
+(scalar-test "⌈ ceiling 2.3→3" (apl-ceil (apl-scalar 2.3)) 3)
+
+(scalar-test "⌈ max 3 5 → 5" (apl-max (apl-scalar 3) (apl-scalar 5)) 5)
+
+(scalar-test "⌊ floor 2.7→2" (apl-floor (apl-scalar 2.7)) 2)
+
+(scalar-test "⌊ min 3 5 → 3" (apl-min (apl-scalar 3) (apl-scalar 5)) 3)
+
+(scalar-test "* exp monadic e^0=1" (apl-exp (apl-scalar 0)) 1)
+
+(scalar-test
+  "* pow dyadic 2^10=1024"
+  (apl-pow (apl-scalar 2) (apl-scalar 10))
+  1024)
+
+(scalar-test "⍟ ln 1=0" (apl-ln (apl-scalar 1)) 0)
+
+(scalar-test "| abs positive" (apl-abs (apl-scalar 5)) 5)
+
+(scalar-test "| abs negative" (apl-abs (apl-scalar -5)) 5)
+
+(scalar-test "| mod 3|7=1" (apl-mod (apl-scalar 3) (apl-scalar 7)) 1)
+
+(scalar-test "! factorial 5!=120" (apl-fact (apl-scalar 5)) 120)
+
+(scalar-test "! factorial 0!=1" (apl-fact (apl-scalar 0)) 1)
+
+(scalar-test
+  "! binomial 4 choose 2 = 6"
+  (apl-binomial (apl-scalar 4) (apl-scalar 2))
+  6)
+
+(scalar-test "○ pi×0=0" (apl-pi-times (apl-scalar 0)) 0)
+
+(scalar-test "○ trig sin(0)=0" (apl-trig (apl-scalar 1) (apl-scalar 0)) 0)
+
+(scalar-test "○ trig cos(0)=1" (apl-trig (apl-scalar 2) (apl-scalar 0)) 1)
+
+; ============================================================
+; Comparison tests
+; ============================================================
+
+(scalar-test "< less: 3<5 → 1" (apl-lt (apl-scalar 3) (apl-scalar 5)) 1)
+
+(scalar-test "< less: 5<3 → 0" (apl-lt (apl-scalar 5) (apl-scalar 3)) 0)
+
+(scalar-test
+  "≤ le equal: 3≤3 → 1"
+  (apl-le (apl-scalar 3) (apl-scalar 3))
+  1)
+
+(scalar-test "= eq: 5=5 → 1" (apl-eq (apl-scalar 5) (apl-scalar 5)) 1)
+
+(scalar-test "= ne: 5=6 → 0" (apl-eq (apl-scalar 5) (apl-scalar 6)) 0)
+
+(scalar-test "≥ ge: 5≥3 → 1" (apl-ge (apl-scalar 5) (apl-scalar 3)) 1)
+
+(scalar-test "> gt: 5>3 → 1" (apl-gt (apl-scalar 5) (apl-scalar 3)) 1)
+
+(scalar-test "≠ ne: 5≠3 → 1" (apl-ne (apl-scalar 5) (apl-scalar 3)) 1)
+
+(ravel-test
+  "comparison vector broadcast: 1 2 3 < 2 → 1 0 0"
+  (apl-lt (apl-vector (list 1 2 3)) (apl-scalar 2))
+  (list 1 0 0))
+
+; ============================================================
+; Logical tests
+; ============================================================
+
+(scalar-test "~ not 0 → 1" (apl-not (apl-scalar 0)) 1)
+
+(scalar-test "~ not 1 → 0" (apl-not (apl-scalar 1)) 0)
+
+(ravel-test
+  "~ not vector: 1 0 1 0 → 0 1 0 1"
+  (apl-not (apl-vector (list 1 0 1 0)))
+  (list 0 1 0 1))
+
+(scalar-test
+  "∧ and 1∧1 → 1"
+  (apl-and (apl-scalar 1) (apl-scalar 1))
+  1)
+
+(scalar-test
+  "∧ and 1∧0 → 0"
+  (apl-and (apl-scalar 1) (apl-scalar 0))
+  0)
+
+(scalar-test "∨ or 0∨1 → 1" (apl-or (apl-scalar 0) (apl-scalar 1)) 1)
+
+(scalar-test "∨ or 0∨0 → 0" (apl-or (apl-scalar 0) (apl-scalar 0)) 0)
+
+(scalar-test
+  "⍱ nor 0⍱0 → 1"
+  (apl-nor (apl-scalar 0) (apl-scalar 0))
+  1)
+
+(scalar-test
+  "⍱ nor 1⍱0 → 0"
+  (apl-nor (apl-scalar 1) (apl-scalar 0))
+  0)
+
+(scalar-test
+  "⍲ nand 1⍲1 → 0"
+  (apl-nand (apl-scalar 1) (apl-scalar 1))
+  0)
+
+(scalar-test
+  "⍲ nand 1⍲0 → 1"
+  (apl-nand (apl-scalar 1) (apl-scalar 0))
+  1)
+
+; ============================================================
+; plus-m identity test
+; ============================================================
+
+(scalar-test "+ monadic identity: +5 → 5" (apl-plus-m (apl-scalar 5)) 5)
+
+; ============================================================
+; Summary
+; ============================================================
+
+(define
+  apl-scalar-summary
+  (str
+    "scalar "
+    apl-rt-pass
+    "/"
+    apl-rt-count
+    (if (= (len apl-rt-fails) 0) "" (str " FAILS: " apl-rt-fails))))