apl: ⍸ where — monadic indices-of-truthy + dyadic interval-index

- apl-where (monadic): ravel scan, filter non-zero, +⎕IO offsets
- apl-interval-index (dyadic): count of breaks ≤ y; broadcasts over
  scalar or vector Y
- Wired into apl-monadic-fn / apl-dyadic-fn cond chains
- +10 pipeline tests covering both arities, ⎕IO offsetting, edge cases
  (empty mask, all-truthy, y below/above all breaks)
- pipeline 109/109

lib/apl/runtime.sx

@@ -827,6 +827,31 @@
               ((new-ravel (reduce (fn (acc r) (append acc (map (fn (j) (nth ravel (+ (* r cols) j))) (range 0 cols)))) (list) kept-rows)))
               (make-array (cons (len kept-rows) (rest shape)) new-ravel))))))))
 
+(define
+  apl-where
+  (fn
+    (arr)
+    (let
+      ((ravel (get arr :ravel)) (io (disclose (apl-quad-io))))
+      (let
+        ((indices (filter (fn (i) (not (= (nth ravel i) 0))) (range 0 (len ravel)))))
+        (apl-vector (map (fn (i) (+ i io)) indices))))))
+
+(define
+  apl-interval-index
+  (fn
+    (breaks vals)
+    (let
+      ((b-ravel (get breaks :ravel))
+        (v-ravel
+          (if (scalar? vals) (list (disclose vals)) (get vals :ravel))))
+      (let
+        ((result (map (fn (y) (len (filter (fn (b) (<= b y)) b-ravel))) v-ravel)))
+        (if
+          (scalar? vals)
+          (apl-scalar (first result))
+          (make-array (get vals :shape) result))))))
+
 (define
   apl-primes
   (fn

lib/apl/tests/pipeline.sx

@@ -455,3 +455,45 @@
   (list 1 2 3))
 
 (apl-test "⍕ 42 → \"42\" (alias for ⎕FMT)" (apl-run "⍕ 42") "42")
+
+(begin
+  (apl-test
+    "⍸ where: indices of truthy cells"
+    (mkrv (apl-run "⍸ 0 1 0 1 1"))
+    (list 2 4 5))
+  (apl-test
+    "⍸ where: leading truthy"
+    (mkrv (apl-run "⍸ 1 0 0 1 1"))
+    (list 1 4 5))
+  (apl-test
+    "⍸ where: all-zero → empty"
+    (mkrv (apl-run "⍸ 0 0 0"))
+    (list))
+  (apl-test
+    "⍸ where: all-truthy"
+    (mkrv (apl-run "⍸ 1 1 1"))
+    (list 1 2 3))
+  (apl-test
+    "⍸ where: ⎕IO=1 (1-based)"
+    (mkrv (apl-run "⍸ (⍳5)=3"))
+    (list 3))
+  (apl-test
+    "⍸ interval-index: 2 4 6 ⍸ 5 → 2"
+    (mkrv (apl-run "2 4 6 ⍸ 5"))
+    (list 2))
+  (apl-test
+    "⍸ interval-index: 2 4 6 ⍸ 1 3 5 6 7 → 0 1 2 3 3"
+    (mkrv (apl-run "2 4 6 ⍸ 1 3 5 6 7"))
+    (list 0 1 2 3 3))
+  (apl-test
+    "⍸ interval-index: ⍳5 ⍸ 3 → 3"
+    (mkrv (apl-run "(⍳5) ⍸ 3"))
+    (list 3))
+  (apl-test
+    "⍸ interval-index: y below all → 0"
+    (mkrv (apl-run "10 20 30 ⍸ 5"))
+    (list 0))
+  (apl-test
+    "⍸ interval-index: y above all → len breaks"
+    (mkrv (apl-run "10 20 30 ⍸ 100"))
+    (list 3)))

lib/apl/transpile.sx

@@ -46,6 +46,7 @@
       ((= g "⍕") apl-quad-fmt)
       ((= g "⎕FMT") apl-quad-fmt)
       ((= g "⎕←") apl-quad-print)
+      ((= g "⍸") apl-where)
       (else (error "no monadic fn for glyph")))))
 
 (define
@@ -90,6 +91,7 @@
       ((= g "⍉") apl-transpose-dyadic)
       ((= g "⊢") (fn (a b) b))
       ((= g "⊣") (fn (a b) a))
+      ((= g "⍸") apl-interval-index)
       (else (error "no dyadic fn for glyph")))))
 
 (define

plans/apl-on-sx.md

@@ -233,7 +233,7 @@ Phase 9 left seven glyphs that the parser recognises but the runtime
 cannot evaluate, and two source files (`life.apl`, `quicksort.apl`) that
 still need work to run as-written.  Phase 10 closes both.
 
-- [ ] **`⍸` where** — monadic `⍸ B` returns the indices of the truthy
+- [x] **`⍸` where** — monadic `⍸ B` returns the indices of the truthy
   cells (1-based per `⎕IO`).  Dyadic `X ⍸ Y` is interval index (find
   the largest `i` such that `X[i] ≤ Y`).  Add `apl-where` + dyadic
   `apl-interval-index`; wire both into `apl-monadic-fn` / `apl-dyadic-fn`.
@@ -288,6 +288,7 @@ data; format for string templating.
 
 _Newest first._
 
+- 2026-05-08: Phase 10 step 1 — `⍸` where. apl-where (monadic, indices of truthy cells, ⎕IO-respecting) + apl-interval-index (dyadic, count of breaks ≤ y; broadcasts over Y vector or scalar). Wired into apl-monadic-fn / apl-dyadic-fn (cond clauses inserted as proper siblings via sx_insert_child after sx_insert_near silently wrapped multi-form sources in `(begin …)`). +10 tests; pipeline 109/109
 - 2026-05-08: Phase 10 added — fill runtime gaps (⍸ ∪ ∩ ⊥ ⊤ ⊆ ⍎) + life.apl and quicksort.apl as-written
 - 2026-05-07: Phase 9 step 6 — glyph audit. Wired ⍉ → apl-transpose/apl-transpose-dyadic, ⊢ → monadic+dyadic identity-right, ⊣ → identity-left, ⍕ → apl-quad-fmt. +6 tests; **Phase 9 complete, all unchecked items ticked**; pipeline 99/99
 - 2026-05-07: Phase 9 step 5 — primes.apl runs as-written end-to-end. Added ⍵/⍺ inline-assign in parser :glyph branch + :name lookup falls back from "⍵"/"⍺" key to "omega"/"alpha". `apl-run "primes ← {(2=+⌿0=⍵∘.|⍵)/⍵←⍳⍵} ⋄ primes 50"` → 15 primes. +4 e2e tests; pipeline 93/93