diff --git a/lib/apl/runtime.sx b/lib/apl/runtime.sx
index ea26c849..ea252013 100644
--- a/lib/apl/runtime.sx
+++ b/lib/apl/runtime.sx
@@ -873,3 +873,91 @@
                       (first col)
                       (rest col))))
                 (range 0 inner-size)))))))))
+
+(define
+  apl-scan
+  (fn
+    (f arr)
+    (let
+      ((shape (get arr :shape)) (ravel (get arr :ravel)))
+      (if
+        (= (len shape) 0)
+        arr
+        (if
+          (= (len shape) 1)
+          (let
+            ((n (first shape)))
+            (make-array
+              shape
+              (map
+                (fn
+                  (i)
+                  (let
+                    ((slice (take ravel (+ i 1))))
+                    (reduce
+                      (fn
+                        (a b)
+                        (disclose (f (apl-scalar a) (apl-scalar b))))
+                      (first slice)
+                      (rest slice))))
+                (range 0 n))))
+          (let
+            ((last-dim (last shape))
+              (pre-size (reduce * 1 (take shape (- (len shape) 1)))))
+            (make-array
+              shape
+              (flatten
+                (map
+                  (fn
+                    (i)
+                    (let
+                      ((start (* i last-dim))
+                        (row
+                          (map
+                            (fn (j) (nth ravel (+ start j)))
+                            (range 0 last-dim))))
+                      (map
+                        (fn
+                          (k)
+                          (let
+                            ((slice (take row (+ k 1))))
+                            (reduce
+                              (fn
+                                (a b)
+                                (disclose (f (apl-scalar a) (apl-scalar b))))
+                              (first slice)
+                              (rest slice))))
+                        (range 0 last-dim))))
+                  (range 0 pre-size))))))))))
+
+(define
+  apl-scan-first
+  (fn
+    (f arr)
+    (let
+      ((shape (get arr :shape)) (ravel (get arr :ravel)))
+      (if
+        (< (len shape) 2)
+        (apl-scan f arr)
+        (let
+          ((first-dim (first shape))
+            (inner-size (reduce * 1 (rest shape))))
+          (make-array
+            shape
+            (flatten
+              (map
+                (fn
+                  (i)
+                  (map
+                    (fn
+                      (j)
+                      (let
+                        ((col (map (fn (k) (nth ravel (+ j (* k inner-size)))) (range 0 (+ i 1)))))
+                        (reduce
+                          (fn
+                            (a b)
+                            (disclose (f (apl-scalar a) (apl-scalar b))))
+                          (first col)
+                          (rest col))))
+                    (range 0 inner-size)))
+                (range 0 first-dim)))))))))
diff --git a/lib/apl/tests/operators.sx b/lib/apl/tests/operators.sx
index 7f5352b7..8b2be5cc 100644
--- a/lib/apl/tests/operators.sx
+++ b/lib/apl/tests/operators.sx
@@ -82,4 +82,79 @@
   "reduce-first max/ matrix col maxima"
   (rv
     (apl-reduce-first apl-max (make-array (list 3 2) (list 1 9 2 8 3 7))))
-  (list 3 9))
\ No newline at end of file
+  (list 3 9))
+
+(apl-test
+  "scan +\\ vector"
+  (rv (apl-scan apl-add (make-array (list 5) (list 1 2 3 4 5))))
+  (list 1 3 6 10 15))
+
+(apl-test
+  "scan x\\ vector cumulative product"
+  (rv (apl-scan apl-mul (make-array (list 5) (list 1 2 3 4 5))))
+  (list 1 2 6 24 120))
+
+(apl-test
+  "scan max\\ vector running max"
+  (rv (apl-scan apl-max (make-array (list 5) (list 3 1 4 1 5))))
+  (list 3 3 4 4 5))
+
+(apl-test
+  "scan min\\ vector running min"
+  (rv (apl-scan apl-min (make-array (list 5) (list 3 1 4 1 5))))
+  (list 3 1 1 1 1))
+
+(apl-test
+  "scan +\\ single element"
+  (rv (apl-scan apl-add (make-array (list 1) (list 42))))
+  (list 42))
+
+(apl-test
+  "scan +\\ scalar no-op"
+  (rv (apl-scan apl-add (apl-scalar 7)))
+  (list 7))
+
+(apl-test
+  "scan +\\ vector preserves shape"
+  (sh (apl-scan apl-add (make-array (list 5) (list 1 2 3 4 5))))
+  (list 5))
+
+(apl-test
+  "scan +\\ matrix preserves shape"
+  (sh (apl-scan apl-add (make-array (list 2 3) (list 1 2 3 4 5 6))))
+  (list 2 3))
+
+(apl-test
+  "scan +\\ matrix row-wise"
+  (rv (apl-scan apl-add (make-array (list 2 3) (list 1 2 3 4 5 6))))
+  (list 1 3 6 4 9 15))
+
+(apl-test
+  "scan max\\ matrix row-wise running max"
+  (rv (apl-scan apl-max (make-array (list 2 3) (list 3 1 4 1 5 9))))
+  (list 3 3 4 1 5 9))
+
+(apl-test
+  "scan-first +\\ vector same as scan"
+  (rv (apl-scan-first apl-add (make-array (list 5) (list 1 2 3 4 5))))
+  (list 1 3 6 10 15))
+
+(apl-test
+  "scan-first +\\ scalar no-op"
+  (rv (apl-scan-first apl-add (apl-scalar 9)))
+  (list 9))
+
+(apl-test
+  "scan-first +\\ matrix preserves shape"
+  (sh (apl-scan-first apl-add (make-array (list 2 3) (list 1 2 3 4 5 6))))
+  (list 2 3))
+
+(apl-test
+  "scan-first +\\ matrix col-wise"
+  (rv (apl-scan-first apl-add (make-array (list 2 3) (list 1 2 3 4 5 6))))
+  (list 1 2 3 5 7 9))
+
+(apl-test
+  "scan-first max\\ matrix col-wise running max"
+  (rv (apl-scan-first apl-max (make-array (list 3 2) (list 3 1 4 1 5 9))))
+  (list 3 1 4 1 5 9))
\ No newline at end of file
diff --git a/plans/apl-on-sx.md b/plans/apl-on-sx.md
index 69e14f9a..8920b8c5 100644
--- a/plans/apl-on-sx.md
+++ b/plans/apl-on-sx.md
@@ -74,7 +74,7 @@ Core mapping:
 
 ### Phase 4 — operators (THE SHOWCASE)
 - [x] Reduce `f/` (last axis), `f⌿` (first axis) — including `∧/`, `∨/`, `+/`, `×/`, `⌈/`, `⌊/`
-- [ ] Scan `f\`, `f⍀`
+- [x] Scan `f\`, `f⍀`
 - [ ] Each `f¨` — applies `f` to each scalar/element
 - [ ] Outer product `∘.f` — `1 2 3 ∘.× 1 2 3` ↦ multiplication table
 - [ ] Inner product `f.g` — `+.×` is matrix multiply
@@ -118,6 +118,7 @@ data; format for string templating.
 
 _Newest first._
 
+- 2026-05-06: Phase 4 step 2 — scan f\ (last axis) + f⍀ (first axis); apl-scan/apl-scan-first; 125/125 tests
 - 2026-05-06: Phase 4 step 1 — reduce f/ (last axis) + f⌿ (first axis); apl-reduce/apl-reduce-first; 110/110 tests
 - 2026-05-06: Phase 3 complete — membership ∊, dyadic ⍳ (index-of), without ~ (index-of returns nil for not-found); 94/94 tests
 - 2026-05-06: Phase 3 step 6 — enclose ⊂ / disclose ⊃ (box/unbox, rank-0 detect via type-of); 82/82 tests