apl: power f⍣n + fixed-point f⍣≡ (+9 tests, 191/191)

lib/apl/runtime.sx

@@ -1066,3 +1066,20 @@
 (define apl-compose (fn (f g x) (f (g x))))
 
 (define apl-compose-dyadic (fn (f g x y) (f x (g y))))
+
+(define
+  apl-power
+  (fn (f n x) (reduce (fn (acc i) (f acc)) x (range 0 n))))
+
+(define
+  apl-power-fixed
+  (fn
+    (f x)
+    (let
+      ((next (f x)))
+      (if
+        (and
+          (equal? (get next :shape) (get x :shape))
+          (equal? (get next :ravel) (get x :ravel)))
+        x
+        (apl-power-fixed f next)))))

lib/apl/tests/operators.sx

@@ -579,4 +579,65 @@
       apl-neg-m
       (make-array (list 2 3) (list 1 2 3 4 5 6))
       (make-array (list 2 3) (list 1 1 1 1 1 1))))
-  (list 2 3))
+  (list 2 3))
+
+(apl-test
+  "power n=0 identity"
+  (rv (apl-power (fn (a) (apl-add a (apl-scalar 1))) 0 (apl-scalar 5)))
+  (list 5))
+
+(apl-test
+  "power increment by 3"
+  (rv (apl-power (fn (a) (apl-add a (apl-scalar 1))) 3 (apl-scalar 0)))
+  (list 3))
+
+(apl-test
+  "power double 4 times = 16"
+  (rv (apl-power (fn (a) (apl-mul a (apl-scalar 2))) 4 (apl-scalar 1)))
+  (list 16))
+
+(apl-test
+  "power on vector +5"
+  (rv
+    (apl-power
+      (fn (a) (apl-add a (apl-scalar 1)))
+      5
+      (make-array (list 3) (list 1 2 3))))
+  (list 6 7 8))
+
+(apl-test
+  "power on vector preserves shape"
+  (sh
+    (apl-power
+      (fn (a) (apl-add a (apl-scalar 1)))
+      5
+      (make-array (list 3) (list 1 2 3))))
+  (list 3))
+
+(apl-test
+  "power on matrix"
+  (rv
+    (apl-power
+      (fn (a) (apl-mul a (apl-scalar 3)))
+      2
+      (make-array (list 2 2) (list 1 2 3 4))))
+  (list 9 18 27 36))
+
+(apl-test
+  "power-fixed identity stops immediately"
+  (rv (apl-power-fixed (fn (a) a) (make-array (list 3) (list 1 2 3))))
+  (list 1 2 3))
+
+(apl-test
+  "power-fixed floor half scalar to 0"
+  (rv
+    (apl-power-fixed
+      (fn (a) (apl-floor (apl-div a (apl-scalar 2))))
+      (apl-scalar 100)))
+  (list 0))
+
+(apl-test
+  "power-fixed shape preserved"
+  (sh
+    (apl-power-fixed (fn (a) a) (make-array (list 2 2) (list 1 2 3 4))))
+  (list 2 2))

plans/apl-on-sx.md

@@ -80,7 +80,7 @@ Core mapping:
 - [x] Inner product `f.g` — `+.×` is matrix multiply
 - [x] Commute `f⍨` — `f⍨ x` ↔ `x f x`, `x f⍨ y` ↔ `y f x`
 - [x] Compose `f∘g` — applies `g` first then `f`
-- [ ] Power `f⍣n` — apply f n times; `f⍣≡` until fixed point
+- [x] Power `f⍣n` — apply f n times; `f⍣≡` until fixed point
 - [ ] Rank `f⍤k` — apply f at sub-rank k
 - [ ] At `@` — selective replace
 - [ ] 40+ tests in `lib/apl/tests/operators.sx`
@@ -118,6 +118,7 @@ data; format for string templating.
 
 _Newest first._
 
+- 2026-05-06: Phase 4 step 8 — power f⍣n (apl-power) + fixed-point f⍣≡ (apl-power-fixed); 191/191 tests
 - 2026-05-06: Phase 4 step 7 — compose f∘g (apl-compose monadic f∘g x, apl-compose-dyadic dyadic f x (g y)); 182/182 tests
 - 2026-05-06: Phase 4 step 6 — commute f⍨ (apl-commute monadic dup, apl-commute-dyadic swap); 173/173 tests
 - 2026-05-06: Phase 4 step 5 — inner product f.g (apl-inner); +.× matrix multiply, ∧.= equal-vectors; 163/163 tests