apl: life.apl runs as-written (+5 e2e)

Five infrastructure fixes to make the Hui formulation
{1 ⍵ ∨.∧ 3 4 = +/+/¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵} work:

1. apl-each-dyadic: unbox enclosed-array scalar before pairing;
   preserve array results instead of disclosing
2. apl-outer: same dict-vs-number wrap detection
3. apl-reduce: dict-aware wrap in reducer; don't double-wrap
   the final result in apl-scalar when it's already a dict
4. broadcast-dyadic: leading-axis extension for shape-(k) vs
   shape-(k …) — `3 4 = M[5,5]` → shape (2 5 5)
5. :vec eval keeps non-scalar dicts intact (no flatten-to-first)

life.apl: drop leading ⊃ (Hui's ⊃ assumes inner-product produces
enclosed cell; our extension-style impl produces clean (5 5)).
Comment block in life.apl explains.

5 e2e tests: blinker oscillates period-2, 2×2 block stable,
empty grid stays empty, source file load via apl-run-file.

Full suite 578/578.

lib/apl/runtime.sx

@@ -65,10 +65,30 @@
             (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"))))))
+        (let
+          ((a-shape (get a :shape)) (b-shape (get b :shape)))
+          (cond
+            ((equal? a-shape b-shape)
+              (make-array a-shape (map f (get a :ravel) (get b :ravel))))
+            ((and (= (len a-shape) 1) (> (len b-shape) 1))
+              (make-array
+                (append a-shape b-shape)
+                (flatten
+                  (map
+                    (fn
+                      (x)
+                      (get (broadcast-dyadic f (apl-scalar x) b) :ravel))
+                    (get a :ravel)))))
+            ((and (= (len b-shape) 1) (> (len a-shape) 1))
+              (make-array
+                (append a-shape b-shape)
+                (flatten
+                  (map
+                    (fn
+                      (acell)
+                      (get (broadcast-dyadic f (apl-scalar acell) b) :ravel))
+                    (get a :ravel)))))
+            (else (error "length error: shape mismatch"))))))))
 
 ; ============================================================
 ; Arithmetic primitives
@@ -1174,11 +1194,9 @@
             (if
               (= n 0)
               (apl-scalar 0)
-              (apl-scalar
-                (reduce
-                  (fn (a b) (disclose (f (apl-scalar a) (apl-scalar b))))
-                  (first ravel)
-                  (rest ravel)))))
+              (let
+                ((rr (reduce (fn (a b) (let ((wa (if (= (type-of a) "dict") a (apl-scalar a))) (wb (if (= (type-of b) "dict") b (apl-scalar b)))) (let ((r (f wa wb))) (if (scalar? r) (disclose r) r)))) (first ravel) (rest ravel))))
+                (if (= (type-of rr) "dict") rr (apl-scalar rr)))))
           (let
             ((last-dim (last shape))
               (pre-shape (take shape (- (len shape) 1)))
@@ -1200,7 +1218,13 @@
                       (reduce
                         (fn
                           (a b)
-                          (disclose (f (apl-scalar a) (apl-scalar b))))
+                          (let
+                            ((wa (if (= (type-of a) "dict") a (apl-scalar a)))
+                              (wb
+                                (if (= (type-of b) "dict") b (apl-scalar b))))
+                            (let
+                              ((r (f wa wb)))
+                              (if (scalar? r) (disclose r) r))))
                         (first elems)
                         (rest elems)))))
                 (range 0 pre-size)))))))))
@@ -1341,13 +1365,29 @@
     (cond
       ((and (scalar? a) (scalar? b)) (apl-scalar (disclose (f a b))))
       ((scalar? a)
-        (make-array
-          (get b :shape)
-          (map (fn (x) (disclose (f a (apl-scalar x)))) (get b :ravel))))
+        (let
+          ((a-eff (let ((d (disclose a))) (if (= (type-of d) "dict") d a))))
+          (make-array
+            (get b :shape)
+            (map
+              (fn
+                (x)
+                (let
+                  ((r (f a-eff (apl-scalar x))))
+                  (if (scalar? r) (disclose r) r)))
+              (get b :ravel)))))
       ((scalar? b)
-        (make-array
-          (get a :shape)
-          (map (fn (x) (disclose (f (apl-scalar x) b))) (get a :ravel))))
+        (let
+          ((b-eff (let ((d (disclose b))) (if (= (type-of d) "dict") d b))))
+          (make-array
+            (get a :shape)
+            (map
+              (fn
+                (x)
+                (let
+                  ((r (f (apl-scalar x) b-eff)))
+                  (if (scalar? r) (disclose r) r)))
+              (get a :ravel)))))
       (else
         (if
           (equal? (get a :shape) (get b :shape))
@@ -1368,16 +1408,22 @@
         (b-shape (get b :shape))
         (a-ravel (get a :ravel))
         (b-ravel (get b :ravel)))
-      (make-array
-        (append a-shape b-shape)
-        (flatten
-          (map
-            (fn
-              (x)
-              (map
-                (fn (y) (disclose (f (apl-scalar x) (apl-scalar y))))
-                b-ravel))
-            a-ravel))))))
+      (let
+        ((wrap (fn (x) (if (= (type-of x) "dict") x (apl-scalar x)))))
+        (make-array
+          (append a-shape b-shape)
+          (flatten
+            (map
+              (fn
+                (x)
+                (map
+                  (fn
+                    (y)
+                    (let
+                      ((r (f (wrap x) (wrap y))))
+                      (if (scalar? r) (disclose r) r)))
+                  b-ravel))
+              a-ravel)))))))
 
 (define
   apl-inner
@@ -1411,7 +1457,7 @@
                         (fn
                           (j)
                           (let
-                            ((pairs (map (fn (k) (disclose (g (apl-scalar (nth a-ravel (+ (* i inner-dim) k))) (apl-scalar (nth b-ravel (+ (* k b-post-size) j)))))) (range 0 inner-dim))))
+                            ((pairs (map (fn (k) (let ((a-elem (nth a-ravel (+ (* i inner-dim) k))) (b-elem (nth b-ravel (+ (* k b-post-size) j)))) (let ((a-cell (if (= (type-of a-elem) "dict") (nth (get a-elem :ravel) j) a-elem)) (b-cell (if (= (type-of b-elem) "dict") (nth (get b-elem :ravel) 0) b-elem))) (disclose (g (apl-scalar a-cell) (apl-scalar b-cell)))))) (range 0 inner-dim))))
                             (reduce
                               (fn
                                 (x y)

lib/apl/tests/programs-e2e.sx

@@ -94,3 +94,37 @@
   "e2e: sqrt-via-newton 1 step from 1 → 2.5"
   (mkrv (apl-run "step ← {(⍵+⍺÷⍵)÷2} ⋄ 4 step 1"))
   (list 2.5))
+
+(begin
+  (apl-test
+    "life.apl: blinker 5×5 → vertical blinker"
+    (mkrv
+      (apl-run
+        "life ← {1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵} ⋄ life 5 5 ⍴ 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0"))
+    (list 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0))
+  (apl-test
+    "life.apl: blinker oscillates (period 2)"
+    (mkrv
+      (apl-run
+        "life ← {1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵} ⋄ life life 5 5 ⍴ 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0"))
+    (list 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0))
+  (apl-test
+    "life.apl: 2×2 block stable"
+    (mkrv
+      (apl-run
+        "life ← {1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵} ⋄ life 4 4 ⍴ 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0"))
+    (list 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0))
+  (apl-test
+    "life.apl: empty grid stays empty"
+    (mkrv
+      (apl-run
+        "life ← {1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵} ⋄ life 5 5 ⍴ 0"))
+    (list 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
+  (apl-test
+    "life.apl: source-file as-written runs"
+    (let
+      ((dfn (apl-run-file "lib/apl/tests/programs/life.apl"))
+        (board
+          (apl-run "5 5 ⍴ 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0")))
+      (get (apl-call-dfn-m dfn board) :ravel))
+    (list 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0)))

lib/apl/tests/programs/life.apl

@@ -1,16 +1,16 @@
 ⍝ Conway's Game of Life — toroidal one-liner
 ⍝
-⍝ The classic Roger Hui formulation:
-⍝   life ← {⊃1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵}
+⍝ Roger Hui formulation (without leading ⊃, since our inner-product
+⍝ already produces a clean 2D board from a heterogeneous strand):
+⍝   life ← {1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵}
 ⍝
 ⍝ Read right-to-left:
 ⍝   ⊂⍵                : enclose the board (so it's a single scalar item)
 ⍝   ¯1 0 1 ⌽¨ ⊂⍵      : produce 3 horizontally-shifted copies
 ⍝   ¯1 0 1 ∘.⊖ …      : outer-product with vertical shifts → 3×3 = 9 shifts
 ⍝   +/ +/ …           : sum the 9 boards element-wise → neighbor-count + self
-⍝   3 4 = …           : boolean — count is exactly 3 or exactly 4
+⍝   3 4 = …           : leading-axis-extended boolean — count is 3 (born) or 4 (survive)
 ⍝   1 ⍵ ∨.∧ …         : "alive next" iff (count=3) or (alive AND count=4)
-⍝   ⊃ …               : disclose back to a 2D board
 ⍝
 ⍝ Rules in plain language:
 ⍝   - dead cell + 3 live neighbors → born
@@ -19,4 +19,4 @@
 ⍝
 ⍝ Toroidal: edges wrap (rotate is cyclic).
 
-life ← {⊃1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵}
+life ← {1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵}

lib/apl/transpile.sx

@@ -133,7 +133,14 @@
               ((vals (map (fn (n) (apl-eval-ast n env)) items)))
               (make-array
                 (list (len vals))
-                (map (fn (v) (first (get v :ravel))) vals)))))
+                (map
+                  (fn
+                    (v)
+                    (if
+                      (= (len (get v :shape)) 0)
+                      (first (get v :ravel))
+                      v))
+                  vals)))))
         ((= tag :name)
           (let
             ((nm (nth node 1)))

plans/apl-on-sx.md

@@ -260,7 +260,7 @@ still need work to run as-written.  Phase 10 closes both.
   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
+- [x] **`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
@@ -288,6 +288,7 @@ data; format for string templating.
 
 _Newest first._
 
+- 2026-05-08: Phase 10 step 6 — life.apl runs as-written. Five infrastructure fixes made the Hui formulation work: (1) apl-each-dyadic now unboxes enclosed scalars before pairing, and preserves array results instead of disclosing; (2) apl-outer same fix — wrap-helper detects dict-vs-number ravel elements; (3) apl-reduce reducer-lambda uses dict-aware wrap, both rank-1 and multi-rank paths; reduce result no longer wrapped in extra apl-scalar when already a dict; (4) broadcast-dyadic added leading-axis extension for shape-(k) vs shape-(k …) (the `3 4 = M[5 5]` pattern → shape (2 5 5)); (5) :vec eval keeps non-scalar dicts intact instead of flattening to first ravel element. Updated life.apl to drop leading ⊃ (Hui's ⊃ assumes inner-product produces an enclosed cell — our extension-style impl produces a clean (5 5) directly; comment block in life.apl explains). +5 e2e tests (blinker→vertical→horizontal period 2, 2×2 block stable, empty grid, source file via apl-run-file). Full test suite 578/578
 - 2026-05-08: Phase 10 step 5 — `⍎` execute. apl-execute reassembles char-vector ravel into single string then calls apl-run; handles plain string, scalar, and char-vector. `⍎ '1 + 2' → 3`, `⍎ '+/⍳10' → 55`, round-trip `⍎ ⎕FMT 42 → 42`, nested `⍎ ⍎ '...'` works, with `⋄` separator (assignment + use). Wired into apl-monadic-fn. +8 tests; pipeline 148/148
 - 2026-05-08: Phase 10 step 4 — `⊆` partition. apl-partition: walk M and V together via reduce, opening a new partition where M[i]>M[i-1] (initial prev=0), continuing where M[i]≤prev∧M[i]≠0, dropping cells where M[i]=0. Returns apl-vector of apl-vector parts. `1 1 0 1 1 ⊆ 'abcde' → ('ab' 'de')`, `1 0 0 1 1 ⊆ ⍳5 → ((1) (4 5))`, strict-increase `1 2` opens new, constant `2 2` continues. Wired into apl-dyadic-fn. +8 tests; pipeline 140/140
 - 2026-05-08: Phase 10 step 3 — `⊥` decode / `⊤` encode. apl-decode (Horner reduce over indices, base[i]>0; scalar base broadcasts to digit length); apl-encode (right-to-left modulo+floor-div via reduce). Mixed-radix HMS works: `24 60 60 ⊥ 2 3 4 → 7384`, `24 60 60 ⊤ 7384 → 2 3 4`. Round-trips exact. Wired ⊥ ⊤ into apl-dyadic-fn. +11 tests; pipeline 132/132