plans: Phase 10 — runtime gaps (⍸ ∪ ∩ ⊥ ⊤ ⊆ ⍎) + life/quicksort as-written

plans/apl-on-sx.md

@@ -227,6 +227,53 @@ Today they are documentation; we paraphrase the algorithms in
   in the runtime — parser sees them as functions but eval errors;
   next-phase work.)_
 
+### Phase 10 — fill runtime gaps + life/quicksort source files run
+
+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
+  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`.
+  Tests: `⍸ 0 1 0 1 1 → 2 4 5`, `⍸ ⍳5 = ¯1+⍳5 → empty`,
+  `2 4 6 ⍸ 5 → 2`.
+- [ ] **`∪` unique / `∩` intersection** — monadic `∪ V` returns V with
+  duplicates removed (first-occurrence order); dyadic `A ∪ B` is
+  union; `A ∩ B` is intersection (members of A that are also in B).
+  Add `apl-unique`, `apl-union`, `apl-intersect`.  Tests cover empty,
+  single, repeats, mixed numerics.
+- [ ] **`⊥` decode / `⊤` encode** — `B ⊥ V` evaluates digits `V` in
+  base(s) `B` (Horner-style); `B ⊤ N` is the inverse, returning the
+  digits of `N` in base(s) `B`.  Both broadcast `B` as scalar or
+  conformable vector.  Add `apl-decode` and `apl-encode`.  Tests:
+  `2 ⊥ 1 0 1 → 5`, `10 ⊥ 1 2 3 → 123`, `2 2 2 ⊤ 5 → 1 0 1`,
+  `24 60 60 ⊤ 7384 → 2 3 4`.
+- [ ] **`⊆` partition** — dyadic `M ⊆ V` partitions `V` into vectors
+  driven by mask `M`: a new partition starts wherever `M[i] > M[i-1]`,
+  and 0 cells are dropped.  Returns a vector of (boxed) partitions.
+  Add `apl-partition`.  Tests: `1 1 0 1 1 ⊆ 'abcde' → ('ab' 'de')`,
+  `1 0 0 1 1 ⊆ ⍳5 → ((⊂ 1) (⊂ 4 5))`.
+- [ ] **`⍎` execute** — monadic `⍎ S` evaluates `S` (a character
+  vector) as APL source in the *current* environment, returning the
+  result.  Implement as `(fn (s) (apl-run s))` — env is the global
+  one; nested execute is fine.  Wire into `apl-monadic-fn`.  Tests:
+  `⍎ '1 + 2' → 3`, `⍎ '+/⍳10' → 55`.
+- [ ] **`life.apl` runs as-written** — Conway's life one-liner uses
+  `⊃+/⌽¨ -1 0 1 ∘.,¯1 0 1` (each + outer-comma + disclose + reduce
+  over a list of rotations) and the rule expression.  Probe what
+  fails when `apl-run-file "lib/apl/tests/programs/life.apl"` is
+  called on a 5×5 blinker grid; fix any remaining parser/runtime
+  gaps; assert blinker oscillates and block stays stable as full
+  end-to-end tests in `programs-e2e.sx`.
+- [ ] **`quicksort.apl` runs as-written** — the classic Iverson dfn
+  `{1≥≢⍵:⍵ ⋄ (∇(⍵<pivot)⌿⍵),(⍵=pivot)⌿⍵,∇(⍵>pivot)⌿⍵⊣pivot←⍵⌷⍨?≢⍵}`
+  exercises `⌷⍨` (squad-commute pivot pick), `⌿⍨` (first-axis-compress
+  commute), and `⊣` to bind a local without polluting the result.
+  Set the RNG seed for determinism and assert the sort against
+  `apl-grade-up`.
+
 ## SX primitive baseline
 
 Use vectors for arrays; numeric tower + rationals for numbers; ADTs for tagged data;
@@ -241,6 +288,7 @@ data; format for string templating.
 
 _Newest first._
 
+- 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
 - 2026-05-07: Phase 9 step 4 — apl-run-file = apl-run ∘ file-read; SX has (file-read path) returning content as string. primes/life/quicksort .apl files now load and parse end-to-end (return :dfn AST). +4 tests